Acceptability Ratings of Regular and IrregularPast-tense Forms Evidence for a Dual-systemModel of Language from Word Frequency and

Phonological Neighbourhood Effects

Michael T UllmanGICCS Georgetown University Washington DC USA

What are the computational and representational bases of the mental lexiconof words and of the rules of grammar which productively combine lexicalforms into larger words phrases and sentences lsquolsquoDual-systemrsquorsquo theoriesposit that lexical forms with non-compositional (arbitrary) sound-meaningpairings are stored in memory whereas compositional structures aresubserved by a distinct rule-processing system lsquolsquoSingle-systemrsquorsquo theoriesclaim that lexicon and grammar are both subserved by a single associativememory Investigations of English past tense may help to resolve thiscontroversy On the dual-system view irregular past-tense forms (eg blowndashblew) are retrieved from memory whereas regular past-tense forms (egwalkndashwalked) are produced by the application of an -ed-sufxation rule Onthe single-system view both types of past-tense forms are learned andcomputed in associative memory To test these competing theoriesacceptability ratings were elicited from native English-speaking adults forregular and irregular past-tense forms and their stems in sentence contextsPartialling out stem ratings ratings of irregular past-tense forms (blew)correlated with their frequencies and with measures of the number of similar-sounding irregular verbs (threw grew) whereas ratings of regular part-tenseforms (walked) did not correlate with their frequencies or with measures ofthe number of similar-sounding regular verbs (stalked balked) The resultssuggest that irregular past tenses are retrieved from associative memorywhereas regular past tenses are produced by a sufxation rule

Requests for reprints should be addressed to Michael T Ullman Georgetown Institute forCognitive and Computational Sciences Georgetown University New Research Building3970 Reservoir Road NW Washington DC 20007 USAE-mail michaelgiccsgeorgetownedu

I thank Susan Carey Marie Coppola Zoubin Ghahramani Joseph Locascio Alan Princeand in particular Roumyana Izvorski and Steven Pinker for helpful insights and discussionsThis research was carried out while the author was at MIT Cambridge MA and wassupported in part by NSF grant BNS 91-09766 and NIH grant HD 18381 to Steven Pinker andby a Poitras predoctoral fellowship and a McDonnell-Pew postdoctoral fellowship to MTU

c 1999 Psychology Press Ltd

LANGUAGE AND COGNITIVE PROCESSES 1999 14 (1) 47ndash67

48 ULLMAN

INTRODUCTION

Human language is characterised by two capacities One is the lsquolsquomentallexiconrsquorsquo of memorised words a memory store which must contain at leastthose words with arbitrary soundndashmeaning pairings (ie whose sounds andmeanings cannot be derived from each other) such as walk or hand Theother is the lsquolsquomental grammarrsquorsquo of rules which combine forms intopredictably structured larger words (eg walked hands) phrases andsentences and which productively apply to new words (eg faxndashfaxed) andto novel forms (eg blickndashblicked) (Berko 1958 Chomsky 1965 1995Pinker 1994)

The two capacities have been explained by two competing theoreticalframeworks lsquolsquoDual-systemrsquorsquo theories posit distinct representational andcomputational bases for the two capacities Word sounds and meanings arestored in either a rote or an associative memory The rules and principlesunderlying grammatical knowledge and processing are subserved by one ormore specialised components that are dependent upon the manipulation ofsymbolic representations of words and other linguistic structures(Chomsky 1965 1995 Fodor 1983 Frazier 1987 Pinker 1994)

lsquolsquoSingle-systemrsquorsquo theories on the other hand posit that lexical items andgrammatical rules are represented and processed by a single system Batesand her colleagues have proposed a model in which lexical andgrammatical knowledge is subserved by a large and heterogeneous lexicon(Bates amp Goodman 1997 Bates amp MacWhinney 1989) SimilarlyMacDonald Pearlmutter and Seidenberg (1994 p 676) hypothesise thatlsquolsquothe lexicon is the repository for all types of knowledge associated withwords including their syntactic functionsrsquorsquo Modern connectionism(parallel distributed processing) has offered a computational frameworkfor the single-system perspective On this view the representation andcomputation of lexical items and grammatical rules takes place over a largenumber of interconnected simple processing units Learning occurs byadjusting weights on connections on the basis of statistical contingencies inthe environment Grammatical rules are nothing but descriptions ofbehaviour rather than the mental manipulations posited by dual-systemtheories (Elman et al 1996 Rumelhart amp McClelland 1986)

Demonstrations of lexicongrammar dissociations can strengthen thedual-system view whereas imperfections in such dissociations canstrengthen the single-system view However testing for such dissociationshas been problematic because tasks probing for lexicon and for grammarusually differ in ways other than their use of the two capacities For exampleit is difcult to match measures of grammatical processing in sentencecomprehension with measures of lexical memory (see Bates HarrisMarchman Wulfeck amp Kritchevsky 1995)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 49

One well-studied approach which largely overcomes this problem hasbeen the investigation of English past tense Irregular past-tensetransformations are largely unpredictable in sound (eg clingndashclungbringndashbrought) and do not apply productively (new irregulars rarely enterthe language) In contrast regular past-tense transformations arepredictable in sound (verb + -ed) and apply productively to new wordsand to novel forms (eg faxndashfaxed blickndashblicked) Thus irregular formshave arbitrary mappings with their stems just as non-compositional lexicalforms have arbitrary mappings with their meanings whereas the structureof regular past-tense forms can be described by a rule which applies in aproductive manner Crucially irregulars and regulars are matched incomplexity (one word) meaning (past) and syntax (tensed) and can alsobe matched on syllable structure (eg sleptndashslipped) word frequency andother factors

According to a dual-system view irregular forms (blew) are stored inand retrieved from lexical memory whereas regular forms (walked) areproduced in real-time by a distinct symbol-manipulation system whichapplies an -ed-sufxation rule to the verb stem (walk) Retrieval of anirregular blocks the rule (blew pre-empts blowed) when an irregular is notsuccessfully retrieved the rule may be applied resulting in lsquolsquoover-regularisationrsquorsquo errors such as blowed (Pinker 1991 Pinker amp Prince1988)

Two alternative theories have been proposed motivated in part by theobservation that irregular transformations are not completely unpredict-able and unproductive but rather follow subregularities (eg springndashsprang ringndashrang singndashsang) and can lead to the generation of novelforms (eg splingndashsplang) One theory posits that rules underlie thecomputation of irregulars (eg computing indasha in springndashsprang ringndashrang)as well as regulars (Chomsky amp Halle 1968 Halle amp Mohanan 1985 Lingamp Marinov 1993) The second theory is consistent with the single-systemview and claims that regulars and irregulars are learned in and computedover an associative memory In support of this theory a number ofconnectionist models have been developed in which input and output unitsrepresent the sounds of verb stems and past-tense forms respectively andin which the weights of a matrix of inputndashoutput connections are adjustedaccording to how the statistical structure of stemndashpast pairs inuences thebehaviour of the network (Daugherty amp Seidenberg 1992 Hare amp Elman1995 Hare Elman amp Daugherty 1995 MacWhinney amp Leinbach 1991Marchman 1993 Plunkett amp Marchman 1991 1993 Rumelhart andMcClelland 1986)

Here I argue in favour of the dual-system perspective I presentevidence for dissociations between the computation of regular andirregular past-tense forms with respect to their sensitivity to word

50 ULLMAN

frequency and to their phonological similarity with other verbs I arguethat this evidence suggests that connectionist models are successful atcapturing important aspects of the representation and computation ofirregular verbs but that regular verbs are computed by a distinct rule-processing system

Evidence suggests that the more often a word is encountered the betterit is remembered (eg Rubenstein Gareld amp Milliken 1970) Accordingto the dual-system view irregular past-tense forms (blew) are retrievedfrom memory so they are expected to be frequency-sensitive with high-frequency forms being remembered better than low-frequency formsRegular past-tense forms (walked) are rule-produced in real-time so theyshould show no such lsquolsquofrequency effectsrsquorsquo once access to their stem forms(walk) to which the -ed-sufxation rule is applied is controlled for

In contrast if the single-system view is correct and regulars as well asirregulars are memorised in associative memory then both past-tensetypes may show word frequency effects (eg Daugherty amp Seidenberg1992) Moreover many single-system models expect lsquolsquophonologicalneighbourhood effectsrsquorsquo The memory traces representing the distributedphonological stemndashpast mappings shared among lsquolsquoneighbouringrsquorsquo irregulars(eg singndashsang ringndashrang springndashsprang) or regulars (eg slipndashslippedclipndashclipped tripndashtripped) should be strengthened by the learning of anyform with these mappings Thus hearing singndashsang should strengthen notonly the memory traces unique to singndashsang but also those shared betweensingndashsang ringndashrang and springndashsprang (eg Plunkett amp Marchman 19911993 Rumelhart amp McClelland 1986) Moreover because there are manyregular verbs and they follow a consistent pattern it has been claimed thatthe contribution of neighbouring regulars to a given regular verbrsquos memorytraces may largely overwhelm the contribution of the verbrsquos individualpast-tense frequency resulting in weakened past tense frequency effectsfor regular verbs (Daugherty amp Seidenberg 1992 Seidenberg 1992)

Although traditional dual-system models assume that irregular past-tense forms are stored in rote memory more recent models have beeninuenced by the partial regularity (eg springndashsprang ringndashrang ingndashung) and partial productivity (eg splingndashsplang) of irregulars and haveadopted the single-system connectionist perspective that irregulars arelearned in an associative memory (Pinker 1991) If irregulars are retrievedfrom associative memory in a manner similar to that hypothesised bysingle-system models whereas regulars are rule-products then phonolo-gical neighbourhood effects should be found for irregular but not regularforms Finally if irregulars as well as regulars are rule-produced (Halle ampMohanan 1985 Ling amp Marinov 1993) neither irregular nor regularforms should show either word-frequency or phonological neighbourhoodeffects

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 51

There have been few studies of word-frequency and phonologicalneighbourhood effects contrasting regular and irregular past-tense formsPrasada Pinker and Snyder (1990) presented adult subjects with a series ofverb stems and asked them to produce the past-tense form of each verb asquickly and accurately as possible The subjects took signicantly moretime to produce low-frequency than high-frequency past-tense forms forirregular verbs holding stem frequency constant However they foundthat production times were not signicantly longer for low-frequency thanhigh-frequency regular past-tense forms holding stem frequency constantThis result is consistent with the hypothesis that irregular but not regularpast-tense forms are retrieved from memory Stemberger and MacWhin-ney (1988) examined errors on intended past-tense forms in spontaneousspeech and also gave subjects a production task of regular past-tenseforms They reported frequency effects for regulars in the production taskbut not in spontaneous speech however the frequency effects must betreated with caution because there was no control for any measure ofaccess to the verb stems such as stem frequency Similarly althoughMarchman (1997) reported frequency effects for both regular and irregularverbs in a past-tense elicitation task given to children stem access was notcontrolled for

Bybee and Moder (1983) and Prasada and Pinker (1993) investigatedphonological neighbourhood effects in novel verbs Bybee and Moder(1983) presented subjects with novel verbs in obligatory past-tensesentence contexts (Sam likes to Yesterday he ) The verb stemsvaried in phonological proximity to the prototypical pattern which theauthors dened for the i-H (eg stringndashstrung) group of irregular verbssCCV[velar nasal] They found a continuous effect of similarity as afunction of proximity to the prototype The closer a real or novel verb stemwas to the prototype the more likely it was to be inected to the H-formThus spling was more likely to be inected as splung than vin was as vunThey took this quasi-productivity as evidence that irregular verbs areorganised into family resemblance categories (Rosch 1978) Prasada andPinker (1993) replicated Bybee and Moderrsquos (1983) nding that theproduction of an irregular-sounding past-tense form for a novel verbincreases with the similarity of that verb to the prototype of an irregularneighbourhood (splingndashsplung versus vinndashvun) However Prasada andPinker found that subjects were not signicantly more likely to produceregularly sufxed past-tense forms of familiar-sounding novel verbs likeplip than of odd-sounding novel verbs like ploamphmdasheven though thesubjects rated the stem ploamph to be less acceptable than the stem plipThe authors found a similar distinction between acceptability ratings ofirregular-sounding (splung) and -ed-sufxed (plipped) past-tense forms ofnovel verbs Subjects gave higher ratings to forms like splung than vun

52 ULLMAN

whereas forms like plipped were not given higher ratings than those likeploamphed once the naturalness of their stems was held constant In herpast tense elicitation task given to children Marchman (1997) reportedthat errors on irregulars were not predicted by the number of similarirregular neighbours In contrast errors on regulars were affected by thenumber of similar regular neighbours However this surprising contrastmust be treated with caution because no statistics were reported for thedifference for regulars and stem access was not controlled for so anysimilarity effects of stem forms were not factored out

There has thus been no systematic psycholinguistic investigation of bothfrequency and phonological neighbourhood effects of the computation ofregular (walkndashwalked) and irregular (blowndashblew) past-tense formsholding stem frequency constant Here I address this empirical gapdescribing a study in which acceptability ratings were elicited from normaladults for regular and irregular past-tense forms and were analysed forfrequency and phonological neighbourhood effects

METHODS

On a 7-point scale subjects were asked to give acceptability ratings forpast-tense forms of regular and irregular verbs in past-tense sentencecontexts and of their stem forms in present-tense sentence contexts

Subjects

Each past-tense and stem form was given acceptability ratings by 32 MITundergraduates who were paid for their participation in the experimentAll were native speakers of American or Canadian English

Verbs

Subjects were shown 137 verbs with monosyllabic stems (see Appendix 1for a full list) 89 were irregular verbs (blowndashblew) and 48 were regularverbs (walkndashwalked) In addition to these 137 verbs whose ratings areanalysed in this paper the questionnaire contained another 335 verbs notdiscussed here (see Appendix 2)

The 89 irregular verbs were drawn from Pinker and Prince (1988)Doublet verbs which have acceptable irregular and regular past-tenseforms (divendashdovedived) were excluded In this study doublets weredened as those verbs with an irregular past-tense form whosecorresponding regularisationrsquos mean acceptability rating was greater than35 out of 7 All regularisations of the non-doublet irregular verbs (blowed)had relative frequency counts of 0 according to both the Francis andKucAEligera (1982) and Associated Press word-frequency counts (see below for

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 53

details) The mean ( standard deviation) of the ln-transformed past-tensefrequencies for the 89 irregulars was 359 155 for the Francis and KucAEligerafrequency counts and 663 215 for the Associated Press counts

The 48 lsquolsquoconsistentrsquorsquo regulars were drawn from the Francis and KucAEligeraand the Associated Press frequency counts Their stems were phonologi-cally similar to the stems of other regular verbs and dissimilar to the stemsof irregular verbs and thus they and their phonological neighbours areconsistently regularised (eg balkndashbalked stalkndashstalked) Thus none oftheir stems rhyme with the stems of irregulars nor do they have t or d asa nal consonant because many irregular stems end in one of these twophonemes (eg wet bite ride bend) The mean ln-transformed past-tensefrequency for the 48 consistent regulars was 177 151 for the Francis andKucAEligera counts and 411 234 for the Associated Press counts

PresentationThe position of each past-tense sentence in the questionnaire wasrandomised and the order of regulars and irregulars was counterbalancedacross subjects The following is an example sentence

walkJohn and Ralph walked to the store

1 2 3 4 5 6 7worst best

Stem naturalness ratings were elicited for all verbs in present-tensesentences in any person other than third person singular There was noattempt to make the stem sentence of each verb similar in content to thatof its past-tense sentence Each verb stem was presented in a formatsimilar to that in which the past-tense forms were presented For example

dropPeople often drop things when they have oily hands

1 2 3 4 5 6 7worst best

Because ratings were gathered on a large number of verb forms the fullquestionnaires were broken down into sub-questionnaires Each sub-questionnaire contained both the stem and past-tense sentences for a givenverb Each subject completed one or more sub-questionnaires Thusalthough each verb form was rated by 32 subjects not all verbs were ratedby the same subject

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

48 ULLMAN

INTRODUCTION

Human language is characterised by two capacities One is the lsquolsquomentallexiconrsquorsquo of memorised words a memory store which must contain at leastthose words with arbitrary soundndashmeaning pairings (ie whose sounds andmeanings cannot be derived from each other) such as walk or hand Theother is the lsquolsquomental grammarrsquorsquo of rules which combine forms intopredictably structured larger words (eg walked hands) phrases andsentences and which productively apply to new words (eg faxndashfaxed) andto novel forms (eg blickndashblicked) (Berko 1958 Chomsky 1965 1995Pinker 1994)

The two capacities have been explained by two competing theoreticalframeworks lsquolsquoDual-systemrsquorsquo theories posit distinct representational andcomputational bases for the two capacities Word sounds and meanings arestored in either a rote or an associative memory The rules and principlesunderlying grammatical knowledge and processing are subserved by one ormore specialised components that are dependent upon the manipulation ofsymbolic representations of words and other linguistic structures(Chomsky 1965 1995 Fodor 1983 Frazier 1987 Pinker 1994)

lsquolsquoSingle-systemrsquorsquo theories on the other hand posit that lexical items andgrammatical rules are represented and processed by a single system Batesand her colleagues have proposed a model in which lexical andgrammatical knowledge is subserved by a large and heterogeneous lexicon(Bates amp Goodman 1997 Bates amp MacWhinney 1989) SimilarlyMacDonald Pearlmutter and Seidenberg (1994 p 676) hypothesise thatlsquolsquothe lexicon is the repository for all types of knowledge associated withwords including their syntactic functionsrsquorsquo Modern connectionism(parallel distributed processing) has offered a computational frameworkfor the single-system perspective On this view the representation andcomputation of lexical items and grammatical rules takes place over a largenumber of interconnected simple processing units Learning occurs byadjusting weights on connections on the basis of statistical contingencies inthe environment Grammatical rules are nothing but descriptions ofbehaviour rather than the mental manipulations posited by dual-systemtheories (Elman et al 1996 Rumelhart amp McClelland 1986)

Demonstrations of lexicongrammar dissociations can strengthen thedual-system view whereas imperfections in such dissociations canstrengthen the single-system view However testing for such dissociationshas been problematic because tasks probing for lexicon and for grammarusually differ in ways other than their use of the two capacities For exampleit is difcult to match measures of grammatical processing in sentencecomprehension with measures of lexical memory (see Bates HarrisMarchman Wulfeck amp Kritchevsky 1995)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 49

One well-studied approach which largely overcomes this problem hasbeen the investigation of English past tense Irregular past-tensetransformations are largely unpredictable in sound (eg clingndashclungbringndashbrought) and do not apply productively (new irregulars rarely enterthe language) In contrast regular past-tense transformations arepredictable in sound (verb + -ed) and apply productively to new wordsand to novel forms (eg faxndashfaxed blickndashblicked) Thus irregular formshave arbitrary mappings with their stems just as non-compositional lexicalforms have arbitrary mappings with their meanings whereas the structureof regular past-tense forms can be described by a rule which applies in aproductive manner Crucially irregulars and regulars are matched incomplexity (one word) meaning (past) and syntax (tensed) and can alsobe matched on syllable structure (eg sleptndashslipped) word frequency andother factors

According to a dual-system view irregular forms (blew) are stored inand retrieved from lexical memory whereas regular forms (walked) areproduced in real-time by a distinct symbol-manipulation system whichapplies an -ed-sufxation rule to the verb stem (walk) Retrieval of anirregular blocks the rule (blew pre-empts blowed) when an irregular is notsuccessfully retrieved the rule may be applied resulting in lsquolsquoover-regularisationrsquorsquo errors such as blowed (Pinker 1991 Pinker amp Prince1988)

Two alternative theories have been proposed motivated in part by theobservation that irregular transformations are not completely unpredict-able and unproductive but rather follow subregularities (eg springndashsprang ringndashrang singndashsang) and can lead to the generation of novelforms (eg splingndashsplang) One theory posits that rules underlie thecomputation of irregulars (eg computing indasha in springndashsprang ringndashrang)as well as regulars (Chomsky amp Halle 1968 Halle amp Mohanan 1985 Lingamp Marinov 1993) The second theory is consistent with the single-systemview and claims that regulars and irregulars are learned in and computedover an associative memory In support of this theory a number ofconnectionist models have been developed in which input and output unitsrepresent the sounds of verb stems and past-tense forms respectively andin which the weights of a matrix of inputndashoutput connections are adjustedaccording to how the statistical structure of stemndashpast pairs inuences thebehaviour of the network (Daugherty amp Seidenberg 1992 Hare amp Elman1995 Hare Elman amp Daugherty 1995 MacWhinney amp Leinbach 1991Marchman 1993 Plunkett amp Marchman 1991 1993 Rumelhart andMcClelland 1986)

Here I argue in favour of the dual-system perspective I presentevidence for dissociations between the computation of regular andirregular past-tense forms with respect to their sensitivity to word

50 ULLMAN

frequency and to their phonological similarity with other verbs I arguethat this evidence suggests that connectionist models are successful atcapturing important aspects of the representation and computation ofirregular verbs but that regular verbs are computed by a distinct rule-processing system

Evidence suggests that the more often a word is encountered the betterit is remembered (eg Rubenstein Gareld amp Milliken 1970) Accordingto the dual-system view irregular past-tense forms (blew) are retrievedfrom memory so they are expected to be frequency-sensitive with high-frequency forms being remembered better than low-frequency formsRegular past-tense forms (walked) are rule-produced in real-time so theyshould show no such lsquolsquofrequency effectsrsquorsquo once access to their stem forms(walk) to which the -ed-sufxation rule is applied is controlled for

In contrast if the single-system view is correct and regulars as well asirregulars are memorised in associative memory then both past-tensetypes may show word frequency effects (eg Daugherty amp Seidenberg1992) Moreover many single-system models expect lsquolsquophonologicalneighbourhood effectsrsquorsquo The memory traces representing the distributedphonological stemndashpast mappings shared among lsquolsquoneighbouringrsquorsquo irregulars(eg singndashsang ringndashrang springndashsprang) or regulars (eg slipndashslippedclipndashclipped tripndashtripped) should be strengthened by the learning of anyform with these mappings Thus hearing singndashsang should strengthen notonly the memory traces unique to singndashsang but also those shared betweensingndashsang ringndashrang and springndashsprang (eg Plunkett amp Marchman 19911993 Rumelhart amp McClelland 1986) Moreover because there are manyregular verbs and they follow a consistent pattern it has been claimed thatthe contribution of neighbouring regulars to a given regular verbrsquos memorytraces may largely overwhelm the contribution of the verbrsquos individualpast-tense frequency resulting in weakened past tense frequency effectsfor regular verbs (Daugherty amp Seidenberg 1992 Seidenberg 1992)

Although traditional dual-system models assume that irregular past-tense forms are stored in rote memory more recent models have beeninuenced by the partial regularity (eg springndashsprang ringndashrang ingndashung) and partial productivity (eg splingndashsplang) of irregulars and haveadopted the single-system connectionist perspective that irregulars arelearned in an associative memory (Pinker 1991) If irregulars are retrievedfrom associative memory in a manner similar to that hypothesised bysingle-system models whereas regulars are rule-products then phonolo-gical neighbourhood effects should be found for irregular but not regularforms Finally if irregulars as well as regulars are rule-produced (Halle ampMohanan 1985 Ling amp Marinov 1993) neither irregular nor regularforms should show either word-frequency or phonological neighbourhoodeffects

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 51

There have been few studies of word-frequency and phonologicalneighbourhood effects contrasting regular and irregular past-tense formsPrasada Pinker and Snyder (1990) presented adult subjects with a series ofverb stems and asked them to produce the past-tense form of each verb asquickly and accurately as possible The subjects took signicantly moretime to produce low-frequency than high-frequency past-tense forms forirregular verbs holding stem frequency constant However they foundthat production times were not signicantly longer for low-frequency thanhigh-frequency regular past-tense forms holding stem frequency constantThis result is consistent with the hypothesis that irregular but not regularpast-tense forms are retrieved from memory Stemberger and MacWhin-ney (1988) examined errors on intended past-tense forms in spontaneousspeech and also gave subjects a production task of regular past-tenseforms They reported frequency effects for regulars in the production taskbut not in spontaneous speech however the frequency effects must betreated with caution because there was no control for any measure ofaccess to the verb stems such as stem frequency Similarly althoughMarchman (1997) reported frequency effects for both regular and irregularverbs in a past-tense elicitation task given to children stem access was notcontrolled for

Bybee and Moder (1983) and Prasada and Pinker (1993) investigatedphonological neighbourhood effects in novel verbs Bybee and Moder(1983) presented subjects with novel verbs in obligatory past-tensesentence contexts (Sam likes to Yesterday he ) The verb stemsvaried in phonological proximity to the prototypical pattern which theauthors dened for the i-H (eg stringndashstrung) group of irregular verbssCCV[velar nasal] They found a continuous effect of similarity as afunction of proximity to the prototype The closer a real or novel verb stemwas to the prototype the more likely it was to be inected to the H-formThus spling was more likely to be inected as splung than vin was as vunThey took this quasi-productivity as evidence that irregular verbs areorganised into family resemblance categories (Rosch 1978) Prasada andPinker (1993) replicated Bybee and Moderrsquos (1983) nding that theproduction of an irregular-sounding past-tense form for a novel verbincreases with the similarity of that verb to the prototype of an irregularneighbourhood (splingndashsplung versus vinndashvun) However Prasada andPinker found that subjects were not signicantly more likely to produceregularly sufxed past-tense forms of familiar-sounding novel verbs likeplip than of odd-sounding novel verbs like ploamphmdasheven though thesubjects rated the stem ploamph to be less acceptable than the stem plipThe authors found a similar distinction between acceptability ratings ofirregular-sounding (splung) and -ed-sufxed (plipped) past-tense forms ofnovel verbs Subjects gave higher ratings to forms like splung than vun

52 ULLMAN

whereas forms like plipped were not given higher ratings than those likeploamphed once the naturalness of their stems was held constant In herpast tense elicitation task given to children Marchman (1997) reportedthat errors on irregulars were not predicted by the number of similarirregular neighbours In contrast errors on regulars were affected by thenumber of similar regular neighbours However this surprising contrastmust be treated with caution because no statistics were reported for thedifference for regulars and stem access was not controlled for so anysimilarity effects of stem forms were not factored out

There has thus been no systematic psycholinguistic investigation of bothfrequency and phonological neighbourhood effects of the computation ofregular (walkndashwalked) and irregular (blowndashblew) past-tense formsholding stem frequency constant Here I address this empirical gapdescribing a study in which acceptability ratings were elicited from normaladults for regular and irregular past-tense forms and were analysed forfrequency and phonological neighbourhood effects

METHODS

On a 7-point scale subjects were asked to give acceptability ratings forpast-tense forms of regular and irregular verbs in past-tense sentencecontexts and of their stem forms in present-tense sentence contexts

Subjects

Each past-tense and stem form was given acceptability ratings by 32 MITundergraduates who were paid for their participation in the experimentAll were native speakers of American or Canadian English

Verbs

Subjects were shown 137 verbs with monosyllabic stems (see Appendix 1for a full list) 89 were irregular verbs (blowndashblew) and 48 were regularverbs (walkndashwalked) In addition to these 137 verbs whose ratings areanalysed in this paper the questionnaire contained another 335 verbs notdiscussed here (see Appendix 2)

The 89 irregular verbs were drawn from Pinker and Prince (1988)Doublet verbs which have acceptable irregular and regular past-tenseforms (divendashdovedived) were excluded In this study doublets weredened as those verbs with an irregular past-tense form whosecorresponding regularisationrsquos mean acceptability rating was greater than35 out of 7 All regularisations of the non-doublet irregular verbs (blowed)had relative frequency counts of 0 according to both the Francis andKucAEligera (1982) and Associated Press word-frequency counts (see below for

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 53

details) The mean ( standard deviation) of the ln-transformed past-tensefrequencies for the 89 irregulars was 359 155 for the Francis and KucAEligerafrequency counts and 663 215 for the Associated Press counts

The 48 lsquolsquoconsistentrsquorsquo regulars were drawn from the Francis and KucAEligeraand the Associated Press frequency counts Their stems were phonologi-cally similar to the stems of other regular verbs and dissimilar to the stemsof irregular verbs and thus they and their phonological neighbours areconsistently regularised (eg balkndashbalked stalkndashstalked) Thus none oftheir stems rhyme with the stems of irregulars nor do they have t or d asa nal consonant because many irregular stems end in one of these twophonemes (eg wet bite ride bend) The mean ln-transformed past-tensefrequency for the 48 consistent regulars was 177 151 for the Francis andKucAEligera counts and 411 234 for the Associated Press counts

PresentationThe position of each past-tense sentence in the questionnaire wasrandomised and the order of regulars and irregulars was counterbalancedacross subjects The following is an example sentence

walkJohn and Ralph walked to the store

1 2 3 4 5 6 7worst best

Stem naturalness ratings were elicited for all verbs in present-tensesentences in any person other than third person singular There was noattempt to make the stem sentence of each verb similar in content to thatof its past-tense sentence Each verb stem was presented in a formatsimilar to that in which the past-tense forms were presented For example

dropPeople often drop things when they have oily hands

1 2 3 4 5 6 7worst best

Because ratings were gathered on a large number of verb forms the fullquestionnaires were broken down into sub-questionnaires Each sub-questionnaire contained both the stem and past-tense sentences for a givenverb Each subject completed one or more sub-questionnaires Thusalthough each verb form was rated by 32 subjects not all verbs were ratedby the same subject

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 49

One well-studied approach which largely overcomes this problem hasbeen the investigation of English past tense Irregular past-tensetransformations are largely unpredictable in sound (eg clingndashclungbringndashbrought) and do not apply productively (new irregulars rarely enterthe language) In contrast regular past-tense transformations arepredictable in sound (verb + -ed) and apply productively to new wordsand to novel forms (eg faxndashfaxed blickndashblicked) Thus irregular formshave arbitrary mappings with their stems just as non-compositional lexicalforms have arbitrary mappings with their meanings whereas the structureof regular past-tense forms can be described by a rule which applies in aproductive manner Crucially irregulars and regulars are matched incomplexity (one word) meaning (past) and syntax (tensed) and can alsobe matched on syllable structure (eg sleptndashslipped) word frequency andother factors

According to a dual-system view irregular forms (blew) are stored inand retrieved from lexical memory whereas regular forms (walked) areproduced in real-time by a distinct symbol-manipulation system whichapplies an -ed-sufxation rule to the verb stem (walk) Retrieval of anirregular blocks the rule (blew pre-empts blowed) when an irregular is notsuccessfully retrieved the rule may be applied resulting in lsquolsquoover-regularisationrsquorsquo errors such as blowed (Pinker 1991 Pinker amp Prince1988)

Two alternative theories have been proposed motivated in part by theobservation that irregular transformations are not completely unpredict-able and unproductive but rather follow subregularities (eg springndashsprang ringndashrang singndashsang) and can lead to the generation of novelforms (eg splingndashsplang) One theory posits that rules underlie thecomputation of irregulars (eg computing indasha in springndashsprang ringndashrang)as well as regulars (Chomsky amp Halle 1968 Halle amp Mohanan 1985 Lingamp Marinov 1993) The second theory is consistent with the single-systemview and claims that regulars and irregulars are learned in and computedover an associative memory In support of this theory a number ofconnectionist models have been developed in which input and output unitsrepresent the sounds of verb stems and past-tense forms respectively andin which the weights of a matrix of inputndashoutput connections are adjustedaccording to how the statistical structure of stemndashpast pairs inuences thebehaviour of the network (Daugherty amp Seidenberg 1992 Hare amp Elman1995 Hare Elman amp Daugherty 1995 MacWhinney amp Leinbach 1991Marchman 1993 Plunkett amp Marchman 1991 1993 Rumelhart andMcClelland 1986)

Here I argue in favour of the dual-system perspective I presentevidence for dissociations between the computation of regular andirregular past-tense forms with respect to their sensitivity to word

50 ULLMAN

frequency and to their phonological similarity with other verbs I arguethat this evidence suggests that connectionist models are successful atcapturing important aspects of the representation and computation ofirregular verbs but that regular verbs are computed by a distinct rule-processing system

Evidence suggests that the more often a word is encountered the betterit is remembered (eg Rubenstein Gareld amp Milliken 1970) Accordingto the dual-system view irregular past-tense forms (blew) are retrievedfrom memory so they are expected to be frequency-sensitive with high-frequency forms being remembered better than low-frequency formsRegular past-tense forms (walked) are rule-produced in real-time so theyshould show no such lsquolsquofrequency effectsrsquorsquo once access to their stem forms(walk) to which the -ed-sufxation rule is applied is controlled for

In contrast if the single-system view is correct and regulars as well asirregulars are memorised in associative memory then both past-tensetypes may show word frequency effects (eg Daugherty amp Seidenberg1992) Moreover many single-system models expect lsquolsquophonologicalneighbourhood effectsrsquorsquo The memory traces representing the distributedphonological stemndashpast mappings shared among lsquolsquoneighbouringrsquorsquo irregulars(eg singndashsang ringndashrang springndashsprang) or regulars (eg slipndashslippedclipndashclipped tripndashtripped) should be strengthened by the learning of anyform with these mappings Thus hearing singndashsang should strengthen notonly the memory traces unique to singndashsang but also those shared betweensingndashsang ringndashrang and springndashsprang (eg Plunkett amp Marchman 19911993 Rumelhart amp McClelland 1986) Moreover because there are manyregular verbs and they follow a consistent pattern it has been claimed thatthe contribution of neighbouring regulars to a given regular verbrsquos memorytraces may largely overwhelm the contribution of the verbrsquos individualpast-tense frequency resulting in weakened past tense frequency effectsfor regular verbs (Daugherty amp Seidenberg 1992 Seidenberg 1992)

Although traditional dual-system models assume that irregular past-tense forms are stored in rote memory more recent models have beeninuenced by the partial regularity (eg springndashsprang ringndashrang ingndashung) and partial productivity (eg splingndashsplang) of irregulars and haveadopted the single-system connectionist perspective that irregulars arelearned in an associative memory (Pinker 1991) If irregulars are retrievedfrom associative memory in a manner similar to that hypothesised bysingle-system models whereas regulars are rule-products then phonolo-gical neighbourhood effects should be found for irregular but not regularforms Finally if irregulars as well as regulars are rule-produced (Halle ampMohanan 1985 Ling amp Marinov 1993) neither irregular nor regularforms should show either word-frequency or phonological neighbourhoodeffects

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 51

There have been few studies of word-frequency and phonologicalneighbourhood effects contrasting regular and irregular past-tense formsPrasada Pinker and Snyder (1990) presented adult subjects with a series ofverb stems and asked them to produce the past-tense form of each verb asquickly and accurately as possible The subjects took signicantly moretime to produce low-frequency than high-frequency past-tense forms forirregular verbs holding stem frequency constant However they foundthat production times were not signicantly longer for low-frequency thanhigh-frequency regular past-tense forms holding stem frequency constantThis result is consistent with the hypothesis that irregular but not regularpast-tense forms are retrieved from memory Stemberger and MacWhin-ney (1988) examined errors on intended past-tense forms in spontaneousspeech and also gave subjects a production task of regular past-tenseforms They reported frequency effects for regulars in the production taskbut not in spontaneous speech however the frequency effects must betreated with caution because there was no control for any measure ofaccess to the verb stems such as stem frequency Similarly althoughMarchman (1997) reported frequency effects for both regular and irregularverbs in a past-tense elicitation task given to children stem access was notcontrolled for

Bybee and Moder (1983) and Prasada and Pinker (1993) investigatedphonological neighbourhood effects in novel verbs Bybee and Moder(1983) presented subjects with novel verbs in obligatory past-tensesentence contexts (Sam likes to Yesterday he ) The verb stemsvaried in phonological proximity to the prototypical pattern which theauthors dened for the i-H (eg stringndashstrung) group of irregular verbssCCV[velar nasal] They found a continuous effect of similarity as afunction of proximity to the prototype The closer a real or novel verb stemwas to the prototype the more likely it was to be inected to the H-formThus spling was more likely to be inected as splung than vin was as vunThey took this quasi-productivity as evidence that irregular verbs areorganised into family resemblance categories (Rosch 1978) Prasada andPinker (1993) replicated Bybee and Moderrsquos (1983) nding that theproduction of an irregular-sounding past-tense form for a novel verbincreases with the similarity of that verb to the prototype of an irregularneighbourhood (splingndashsplung versus vinndashvun) However Prasada andPinker found that subjects were not signicantly more likely to produceregularly sufxed past-tense forms of familiar-sounding novel verbs likeplip than of odd-sounding novel verbs like ploamphmdasheven though thesubjects rated the stem ploamph to be less acceptable than the stem plipThe authors found a similar distinction between acceptability ratings ofirregular-sounding (splung) and -ed-sufxed (plipped) past-tense forms ofnovel verbs Subjects gave higher ratings to forms like splung than vun

52 ULLMAN

whereas forms like plipped were not given higher ratings than those likeploamphed once the naturalness of their stems was held constant In herpast tense elicitation task given to children Marchman (1997) reportedthat errors on irregulars were not predicted by the number of similarirregular neighbours In contrast errors on regulars were affected by thenumber of similar regular neighbours However this surprising contrastmust be treated with caution because no statistics were reported for thedifference for regulars and stem access was not controlled for so anysimilarity effects of stem forms were not factored out

There has thus been no systematic psycholinguistic investigation of bothfrequency and phonological neighbourhood effects of the computation ofregular (walkndashwalked) and irregular (blowndashblew) past-tense formsholding stem frequency constant Here I address this empirical gapdescribing a study in which acceptability ratings were elicited from normaladults for regular and irregular past-tense forms and were analysed forfrequency and phonological neighbourhood effects

METHODS

On a 7-point scale subjects were asked to give acceptability ratings forpast-tense forms of regular and irregular verbs in past-tense sentencecontexts and of their stem forms in present-tense sentence contexts

Subjects

Each past-tense and stem form was given acceptability ratings by 32 MITundergraduates who were paid for their participation in the experimentAll were native speakers of American or Canadian English

Verbs

Subjects were shown 137 verbs with monosyllabic stems (see Appendix 1for a full list) 89 were irregular verbs (blowndashblew) and 48 were regularverbs (walkndashwalked) In addition to these 137 verbs whose ratings areanalysed in this paper the questionnaire contained another 335 verbs notdiscussed here (see Appendix 2)

The 89 irregular verbs were drawn from Pinker and Prince (1988)Doublet verbs which have acceptable irregular and regular past-tenseforms (divendashdovedived) were excluded In this study doublets weredened as those verbs with an irregular past-tense form whosecorresponding regularisationrsquos mean acceptability rating was greater than35 out of 7 All regularisations of the non-doublet irregular verbs (blowed)had relative frequency counts of 0 according to both the Francis andKucAEligera (1982) and Associated Press word-frequency counts (see below for

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 53

details) The mean ( standard deviation) of the ln-transformed past-tensefrequencies for the 89 irregulars was 359 155 for the Francis and KucAEligerafrequency counts and 663 215 for the Associated Press counts

The 48 lsquolsquoconsistentrsquorsquo regulars were drawn from the Francis and KucAEligeraand the Associated Press frequency counts Their stems were phonologi-cally similar to the stems of other regular verbs and dissimilar to the stemsof irregular verbs and thus they and their phonological neighbours areconsistently regularised (eg balkndashbalked stalkndashstalked) Thus none oftheir stems rhyme with the stems of irregulars nor do they have t or d asa nal consonant because many irregular stems end in one of these twophonemes (eg wet bite ride bend) The mean ln-transformed past-tensefrequency for the 48 consistent regulars was 177 151 for the Francis andKucAEligera counts and 411 234 for the Associated Press counts

PresentationThe position of each past-tense sentence in the questionnaire wasrandomised and the order of regulars and irregulars was counterbalancedacross subjects The following is an example sentence

walkJohn and Ralph walked to the store

1 2 3 4 5 6 7worst best

Stem naturalness ratings were elicited for all verbs in present-tensesentences in any person other than third person singular There was noattempt to make the stem sentence of each verb similar in content to thatof its past-tense sentence Each verb stem was presented in a formatsimilar to that in which the past-tense forms were presented For example

dropPeople often drop things when they have oily hands

1 2 3 4 5 6 7worst best

Because ratings were gathered on a large number of verb forms the fullquestionnaires were broken down into sub-questionnaires Each sub-questionnaire contained both the stem and past-tense sentences for a givenverb Each subject completed one or more sub-questionnaires Thusalthough each verb form was rated by 32 subjects not all verbs were ratedby the same subject

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

50 ULLMAN

frequency and to their phonological similarity with other verbs I arguethat this evidence suggests that connectionist models are successful atcapturing important aspects of the representation and computation ofirregular verbs but that regular verbs are computed by a distinct rule-processing system

Evidence suggests that the more often a word is encountered the betterit is remembered (eg Rubenstein Gareld amp Milliken 1970) Accordingto the dual-system view irregular past-tense forms (blew) are retrievedfrom memory so they are expected to be frequency-sensitive with high-frequency forms being remembered better than low-frequency formsRegular past-tense forms (walked) are rule-produced in real-time so theyshould show no such lsquolsquofrequency effectsrsquorsquo once access to their stem forms(walk) to which the -ed-sufxation rule is applied is controlled for

In contrast if the single-system view is correct and regulars as well asirregulars are memorised in associative memory then both past-tensetypes may show word frequency effects (eg Daugherty amp Seidenberg1992) Moreover many single-system models expect lsquolsquophonologicalneighbourhood effectsrsquorsquo The memory traces representing the distributedphonological stemndashpast mappings shared among lsquolsquoneighbouringrsquorsquo irregulars(eg singndashsang ringndashrang springndashsprang) or regulars (eg slipndashslippedclipndashclipped tripndashtripped) should be strengthened by the learning of anyform with these mappings Thus hearing singndashsang should strengthen notonly the memory traces unique to singndashsang but also those shared betweensingndashsang ringndashrang and springndashsprang (eg Plunkett amp Marchman 19911993 Rumelhart amp McClelland 1986) Moreover because there are manyregular verbs and they follow a consistent pattern it has been claimed thatthe contribution of neighbouring regulars to a given regular verbrsquos memorytraces may largely overwhelm the contribution of the verbrsquos individualpast-tense frequency resulting in weakened past tense frequency effectsfor regular verbs (Daugherty amp Seidenberg 1992 Seidenberg 1992)

Although traditional dual-system models assume that irregular past-tense forms are stored in rote memory more recent models have beeninuenced by the partial regularity (eg springndashsprang ringndashrang ingndashung) and partial productivity (eg splingndashsplang) of irregulars and haveadopted the single-system connectionist perspective that irregulars arelearned in an associative memory (Pinker 1991) If irregulars are retrievedfrom associative memory in a manner similar to that hypothesised bysingle-system models whereas regulars are rule-products then phonolo-gical neighbourhood effects should be found for irregular but not regularforms Finally if irregulars as well as regulars are rule-produced (Halle ampMohanan 1985 Ling amp Marinov 1993) neither irregular nor regularforms should show either word-frequency or phonological neighbourhoodeffects

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 51

There have been few studies of word-frequency and phonologicalneighbourhood effects contrasting regular and irregular past-tense formsPrasada Pinker and Snyder (1990) presented adult subjects with a series ofverb stems and asked them to produce the past-tense form of each verb asquickly and accurately as possible The subjects took signicantly moretime to produce low-frequency than high-frequency past-tense forms forirregular verbs holding stem frequency constant However they foundthat production times were not signicantly longer for low-frequency thanhigh-frequency regular past-tense forms holding stem frequency constantThis result is consistent with the hypothesis that irregular but not regularpast-tense forms are retrieved from memory Stemberger and MacWhin-ney (1988) examined errors on intended past-tense forms in spontaneousspeech and also gave subjects a production task of regular past-tenseforms They reported frequency effects for regulars in the production taskbut not in spontaneous speech however the frequency effects must betreated with caution because there was no control for any measure ofaccess to the verb stems such as stem frequency Similarly althoughMarchman (1997) reported frequency effects for both regular and irregularverbs in a past-tense elicitation task given to children stem access was notcontrolled for

Bybee and Moder (1983) and Prasada and Pinker (1993) investigatedphonological neighbourhood effects in novel verbs Bybee and Moder(1983) presented subjects with novel verbs in obligatory past-tensesentence contexts (Sam likes to Yesterday he ) The verb stemsvaried in phonological proximity to the prototypical pattern which theauthors dened for the i-H (eg stringndashstrung) group of irregular verbssCCV[velar nasal] They found a continuous effect of similarity as afunction of proximity to the prototype The closer a real or novel verb stemwas to the prototype the more likely it was to be inected to the H-formThus spling was more likely to be inected as splung than vin was as vunThey took this quasi-productivity as evidence that irregular verbs areorganised into family resemblance categories (Rosch 1978) Prasada andPinker (1993) replicated Bybee and Moderrsquos (1983) nding that theproduction of an irregular-sounding past-tense form for a novel verbincreases with the similarity of that verb to the prototype of an irregularneighbourhood (splingndashsplung versus vinndashvun) However Prasada andPinker found that subjects were not signicantly more likely to produceregularly sufxed past-tense forms of familiar-sounding novel verbs likeplip than of odd-sounding novel verbs like ploamphmdasheven though thesubjects rated the stem ploamph to be less acceptable than the stem plipThe authors found a similar distinction between acceptability ratings ofirregular-sounding (splung) and -ed-sufxed (plipped) past-tense forms ofnovel verbs Subjects gave higher ratings to forms like splung than vun

52 ULLMAN

whereas forms like plipped were not given higher ratings than those likeploamphed once the naturalness of their stems was held constant In herpast tense elicitation task given to children Marchman (1997) reportedthat errors on irregulars were not predicted by the number of similarirregular neighbours In contrast errors on regulars were affected by thenumber of similar regular neighbours However this surprising contrastmust be treated with caution because no statistics were reported for thedifference for regulars and stem access was not controlled for so anysimilarity effects of stem forms were not factored out

There has thus been no systematic psycholinguistic investigation of bothfrequency and phonological neighbourhood effects of the computation ofregular (walkndashwalked) and irregular (blowndashblew) past-tense formsholding stem frequency constant Here I address this empirical gapdescribing a study in which acceptability ratings were elicited from normaladults for regular and irregular past-tense forms and were analysed forfrequency and phonological neighbourhood effects

METHODS

On a 7-point scale subjects were asked to give acceptability ratings forpast-tense forms of regular and irregular verbs in past-tense sentencecontexts and of their stem forms in present-tense sentence contexts

Subjects

Each past-tense and stem form was given acceptability ratings by 32 MITundergraduates who were paid for their participation in the experimentAll were native speakers of American or Canadian English

Verbs

Subjects were shown 137 verbs with monosyllabic stems (see Appendix 1for a full list) 89 were irregular verbs (blowndashblew) and 48 were regularverbs (walkndashwalked) In addition to these 137 verbs whose ratings areanalysed in this paper the questionnaire contained another 335 verbs notdiscussed here (see Appendix 2)

The 89 irregular verbs were drawn from Pinker and Prince (1988)Doublet verbs which have acceptable irregular and regular past-tenseforms (divendashdovedived) were excluded In this study doublets weredened as those verbs with an irregular past-tense form whosecorresponding regularisationrsquos mean acceptability rating was greater than35 out of 7 All regularisations of the non-doublet irregular verbs (blowed)had relative frequency counts of 0 according to both the Francis andKucAEligera (1982) and Associated Press word-frequency counts (see below for

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 53

details) The mean ( standard deviation) of the ln-transformed past-tensefrequencies for the 89 irregulars was 359 155 for the Francis and KucAEligerafrequency counts and 663 215 for the Associated Press counts

The 48 lsquolsquoconsistentrsquorsquo regulars were drawn from the Francis and KucAEligeraand the Associated Press frequency counts Their stems were phonologi-cally similar to the stems of other regular verbs and dissimilar to the stemsof irregular verbs and thus they and their phonological neighbours areconsistently regularised (eg balkndashbalked stalkndashstalked) Thus none oftheir stems rhyme with the stems of irregulars nor do they have t or d asa nal consonant because many irregular stems end in one of these twophonemes (eg wet bite ride bend) The mean ln-transformed past-tensefrequency for the 48 consistent regulars was 177 151 for the Francis andKucAEligera counts and 411 234 for the Associated Press counts

PresentationThe position of each past-tense sentence in the questionnaire wasrandomised and the order of regulars and irregulars was counterbalancedacross subjects The following is an example sentence

walkJohn and Ralph walked to the store

1 2 3 4 5 6 7worst best

Stem naturalness ratings were elicited for all verbs in present-tensesentences in any person other than third person singular There was noattempt to make the stem sentence of each verb similar in content to thatof its past-tense sentence Each verb stem was presented in a formatsimilar to that in which the past-tense forms were presented For example

dropPeople often drop things when they have oily hands

1 2 3 4 5 6 7worst best

Because ratings were gathered on a large number of verb forms the fullquestionnaires were broken down into sub-questionnaires Each sub-questionnaire contained both the stem and past-tense sentences for a givenverb Each subject completed one or more sub-questionnaires Thusalthough each verb form was rated by 32 subjects not all verbs were ratedby the same subject

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 51

There have been few studies of word-frequency and phonologicalneighbourhood effects contrasting regular and irregular past-tense formsPrasada Pinker and Snyder (1990) presented adult subjects with a series ofverb stems and asked them to produce the past-tense form of each verb asquickly and accurately as possible The subjects took signicantly moretime to produce low-frequency than high-frequency past-tense forms forirregular verbs holding stem frequency constant However they foundthat production times were not signicantly longer for low-frequency thanhigh-frequency regular past-tense forms holding stem frequency constantThis result is consistent with the hypothesis that irregular but not regularpast-tense forms are retrieved from memory Stemberger and MacWhin-ney (1988) examined errors on intended past-tense forms in spontaneousspeech and also gave subjects a production task of regular past-tenseforms They reported frequency effects for regulars in the production taskbut not in spontaneous speech however the frequency effects must betreated with caution because there was no control for any measure ofaccess to the verb stems such as stem frequency Similarly althoughMarchman (1997) reported frequency effects for both regular and irregularverbs in a past-tense elicitation task given to children stem access was notcontrolled for

Bybee and Moder (1983) and Prasada and Pinker (1993) investigatedphonological neighbourhood effects in novel verbs Bybee and Moder(1983) presented subjects with novel verbs in obligatory past-tensesentence contexts (Sam likes to Yesterday he ) The verb stemsvaried in phonological proximity to the prototypical pattern which theauthors dened for the i-H (eg stringndashstrung) group of irregular verbssCCV[velar nasal] They found a continuous effect of similarity as afunction of proximity to the prototype The closer a real or novel verb stemwas to the prototype the more likely it was to be inected to the H-formThus spling was more likely to be inected as splung than vin was as vunThey took this quasi-productivity as evidence that irregular verbs areorganised into family resemblance categories (Rosch 1978) Prasada andPinker (1993) replicated Bybee and Moderrsquos (1983) nding that theproduction of an irregular-sounding past-tense form for a novel verbincreases with the similarity of that verb to the prototype of an irregularneighbourhood (splingndashsplung versus vinndashvun) However Prasada andPinker found that subjects were not signicantly more likely to produceregularly sufxed past-tense forms of familiar-sounding novel verbs likeplip than of odd-sounding novel verbs like ploamphmdasheven though thesubjects rated the stem ploamph to be less acceptable than the stem plipThe authors found a similar distinction between acceptability ratings ofirregular-sounding (splung) and -ed-sufxed (plipped) past-tense forms ofnovel verbs Subjects gave higher ratings to forms like splung than vun

52 ULLMAN

whereas forms like plipped were not given higher ratings than those likeploamphed once the naturalness of their stems was held constant In herpast tense elicitation task given to children Marchman (1997) reportedthat errors on irregulars were not predicted by the number of similarirregular neighbours In contrast errors on regulars were affected by thenumber of similar regular neighbours However this surprising contrastmust be treated with caution because no statistics were reported for thedifference for regulars and stem access was not controlled for so anysimilarity effects of stem forms were not factored out

There has thus been no systematic psycholinguistic investigation of bothfrequency and phonological neighbourhood effects of the computation ofregular (walkndashwalked) and irregular (blowndashblew) past-tense formsholding stem frequency constant Here I address this empirical gapdescribing a study in which acceptability ratings were elicited from normaladults for regular and irregular past-tense forms and were analysed forfrequency and phonological neighbourhood effects

METHODS

On a 7-point scale subjects were asked to give acceptability ratings forpast-tense forms of regular and irregular verbs in past-tense sentencecontexts and of their stem forms in present-tense sentence contexts

Subjects

Each past-tense and stem form was given acceptability ratings by 32 MITundergraduates who were paid for their participation in the experimentAll were native speakers of American or Canadian English

Verbs

Subjects were shown 137 verbs with monosyllabic stems (see Appendix 1for a full list) 89 were irregular verbs (blowndashblew) and 48 were regularverbs (walkndashwalked) In addition to these 137 verbs whose ratings areanalysed in this paper the questionnaire contained another 335 verbs notdiscussed here (see Appendix 2)

The 89 irregular verbs were drawn from Pinker and Prince (1988)Doublet verbs which have acceptable irregular and regular past-tenseforms (divendashdovedived) were excluded In this study doublets weredened as those verbs with an irregular past-tense form whosecorresponding regularisationrsquos mean acceptability rating was greater than35 out of 7 All regularisations of the non-doublet irregular verbs (blowed)had relative frequency counts of 0 according to both the Francis andKucAEligera (1982) and Associated Press word-frequency counts (see below for

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 53

details) The mean ( standard deviation) of the ln-transformed past-tensefrequencies for the 89 irregulars was 359 155 for the Francis and KucAEligerafrequency counts and 663 215 for the Associated Press counts

The 48 lsquolsquoconsistentrsquorsquo regulars were drawn from the Francis and KucAEligeraand the Associated Press frequency counts Their stems were phonologi-cally similar to the stems of other regular verbs and dissimilar to the stemsof irregular verbs and thus they and their phonological neighbours areconsistently regularised (eg balkndashbalked stalkndashstalked) Thus none oftheir stems rhyme with the stems of irregulars nor do they have t or d asa nal consonant because many irregular stems end in one of these twophonemes (eg wet bite ride bend) The mean ln-transformed past-tensefrequency for the 48 consistent regulars was 177 151 for the Francis andKucAEligera counts and 411 234 for the Associated Press counts

PresentationThe position of each past-tense sentence in the questionnaire wasrandomised and the order of regulars and irregulars was counterbalancedacross subjects The following is an example sentence

walkJohn and Ralph walked to the store

1 2 3 4 5 6 7worst best

Stem naturalness ratings were elicited for all verbs in present-tensesentences in any person other than third person singular There was noattempt to make the stem sentence of each verb similar in content to thatof its past-tense sentence Each verb stem was presented in a formatsimilar to that in which the past-tense forms were presented For example

dropPeople often drop things when they have oily hands

1 2 3 4 5 6 7worst best

Because ratings were gathered on a large number of verb forms the fullquestionnaires were broken down into sub-questionnaires Each sub-questionnaire contained both the stem and past-tense sentences for a givenverb Each subject completed one or more sub-questionnaires Thusalthough each verb form was rated by 32 subjects not all verbs were ratedby the same subject

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

52 ULLMAN

whereas forms like plipped were not given higher ratings than those likeploamphed once the naturalness of their stems was held constant In herpast tense elicitation task given to children Marchman (1997) reportedthat errors on irregulars were not predicted by the number of similarirregular neighbours In contrast errors on regulars were affected by thenumber of similar regular neighbours However this surprising contrastmust be treated with caution because no statistics were reported for thedifference for regulars and stem access was not controlled for so anysimilarity effects of stem forms were not factored out

There has thus been no systematic psycholinguistic investigation of bothfrequency and phonological neighbourhood effects of the computation ofregular (walkndashwalked) and irregular (blowndashblew) past-tense formsholding stem frequency constant Here I address this empirical gapdescribing a study in which acceptability ratings were elicited from normaladults for regular and irregular past-tense forms and were analysed forfrequency and phonological neighbourhood effects

METHODS

On a 7-point scale subjects were asked to give acceptability ratings forpast-tense forms of regular and irregular verbs in past-tense sentencecontexts and of their stem forms in present-tense sentence contexts

Subjects

Each past-tense and stem form was given acceptability ratings by 32 MITundergraduates who were paid for their participation in the experimentAll were native speakers of American or Canadian English

Verbs

Subjects were shown 137 verbs with monosyllabic stems (see Appendix 1for a full list) 89 were irregular verbs (blowndashblew) and 48 were regularverbs (walkndashwalked) In addition to these 137 verbs whose ratings areanalysed in this paper the questionnaire contained another 335 verbs notdiscussed here (see Appendix 2)

The 89 irregular verbs were drawn from Pinker and Prince (1988)Doublet verbs which have acceptable irregular and regular past-tenseforms (divendashdovedived) were excluded In this study doublets weredened as those verbs with an irregular past-tense form whosecorresponding regularisationrsquos mean acceptability rating was greater than35 out of 7 All regularisations of the non-doublet irregular verbs (blowed)had relative frequency counts of 0 according to both the Francis andKucAEligera (1982) and Associated Press word-frequency counts (see below for

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 53

details) The mean ( standard deviation) of the ln-transformed past-tensefrequencies for the 89 irregulars was 359 155 for the Francis and KucAEligerafrequency counts and 663 215 for the Associated Press counts

The 48 lsquolsquoconsistentrsquorsquo regulars were drawn from the Francis and KucAEligeraand the Associated Press frequency counts Their stems were phonologi-cally similar to the stems of other regular verbs and dissimilar to the stemsof irregular verbs and thus they and their phonological neighbours areconsistently regularised (eg balkndashbalked stalkndashstalked) Thus none oftheir stems rhyme with the stems of irregulars nor do they have t or d asa nal consonant because many irregular stems end in one of these twophonemes (eg wet bite ride bend) The mean ln-transformed past-tensefrequency for the 48 consistent regulars was 177 151 for the Francis andKucAEligera counts and 411 234 for the Associated Press counts

PresentationThe position of each past-tense sentence in the questionnaire wasrandomised and the order of regulars and irregulars was counterbalancedacross subjects The following is an example sentence

walkJohn and Ralph walked to the store

1 2 3 4 5 6 7worst best

Stem naturalness ratings were elicited for all verbs in present-tensesentences in any person other than third person singular There was noattempt to make the stem sentence of each verb similar in content to thatof its past-tense sentence Each verb stem was presented in a formatsimilar to that in which the past-tense forms were presented For example

dropPeople often drop things when they have oily hands

1 2 3 4 5 6 7worst best

Because ratings were gathered on a large number of verb forms the fullquestionnaires were broken down into sub-questionnaires Each sub-questionnaire contained both the stem and past-tense sentences for a givenverb Each subject completed one or more sub-questionnaires Thusalthough each verb form was rated by 32 subjects not all verbs were ratedby the same subject

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 53

details) The mean ( standard deviation) of the ln-transformed past-tensefrequencies for the 89 irregulars was 359 155 for the Francis and KucAEligerafrequency counts and 663 215 for the Associated Press counts

The 48 lsquolsquoconsistentrsquorsquo regulars were drawn from the Francis and KucAEligeraand the Associated Press frequency counts Their stems were phonologi-cally similar to the stems of other regular verbs and dissimilar to the stemsof irregular verbs and thus they and their phonological neighbours areconsistently regularised (eg balkndashbalked stalkndashstalked) Thus none oftheir stems rhyme with the stems of irregulars nor do they have t or d asa nal consonant because many irregular stems end in one of these twophonemes (eg wet bite ride bend) The mean ln-transformed past-tensefrequency for the 48 consistent regulars was 177 151 for the Francis andKucAEligera counts and 411 234 for the Associated Press counts

PresentationThe position of each past-tense sentence in the questionnaire wasrandomised and the order of regulars and irregulars was counterbalancedacross subjects The following is an example sentence

walkJohn and Ralph walked to the store

1 2 3 4 5 6 7worst best

Stem naturalness ratings were elicited for all verbs in present-tensesentences in any person other than third person singular There was noattempt to make the stem sentence of each verb similar in content to thatof its past-tense sentence Each verb stem was presented in a formatsimilar to that in which the past-tense forms were presented For example

dropPeople often drop things when they have oily hands

1 2 3 4 5 6 7worst best

Because ratings were gathered on a large number of verb forms the fullquestionnaires were broken down into sub-questionnaires Each sub-questionnaire contained both the stem and past-tense sentences for a givenverb Each subject completed one or more sub-questionnaires Thusalthough each verb form was rated by 32 subjects not all verbs were ratedby the same subject

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

54 ULLMAN

InstructionsBefore starting the past-tense rating task subjects were asked to givejudgements based on the naturalness of the past-tense form printed initalics in each sentence The instructions stressed that the experimentswere not asking for judgements about the real-world plausibility of thesentences but rather about the naturalness of the past-tense form in thesentence lsquolsquoIs the verb in a form that lsquosoundsrsquo right to you and that youwould naturally use in your own speechrsquorsquo The subjects were asked to usethe entire scale between 1 and 7 and it was stressed that lsquolsquoit is important toremember that we are looking for your intuitions and gut feelings and notwhat you believe the correct form to be according to what the dictionarysays or what your teachers have told yoursquorsquo The instructions preceding thestem rating task were similar to those of the past-tense rating taskrequesting the subject to judge the naturalness of the present-tense formsof verbs

PREDICTORS

If past-tense forms are retrieved from an associative memory representingdistributed stemndashpast mappings their acceptability ratings may bepredicted by their word frequencies as well as by some function of thenumber (type frequency) and similarity of their phonological neighboursand of the word frequencies of these neighbours (their token frequencies)In contrast if past-tense forms are produced by the application of a rule totheir stems their past-tense frequencies and the structure of theirphonological neighbours should not affect their acceptability ratings oncea measure of stem access has been held constant To test these distinctionsmeasures of past-tense frequency and phonological neighbourhoodinuences were acquired

Past-tense Frequency

Two relative frequency counts were used in all word-frequency analyses(1) frequency counts derived by Francis and KucAEligera (1982) from 1 millionwords of text drawn from several sources selected to cover a range oftopics (2) frequency counts extracted by a stochastic part-of-speechanalyser from a 44 million word corpus of unedited Associated Press newswires between February and December 1988 (Church 1988) Hereafterthe two frequency counts are referred to as lsquolsquoFKrsquorsquo and lsquolsquoAPrsquorsquo respectivelyBoth counts distinguished different parts of speech for example talkedused as a past tense has a separate count from talked used as a pastparticiple All analyses were carried out on the natural logarithm of eachraw frequency count which was rst augmented by 11 to avoid ln(0)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 55

Neighbourhood Strength

To test the single-system connectionist hypothesis that we learn mappingsbetween distributed phonological representations of stem and past-tenseforms in associative memory and that similar-sounding stemndashpast pairs(blowndashblew growndashgrew throwndashthrew) share memory traces representingcommon mappings (eg Plunkett amp Marchman 1991 1993 Rumelhart ampMcClelland 1986) the lsquolsquoneighbourhood strengthrsquorsquo function was developedThe function attempts to capture any inuence of phonological neighbourson the memory trace strength of a given verbrsquos stemndashpast mappings

For each stemndashpast pair rated by subjects in the experiment (eg blowndashblew) a neighbourhood strength value was calculated to measure anyinuence of neighbouring verbs (eg throwndashthrew growndashgrew) For eachirregular verb lsquolsquoirregular neighbourhood strengthrsquorsquo was calculated as afunction of the phonological structure its neighbouring irregular verbs Foreach regular verb (walked) lsquolsquoregular neighbourhood strengthrsquorsquo wascalculated as a function of the phonological structure of its regular verbneighbours (balked stalked)

To explain the neighbourhood strength function let us step through theprocess of calculating the irregular neighbourhood strength of blowndashblewIn brief this value is the sum of the contributions from all irregular verbswith a similar-sounding stem growndashgrew throwndashthrew gondashwent etc Eachsuch neighbouring irregular verbrsquos contribution to the memory traces ofblowndashblew increases with its token frequency and with the phonologicalsimilarity of its stem to blow If the two past-tense forms are similar (blewand grew) then the neighbouring verb is considered to be a lsquolsquofriendrsquorsquostrengthening the memory traces of blowndashblew If the the two past-tenseforms are dissimilar (blew and went) then the neighbouring verb isconsidered to be an lsquolsquoenemyrsquorsquo weakening the memory traces of blowndashblew

First each irregular Neighbour of blowndashblew was selected from an on-line database of 5350 verbs A Neighbour is dened as having amonosyllabic stem which is phonologically similar to blow such thatsimilarity(stem(Neighbour) blow) gt a similarity(blow blow) Accordingto the similarity metric used (Tversky 1977 see below) the similaritybetween two objects increases with the number of their shared featuresTherefore the similarity of a form with itself increases with the number ofphonemes in the form Longer forms are more self-similar than shorterforms A reasonable minimum similarity for a Neighbour to affect blowndashblewrsquos neighbourhood strength is some percentage of blowrsquos reexivesimilarity The free parameter a was assigned the value 025 which wasselected by nding a good t between irregular neighbourhood strengthsand the acceptability ratings of a randomly selected subset of irregular

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

56 ULLMAN

verbs in the experiment The pattern of results yielded by several othervalues of a was similar to that reported in this paper

The greater the phonological similarity between blowndashblew and thestemndashpast pair of a lsquolsquofriendlyrsquorsquo Neighbour (eg growndashgrew) the greater thedegree of mutual strengthening of the two pairs Each shared stemndashpastfeature mapping strengthened in the learning of one pair should alsostrengthen the representation of the other pair Conversely if two verbstems share many features but those features are mapped to distinct past-tense features (eg blowndashblew gondashwent) then these neighbours areconsidered to be enemies and the learning of one pair should weaken themappings of the other (eg Seidenberg 1992) Given that we do not knowwhich stem features map to which past-tense features a function wasselected which approximated these characteristics The contributionof thelearning of the Neighbourrsquos stemndashpast mapping to the memory tracemappings of blowndashblew was captured as contribution(blowndashblew Neigh-bour) = similarity(blew past(Neighbour)) plusmn b similarity(blow stem(Neigh-bour)) where b is a free parameter (see below)

Thus holding stem similarity constant contributionincreases positivelywith increasing similarity between the two past-tense forms and decreaseswith decreasing similarity between the two past-tense forms Whensimilarity between the two pastndashtense forms decreases to the value of b

similarity(blow stem(Neighbour)) then contribution = 0 When thesimilarity decreases below this value contributionbecomes negative Thusthis model assumes that the learning of an enemy Neighbour (eg gondashwent)may weaken the representation of blowndashblew The free parameter b wasassigned the value of 05 Thus we expect the contributionof a Neighbourto be negative weakening the learned mapping between blow and blewwhen the similarity between the Neighbourrsquos past-tense form and blew isless than half of that between the Neighbourrsquos stem and blow Forexample bringndashbrought may be an enemy of sing-sang

The contribution of the Neighbour is weighted by its AP past-tensefrequencymdashthe natural logarithm of the AP frequency count rstaugmented by 11 to avoid ln(0) and to capture the contribution of verbswith AP frequency counts of 0 Contribution(blowndashblew Neighbour) =

frequency(past(Neighbour)) (similarity(blew past(Neighbour)) plusmn b simi-larity(blow stem(Neighbour))) Thus as the past-tense frequency of theNeighbour increases its contribution to blowndashblewrsquos memory tracesincreases although that contribution can be positive (strengthening itsmappings) or negative (weakening its mappings)

The irregular neighbourhood strength of blowndashblew and of otherirregular verbs is calculated as the sum of the contribution of eachirregular Neighbour The same procedure was followed for the calculationof regular neighbourhood strength for regular verbs (eg walkndashwalked)

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 57

based on monosyllabic neighbouring regular verbs (eg balkndashbalked stalkndashstalked)

Similarity The similarity between two past-tense forms or two stemforms was calculated on the basis of the Contrast Model (Tversky 1977)According to this model the similarity between two objects or forms a andb is a function of the sum of the features the two forms have in commonminus a function of those features they do not have in common

similarity(ab) = hf(A F B) plusmn af(A plusmn B) plusmn bf(B plusmn A)

where A and B are the sets of features representing a and b and h a and b

are free parameters Thus two forms can be similar (their similarity value ispositive) neutral (their similarity value is 0) or dissimilar (their similarityvalue is negative)

Similarity values were computed for all pairs of English phonemes Eachphoneme was represented by a set of distinctive features (Chomsky ampHalle 1968) To reect logarithmic effects widely observed in learning andperception the natural logarithm was selected as the function f to beapplied to the shared and unshared features The free parameters h a andb were assigned values of 1 4 and 4 respectively on the basis of informallyacquired similarity judgements over a range of phoneme pairs Thusunshared features have an inuence four times that of shared features Thesimilarity of two phonemes a and b was therefore captured as

similarity(ab) = ln(A F B) plusmn 4ln(A plusmn B) plusmn 4ln(B plusmn A)

where A and B are the sets of distinctive features representing phonemes aand b

These similarity values between all pairs of English phonemes were thenused to compute similarities between pairs of stem forms and pairs of past-tense forms For each pair of verb forms a and b dynamic programmingwas used to calculate a maximum similarity between these forms whichwere treated as ordered sets of phonemes All phoneme pairs between thetwo forms were compared and a path of maximum similarity (of theexamined paths the one with the largest sum of similarity values) wasselected Where more than one phoneme from one word form had to belsquolsquosquishedrsquorsquo onto a single phoneme on the other word form (eg stacktack) a cost (negative value) was incurred This cost was set to themaximum similarity between two phonemesmdashthe total number ofdistinctive features of which there were 20 Both the phoneme comparisonand the lsquolsquosquishing costrsquorsquo were weighted according to the phonemesrsquoposition in their word forms If both phonemes were in the rhyme portionof the last syllable of their respective words their weighting was increased

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

58 ULLMAN

from 1 to 4 In other words the rhyme portion of the last syllable wasweighted four times more than earlier segments of the word Thisweighting was assigned on the basis of informally acquired similarityjudgements over a range of verb pairs which underscored the importanceof rhyme

Procedure All neighbourhood strength values were computed by aprogram that was written in the C programming language on a Sunworkstation For each verb (eg blowndashblew) for which irregular or regularneighbourhood strength was calculated all necessary information (numberof syllables phonetic representations and frequencies of stem and past-tense forms) of the set of verbs contributing to its neighbourhood strengthwas extracted from an on-line database of 5350 verbs This database wasconstructed from several sources including the CELEX database from theCentre for Lexical Information at the University of Nijmegen in theNetherlands and the FK and AP frequency counts The pronunciationrepresentations were based on British speech Although many of theserepresentations did not differ from representations of General Americanpronunciations there were some clear distinctions such as words ending inr (eg swear) Phonological similarity values between certain pairs of verbforms may therefore not have been accurate reections of the phonologicalsimilarity of the two verb forms for the subjects tested However suchinaccuracies should decrease the goodness of t between neighbourhoodstrength and subjectsrsquo acceptability ratings suggesting that any associa-tions that are found between the two variables may be even stronger thanthe analyses would indicate

RESULTS AND DISCUSSION

Acceptability ratings of irregular past-tense forms (blew) correlatedpositively with their past-tense frequencies partialling out stem ratings[FK r(86) = 051 P 0001 AP r(86) = 056 P 0001] or partiallingout stem ratings and irregular neighbourhood strength (threw grew) [FKr(85) = 054 P 0001 AP r(85) = 058 P 0001] (P-values for allcorrelations are reported as two-tailed) In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate with their frequenciespartialling out stem ratings [FK r(45) = plusmn 017 P = 0241 AP r(45) =

011 P = 0468] or partialling out stem ratings and regular neighbourhoodstrength (balked stalked) [FK r(44) = plusmn 017 P = 0260 AP r(44) = 011P = 0483] The acceptability ratings of irregular and regular past-tenseforms had similar means (669 and 670 respectively) standard deviations(027 and 022) and ranges (57ndash70 and 58ndash70) Thus differences in

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 59

acceptability rating variance between the two groups are unlikely toaccount for the contrasting correlations

The contrasting correlations might be explained by the larger samplesize of irregular verbs (89 vs 48 regular verbs) or by the larger range of theirregular verbsrsquo past-tense frequencies (ln-transformed AP frequencyrange of 11ndash131 vs 01ndash90 for regulars) To control for these factors 48irregular verbs whose past-tense forms had ln-transformed AP frequenciesless than 90 were randomly selected from the larger sample of 89 irregularverbs Like the larger sample of irregulars and unlike the regular verbsthe acceptability ratings of the smaller sample of irregular past-tense formscorrelated signicantly with their past-tense frequencies partialling outstem ratings [FK r(45) = 038 P = 0009 AP r(45) = 046 P = 0001] orpartialling out stem ratings and irregular neighbourhood strength [FKr(44) = 040 P = 0006 AP r(44) = 045 P = 0002]

Acceptability ratings of irregular past-tense forms (blew) correlatedwith their irregular neighbourhood strengths (threw grew) partialling outstem ratings and past-tense frequencies [FK r(85) = 024 P = 0022 APr(85) = 024 P = 0028] This pattern also held with the same sample of48 lower-frequency irregular verbs described above [FK r(44) = 042 P= 0004 AP r(44) = 038 P = 0009] In contrast acceptability ratings ofregular past-tense forms (walked) did not correlate at all with theirregular neighbourhood strengths (balked stalked) partialling out stemratings and past-tense frequencies [FK r(44) = plusmn 003 P = 0859 APr(44) = plusmn 004 P = 0774]

Connectionist simulations of the learning and computation of themapping between word spelling and pronunciation a domain whichconnectionist modellers have claimed is similar to the learning andcomputation of the mapping between verb and past-tense form (PlautMcClelland Seidenberg amp Patterson 1996 Seidenberg 1992) haveyielded an interaction between neighbourhood and frequency effectsHigher-frequency items show less of a neighbourhood effect than lower-frequency items (eg Seidenberg amp McClelland 1989) This pattern hasalso been observed empirically in subjectsrsquo performance (eg Andrews1982 Seidenberg Waters Barnes amp Tanenhaus 1984) Thus if regular aswell as irregular past-tense forms are learned in a single-system associativememory both might be expected to show neighbourhood-strengthword-frequency trade-offs In contrast under the dual-system view this trade-offshould be found only for irregular verbs

The irregular verbs were divided into two groups one of low past-tensefrequency and one of high past-tense frequency with the median AP past-tense frequency serving as the divider The regular verbs were likewisemedian-split into low- and high-frequency groups Irregular past-tenseacceptability ratings (blew) correlated signicantly with irregular neigh-

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

60 ULLMAN

bourhood strength (threw grew) for the low-frequency verbs [FK r(41) =

033 P = 0030 AP r(41) = 034 P = 0026] but not for the high-frequencyverbs [FK r(40) = 009 P = 0574 AP r(40) = 008 P = 0637] partiallingout stem ratings and past-tense frequencies This pattern also held with thesame sample of 48 lower-frequency irregular verbs described above whichwere likewise median-split into low- and high-frequency groups Past-tenseacceptability ratings correlated signicantly with neighbourhood strengthfor the low-frequency verbs [FK r(20) = 063 P = 0002 AP r(20) = 059P = 0004] but not for the high-frequency verbs [FK r(20) = 017 P =

0458 AP r(20) = 020 P = 0373] partialling out stem ratings and past-tense frequencies In contrast regular past-tense acceptability ratings(walked) did not correlate at all with their regular neighbourhoodstrengths (balked stalked) for either the low-frequency verbs [FK r(20)= plusmn 014 P = 0532 AP r(20) = 0 P = 0957] or the high-frequency verbs[FK r(20) = 006 P = 0785 AP r(20) = plusmn 001 P = 0966] partialling outstem ratings and past-tense frequencies The contrast suggests thatirregulars but not regulars are learned in an associative memory whichcan be modelled by connectionist networks that yield frequencyneighbourhood interactions

This view is strengthened by the fact that the frequencies of the regularpast-tense items (mean 1n-transformed FK 173 AP 410) were lowerthan those of the full set of 89 irregular past-tense items (FK 359 AP663) as well as those of the smaller sample of 48 irregular past-tense forms(FK 314 AP 621) Crucially this contrast also held for the lowerfrequency half of the 48 regular and 48 irregular verbs with the formerhaving mean frequencies (FK 059 AP 216) well below those of the latter(FK 204 AP 476) despite the nding that the irregulars and not theregulars showed neighbourhood effects

It might be claimed that the lack of neighbourhood effects amongregulars is consistent with the properties of sigmoid activation functions(eg the logistic function) in connectionist models On this view becausethere are a large number of regulars following the same sufxation patternthe inuence of additional regular neighbours on their underlying memorytraces should be diminished Thus differences in neighbourhood strengthamong regulars might correspond to small differences in acceptabilityratings resulting in weakened neighbourhood strength effects for regularverbs However an examination of the data suggested that such anexplanation might not be consistent with the nding that there was noteven a trend of neighbourhood effects among the regulars The range ofthe neighbourhood strengths of the regular items (1717ndash25124 SD 6303)was considerably larger than the range of the irregular neighbourhoodstrengths of the full set of 89 irregulars (range ndash4710ndash5633 SD 1744) and ofthe smaller set of 48 irregulars (range ndash2309ndash5633 SD 1918) Thus it would

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 61

be surprising if no trend at all were found for regular phonologicalneighbourhood effects We also examined neighbourhood strength effectsin the range of overlap between irregular and regular neighbourhoodstrengths Whereas those irregulars with the largest irregular neighbour-hood strengths (n = 32 range 25ndash5633) showed the expected signicantpositive correlation between neighbourhood strength and past-tenseacceptability ratings partialling out stem ratings and past-tense frequen-cies [FK r(28) = 048 P = 0008 AP r(28) = 049 P = 0006] thoseregulars with the smallest regular neighbourhood strengths (n = 32 range1717ndash20535) did not show any positive correlation at all betweenneighbourhood strength and acceptability ratings in the analogous analysis[FK r(28) = plusmn 024 P = 0199 AP r(28) = plusmn 026 P = 0162]

Thus the frequency and neighbourhood strength contrasts shown in thisstudy between irregular and regular verbs are predicted by a dual-systemmodel in which irregular past-tense forms are learned in and retrievedfrom associative memory whereas consistent regular past-tense formswhose stems are not phonologically similar to the stems of irregulars arerule-products The results cannot be explained by connectionist modelsthat expect any past tense frequency or neighbourhood effects forconsistent regular verbs Moreover it is unclear whether the lack of evena trend suggesting frequency effects can be explained by connectionistmodels that expect weakened frequency effects among regulars with largeand consistent neighbourhoods (Daugherty amp Seidenberg 1992 Seiden-berg 1992) Finally the ndings also preclude models which claim thatirregular as well as regular past-tense forms are rule-produced (Chomskyamp Halle 1968 Halle amp Mohanan 1985 Ling amp Marinov 1993)

Manuscript received October 1997Revised manuscript received July 1998

REFERENCESAndrews S (1982) Phonological recoding Is the regularity effect consistent Memory and

Cognition 10 565ndash575Bates E amp Goodman JC (1997) On the inseparability of grammar and the lexicon

Evidence from acquisition aphasia and real-time processing Language and CognitiveProcesses 12 507ndash584

Bates E Harris C Marchman V Wulfeck B amp Kritchevsky M (1995) Production ofcomplex syntax in normal aging and Alzheimerrsquos disease Language and CognitiveProcesses 10 487ndash539

Bates E amp MacWhinney B (1989) Functionalism and the competition model In BMacWhinney amp E Bates (Eds) The crosslinguistic study of sentence processing (pp 3ndash76)New York Cambridge University Press

Berko J (1958) The childrsquos learning of English morphology Word 14 150ndash177

62 ULLMAN

Bybee JL amp Moder CL (1983) Morphological classes as natural categories Language59 251ndash270

Comsky N (1965) Aspects of the theory of syntax Cambridge MA MIT PressChomsky N (1995) The minimalist program Cambridge MA MIT PressChomsky N amp Halle M (1968) The sound pattern of English New York Harper amp

RowChurch K (1988) A stochastic parts program and noun phrase parser for unrestricted text

Paper presented at the Second Conference on Applied Natural Language ProcessingAustin TX

Daugherty K amp Seidenberg M (1992) Rules or connections The past tense revisited InProceedings of the Fourteenth Annual Conference of the Cognitive Science Society (pp259ndash264) Hillsdale NJ Lawrence Erlbaum Associates Inc

Elman J Bates E Johnson M Karmiloff-Smith A Parisi D amp Plunkett K (1996)Rethinking innateness A connectionist perspective on development Cambridge MA MITPress

Fodor J (1983) Modularity of mind Cambridge MA MIT PressFrancis N amp KucAEligera H (1982) Frequency analysis of English usage Lexicon and

grammar Boston MA Houghton MifinFrazier L (1987) Sentence processing A tutorial review In M Coltheart (Ed) Attention

and performance XII (pp 559ndash586) Hove UK Lawrence Erlbaum Associates LtdHalle M amp Mohanan KP (1985) Segmental phonology of modern English Linguistic

Inquiry 16 57ndash116Hare M amp Elman J (1995) Learning and morphological change Cognition 56 61ndash98Hare M Elman JL amp Daugherty KG (1995) Default generalization in connectionist

networks Language and Cognitive Processes 10 601ndash630Kim JJ Pinker S Prince A amp Prasada S (1991) Why no mere mortal has ever own

out to center eld Cognitive Science 15 173ndash218Ling C amp Marinov M (1993) Answering the connectionist challenge A symbolic model

of the past tense acquisitions Cognition 49 235ndash290MacDonald MC Pearlmutter NL amp Seidenberg MS (1994) Lexical nature of syntactic

ambiguity resolution Psychological Review 101 676ndash703MacWhinney B amp Leinbach J (1991) Implementations are not conceptualizations

Revising the verb learning model Cognition 40 121ndash157Marchman VA (1993) Constraints on plasticity in a connectionist model of the English

past tense Journal of Cognitive Neuroscience 5 215ndash234Marchman VA (1997) Childrenrsquos productivity in the English past tense The role of

frequency phonology and neighbourhood structure Cognitive Science 21 283ndash304Pinker S (1991) Rules of language Science 253 530ndash535Pinker S (1994) The language instinct New York William MorrowPinker S amp Prince A (1988) On language and connectionism Analysis of a parallel

distributed processing model of language acquisition Cognition 28 73ndash193Plaut DC McClelland JL Seidenberg MS amp Patterson K (1996) Understanding

normal and impaired word reading Computational principles in quasi-regular domainsPsychological Review 103 56ndash115

Plunkett K amp Marchman V (1991) U-shaped learning and frequency effects in amulti-layered perceptron Implications for child language acquisition Cognition 3843ndash102

Plunkett K amp Marchman V (1993) From rote learning to system building Acquiring verbmorphology in children and connectionist nets Cognition 48 21ndash69

Prasada S amp Pinker S (1993) Generalisation of regular and irregular morphologicalpatterns Language and Cognitive Processes 8 1ndash56

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 63

Prasada S Pinker S amp Snyder W (1990) Some evidence that irregular forms are retrievedfrom memory but regular forms are rule-generated Paper presented at the 31st AnnualMeeting of the Pschyonomics Society New Orleans LA 16ndash18 November

Rosch E (1978) Principles of categorization In E Rosch amp BB Lloyd (Eds) Cognitionand categorization (pp 27ndash48) Hillsdale NJ Lawrence Erlbaum Associates Inc

Rubenstein H Gareld L amp Milliken JA (1970) Homographic entries in the internallexicon Journal of Verbal Learning and Verbal Behavior 9 487ndash492

Rumelhart DE amp McClelland JL (1986) On learning the past tenses of English verbs InJLMcClelland DE Rumelhart amp the PDP Research Group (Eds) Parallel distributedprocessing Explorations in the microstructures of cognition Vol 2 (pp 216ndash271)Cambridge MA BradfordMIT Press

Seidenberg M (1992) Connectionism without tears In S Davis (Ed) ConnectionismTheory and Practice (pp 84ndash137) New York Oxford University Press

Seidenberg MS amp McClelland JL (1989) A distributed developmental model of wordrecognition and naming Psychological Review 96 523ndash568

Seidenberg MS Waters GS Barnes MA amp Tanenhaus MK (1984) When doesirregular spelling or pronunciation inuence word recognition Journal of Verbal Learningand Verbal Behavior 23 383ndash404

Stemberger J amp MacWhinney B (1988) Are inected forms stored in the lexicon In MHammond amp M Noonan (Eds) Theoretical morphology Approaches in modern linguistics(pp 101ndash116) New York Academic Press

Stromswold KJ (1990) Learnability and the acquisition of auxiliaries DissertationAbstracts International 52 2535

Tversky A (1977) Features of similarity Psychological Review 84 327ndash352

64 ULLMAN

APPENDIX 1 STIMULIThe following two tables show the stem and past-tense forms of the regular and irregularverbs whose elicited acceptability ratings are reported in this paper Each Francis and KucAEligera(1982) and Associated Press relative frequency count is natural logarithm transformed afterbeing augmented by 1

Irregular verbs

Stem Irregular Past Tense

Form Rating Form Rating FK Freq AP Freq

bleed 690 bled 687 109 270breed 690 bred 668 000 256feed 690 fed 678 219 446lead 678 led 675 441 837read 693 read 681 361 694meet 684 met 690 439 839hide 693 hid 665 194 534slide 681 slid 662 321 522bite 671 bit 659 207 421shoot 696 shot 700 294 761bend 693 bent 675 270 398send 687 sent 678 424 813spend 671 spent 659 371 805lend 656 lent 653 138 480build 690 built 690 309 661lose 700 lost 693 391 827deal 681 dealt 665 219 553feel 693 felt 684 571 793mean 665 meant 675 426 673keep 693 kept 693 475 765sleep 690 slept 696 294 521sweep 665 swept 681 299 619leave 675 left 665 506 886buy 675 bought 678 349 756bring 681 brought 681 489 806catch 662 caught 665 400 664ght 700 fought 678 317 683seek 687 sought 687 358 776teach 675 taught 690 299 604think 675 thought 681 583 849ee 678 ed 684 313 740say 690 said 678 746 1307hear 696 heard 678 486 767make 662 made 690 614 936sell 681 sold 687 304 767tell 671 told 687 565 1018freeze 693 froze 678 069 454speak 696 spoke 684 446 860steal 681 stole 662 239 613get 650 got 650 582 931swear 671 swore 681 270 430tear 668 tore 693 277 574

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 65

Irregular verbs

Stem Irregular Past Tense

Form Rating Form Rating FK Freq AP Freq

wear 700 wore 690 418 668bear 646 bore 600 270 548break 665 broke 675 420 824choose 684 chose 681 363 703ring 681 rang 659 309 502sing 675 sang 653 336 661spring 675 sprang 606 263 424shrink 681 shrank 593 069 523sink 690 sank 615 294 653swim 690 swam 662 194 501run 696 ran 687 490 801sit 700 sat 684 494 709cling 678 clung 668 263 400ing 662 ung 659 230 317sling 671 slung 590 069 160sting 675 stung 637 069 230string 668 strung 600 069 194swing 687 swung 640 378 439wring 634 wrung 571 000 109hang 687 hung 643 398 564stick 690 stuck 653 263 522strike 690 struck 653 371 723dig 659 dug 650 207 469win 693 won 684 382 880blow 687 blew 687 256 687grow 681 grew 656 418 753know 693 knew 687 597 815throw 696 threw 678 385 712draw 700 drew 687 415 736y 696 ew 678 333 752see 671 saw 668 582 846take 690 took 684 605 944shake 684 shook 643 406 632bind 662 bound 631 179 395nd 665 found 696 559 906rise 675 rose 681 411 924write 693 wrote 681 519 850ride 684 rode 659 371 578stride 659 strode 650 239 393drive 684 drove 681 407 722fall 659 fell 687 447 917hold 687 held 693 483 841come 662 came 693 642 952eat 693 ate 696 283 578give 690 gave 693 565 900stand 700 stood 684 529 759go 696 went 696 623 920

66 ULLMAN

Regular verbs

Stem Regular Past Tense

Form Rating Form Rating FK Freq AP Freq

chop 671 chopped 687 069 313drop 687 dropped 690 434 813op 690 opped 659 194 329hop 687 hopped 684 179 368lop 684 lopped 646 069 069sop 668 sopped 643 000 000stop 693 stopped 659 464 762cross 684 crossed 681 329 620toss 693 tossed 687 313 537clap 690 clapped 687 160 391ap 687 apped 684 160 207lap 668 lapped 675 069 138slap 687 slapped 681 194 457jar 628 jarred 681 069 230mar 609 marred 671 000 329spar 634 sparred 650 000 256balk 665 balked 678 109 467stalk 643 stalked 668 194 329talk 693 talked 678 373 717walk 700 walked 668 496 735aim 700 aimed 687 239 557blame 700 blamed 675 179 736claim 687 claimed 696 325 826maim 656 maimed 675 000 160cram 696 crammed 690 000 194ram 656 rammed 678 138 471slam 678 slammed 665 263 564ask 675 asked 675 570 904bask 681 basked 671 069 333bore 637 bored 656 138 194gore 606 gored 600 000 160pore 556 pored 584 069 194soar 693 soared 671 138 608scour 656 scoured 671 000 333prowl 690 prowled 650 069 194scowl 656 scowled 665 160 000chase 675 chased 687 000 559race 690 raced 659 248 525trace 700 traced 693 109 451cook 637 cooked 662 109 363look 681 looked 637 579 763dash 675 dashed 668 160 407gnash 643 gnashed 637 000 000slash 700 slashed 681 194 465crush 696 crushed 696 109 530ush 684 ushed 675 069 179gush 693 gushed 681 179 294rush 696 rushed 684 304 620

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 67

APPENDIX 2 EXCLUDED STIMULIThe full questionnaires contained not only the 89 irregular and 48 regular past-tense formswhose ratings are analysed in this paper but the past-tense forms of an additional 335 verbs aswell These verbs comprised several categories which were omitted for a variety of reasons

1 There were 20 monosyllabic lsquolsquodoubletrsquorsquo verbs like divendashdovedived which take both anirregular and a regular past-tense form

2 There were 111 monosyllabic lsquolsquoinconsistent regularrsquorsquo verbs whose stems are phonolo-gically similar to the stems of irregular verbs (eg glidendashglided cf ridendashrode hidendashhid) Unlikelsquolsquoconsistent regularsrsquorsquo whose stems are phonologically dissimilar to the stems of regular verbsinconsistent regular verbs are predicted by a dual-system view to be memorised if they werenot people would utter forms like glid or glode which does not appear to occur They will bediscussed in a future paper

3 There were 120 prexed or other multisyllabic verbs (these 120 verbs do not include thethree past-tense forms forbid forbad forbade which are discussed below) 61 irregular ordoublets verbs (eg forgondashforwentforgoed interweavendashinterwoveinterweaved) 18 consistentregulars (eg devourndashdevoured overlook-overlooked) and 41 inconsistent regulars (egaccostndashaccostaccosted decidendashdeciddecided) These verbs were excluded from analysisbecause this study focuses on monosyllabic verbs

4 There were four past-tense forms which can take the role of auxiliary or modal (bendashwasbendashwere havendashhad dondashdid) These were treated separately because they may have a distinctlinguistic and psychological status (eg Stromswold 1990)

5 There were 11 irregular past-tense forms belonging to ve verbs with more than oneirregular past as determined by the authorrsquos dialect or by FK and AP frequency countsgreater than 0 for more than one of the irregular past-tense forms spitndashspitspat bidndashbidbadeforbidndashforbidforbadforbade drinkndashdrankdrunk and stinkndashstankstunk

6 There were 18 verbs which the author judged to be possible de-nominals de-adjectivalsor of onomatopoeic origin 8 consistent regulars (eg placendashplaced) and 10 inconsistentregulars (eg trustndashtrusttrusted) These forms were excluded because their computation maydiffer from that of forms not derived from another grammatical category (Kim PinkerPrince amp Prasada 1991)

7 There were four verbs whose stems or past-tense forms seemed to be easilyconfoundable with another word (eg with the consistent regular foundndashfounded the stemcan be confused with the irregular past tense found)

8 There were 18 no-change irregulars 13 irregulars (eg hitndashhit) and 5 doublets (eg wetndashwet) These were eliminated because their stem and past-tense forms can be confounded andbecause the FK and AP frequency counts may not have reliably distinguished betweenpresent and past-tense uses of these verbs

9 There were ve verbs whose irregular past-tense forms are marginally acceptable inAmerican English learnndashlearntlearned spellndashspeltspelled smellndashsmeltsmelled spoilndashspoiltspoiled and cleavendashcleftcleaved

10 There were seven verbs which were not originally classed as doublets but whose lowirregular ratings and high regular ratings suggested doublethood (eg smitendashsmotesmitedweavendashwoveweaved) They were classied neither as doublet nor as non-doublet irregulars

11 There were 11 verbs whose stems have a nal t or d and are thus similar to the stemsof many irregulars but were originally categorised as consistent regulars (eg chatndashchattedboastndashboasted shoutndashshouted) They were analysed neither as inconsistent regulars nor asconsistent regulars

12 There were six verbs with accidental errors in their presentation or apparent errors intheir frequency counts

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 65

Irregular verbs

Stem Irregular Past Tense

Form Rating Form Rating FK Freq AP Freq

wear 700 wore 690 418 668bear 646 bore 600 270 548break 665 broke 675 420 824choose 684 chose 681 363 703ring 681 rang 659 309 502sing 675 sang 653 336 661spring 675 sprang 606 263 424shrink 681 shrank 593 069 523sink 690 sank 615 294 653swim 690 swam 662 194 501run 696 ran 687 490 801sit 700 sat 684 494 709cling 678 clung 668 263 400ing 662 ung 659 230 317sling 671 slung 590 069 160sting 675 stung 637 069 230string 668 strung 600 069 194swing 687 swung 640 378 439wring 634 wrung 571 000 109hang 687 hung 643 398 564stick 690 stuck 653 263 522strike 690 struck 653 371 723dig 659 dug 650 207 469win 693 won 684 382 880blow 687 blew 687 256 687grow 681 grew 656 418 753know 693 knew 687 597 815throw 696 threw 678 385 712draw 700 drew 687 415 736y 696 ew 678 333 752see 671 saw 668 582 846take 690 took 684 605 944shake 684 shook 643 406 632bind 662 bound 631 179 395nd 665 found 696 559 906rise 675 rose 681 411 924write 693 wrote 681 519 850ride 684 rode 659 371 578stride 659 strode 650 239 393drive 684 drove 681 407 722fall 659 fell 687 447 917hold 687 held 693 483 841come 662 came 693 642 952eat 693 ate 696 283 578give 690 gave 693 565 900stand 700 stood 684 529 759go 696 went 696 623 920

66 ULLMAN

Regular verbs

Stem Regular Past Tense

Form Rating Form Rating FK Freq AP Freq

chop 671 chopped 687 069 313drop 687 dropped 690 434 813op 690 opped 659 194 329hop 687 hopped 684 179 368lop 684 lopped 646 069 069sop 668 sopped 643 000 000stop 693 stopped 659 464 762cross 684 crossed 681 329 620toss 693 tossed 687 313 537clap 690 clapped 687 160 391ap 687 apped 684 160 207lap 668 lapped 675 069 138slap 687 slapped 681 194 457jar 628 jarred 681 069 230mar 609 marred 671 000 329spar 634 sparred 650 000 256balk 665 balked 678 109 467stalk 643 stalked 668 194 329talk 693 talked 678 373 717walk 700 walked 668 496 735aim 700 aimed 687 239 557blame 700 blamed 675 179 736claim 687 claimed 696 325 826maim 656 maimed 675 000 160cram 696 crammed 690 000 194ram 656 rammed 678 138 471slam 678 slammed 665 263 564ask 675 asked 675 570 904bask 681 basked 671 069 333bore 637 bored 656 138 194gore 606 gored 600 000 160pore 556 pored 584 069 194soar 693 soared 671 138 608scour 656 scoured 671 000 333prowl 690 prowled 650 069 194scowl 656 scowled 665 160 000chase 675 chased 687 000 559race 690 raced 659 248 525trace 700 traced 693 109 451cook 637 cooked 662 109 363look 681 looked 637 579 763dash 675 dashed 668 160 407gnash 643 gnashed 637 000 000slash 700 slashed 681 194 465crush 696 crushed 696 109 530ush 684 ushed 675 069 179gush 693 gushed 681 179 294rush 696 rushed 684 304 620

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 67

APPENDIX 2 EXCLUDED STIMULIThe full questionnaires contained not only the 89 irregular and 48 regular past-tense formswhose ratings are analysed in this paper but the past-tense forms of an additional 335 verbs aswell These verbs comprised several categories which were omitted for a variety of reasons

1 There were 20 monosyllabic lsquolsquodoubletrsquorsquo verbs like divendashdovedived which take both anirregular and a regular past-tense form

2 There were 111 monosyllabic lsquolsquoinconsistent regularrsquorsquo verbs whose stems are phonolo-gically similar to the stems of irregular verbs (eg glidendashglided cf ridendashrode hidendashhid) Unlikelsquolsquoconsistent regularsrsquorsquo whose stems are phonologically dissimilar to the stems of regular verbsinconsistent regular verbs are predicted by a dual-system view to be memorised if they werenot people would utter forms like glid or glode which does not appear to occur They will bediscussed in a future paper

3 There were 120 prexed or other multisyllabic verbs (these 120 verbs do not include thethree past-tense forms forbid forbad forbade which are discussed below) 61 irregular ordoublets verbs (eg forgondashforwentforgoed interweavendashinterwoveinterweaved) 18 consistentregulars (eg devourndashdevoured overlook-overlooked) and 41 inconsistent regulars (egaccostndashaccostaccosted decidendashdeciddecided) These verbs were excluded from analysisbecause this study focuses on monosyllabic verbs

4 There were four past-tense forms which can take the role of auxiliary or modal (bendashwasbendashwere havendashhad dondashdid) These were treated separately because they may have a distinctlinguistic and psychological status (eg Stromswold 1990)

5 There were 11 irregular past-tense forms belonging to ve verbs with more than oneirregular past as determined by the authorrsquos dialect or by FK and AP frequency countsgreater than 0 for more than one of the irregular past-tense forms spitndashspitspat bidndashbidbadeforbidndashforbidforbadforbade drinkndashdrankdrunk and stinkndashstankstunk

6 There were 18 verbs which the author judged to be possible de-nominals de-adjectivalsor of onomatopoeic origin 8 consistent regulars (eg placendashplaced) and 10 inconsistentregulars (eg trustndashtrusttrusted) These forms were excluded because their computation maydiffer from that of forms not derived from another grammatical category (Kim PinkerPrince amp Prasada 1991)

7 There were four verbs whose stems or past-tense forms seemed to be easilyconfoundable with another word (eg with the consistent regular foundndashfounded the stemcan be confused with the irregular past tense found)

8 There were 18 no-change irregulars 13 irregulars (eg hitndashhit) and 5 doublets (eg wetndashwet) These were eliminated because their stem and past-tense forms can be confounded andbecause the FK and AP frequency counts may not have reliably distinguished betweenpresent and past-tense uses of these verbs

9 There were ve verbs whose irregular past-tense forms are marginally acceptable inAmerican English learnndashlearntlearned spellndashspeltspelled smellndashsmeltsmelled spoilndashspoiltspoiled and cleavendashcleftcleaved

10 There were seven verbs which were not originally classed as doublets but whose lowirregular ratings and high regular ratings suggested doublethood (eg smitendashsmotesmitedweavendashwoveweaved) They were classied neither as doublet nor as non-doublet irregulars

11 There were 11 verbs whose stems have a nal t or d and are thus similar to the stemsof many irregulars but were originally categorised as consistent regulars (eg chatndashchattedboastndashboasted shoutndashshouted) They were analysed neither as inconsistent regulars nor asconsistent regulars

12 There were six verbs with accidental errors in their presentation or apparent errors intheir frequency counts

66 ULLMAN

Regular verbs

Stem Regular Past Tense

Form Rating Form Rating FK Freq AP Freq

chop 671 chopped 687 069 313drop 687 dropped 690 434 813op 690 opped 659 194 329hop 687 hopped 684 179 368lop 684 lopped 646 069 069sop 668 sopped 643 000 000stop 693 stopped 659 464 762cross 684 crossed 681 329 620toss 693 tossed 687 313 537clap 690 clapped 687 160 391ap 687 apped 684 160 207lap 668 lapped 675 069 138slap 687 slapped 681 194 457jar 628 jarred 681 069 230mar 609 marred 671 000 329spar 634 sparred 650 000 256balk 665 balked 678 109 467stalk 643 stalked 668 194 329talk 693 talked 678 373 717walk 700 walked 668 496 735aim 700 aimed 687 239 557blame 700 blamed 675 179 736claim 687 claimed 696 325 826maim 656 maimed 675 000 160cram 696 crammed 690 000 194ram 656 rammed 678 138 471slam 678 slammed 665 263 564ask 675 asked 675 570 904bask 681 basked 671 069 333bore 637 bored 656 138 194gore 606 gored 600 000 160pore 556 pored 584 069 194soar 693 soared 671 138 608scour 656 scoured 671 000 333prowl 690 prowled 650 069 194scowl 656 scowled 665 160 000chase 675 chased 687 000 559race 690 raced 659 248 525trace 700 traced 693 109 451cook 637 cooked 662 109 363look 681 looked 637 579 763dash 675 dashed 668 160 407gnash 643 gnashed 637 000 000slash 700 slashed 681 194 465crush 696 crushed 696 109 530ush 684 ushed 675 069 179gush 693 gushed 681 179 294rush 696 rushed 684 304 620

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 67

APPENDIX 2 EXCLUDED STIMULIThe full questionnaires contained not only the 89 irregular and 48 regular past-tense formswhose ratings are analysed in this paper but the past-tense forms of an additional 335 verbs aswell These verbs comprised several categories which were omitted for a variety of reasons

1 There were 20 monosyllabic lsquolsquodoubletrsquorsquo verbs like divendashdovedived which take both anirregular and a regular past-tense form

2 There were 111 monosyllabic lsquolsquoinconsistent regularrsquorsquo verbs whose stems are phonolo-gically similar to the stems of irregular verbs (eg glidendashglided cf ridendashrode hidendashhid) Unlikelsquolsquoconsistent regularsrsquorsquo whose stems are phonologically dissimilar to the stems of regular verbsinconsistent regular verbs are predicted by a dual-system view to be memorised if they werenot people would utter forms like glid or glode which does not appear to occur They will bediscussed in a future paper

3 There were 120 prexed or other multisyllabic verbs (these 120 verbs do not include thethree past-tense forms forbid forbad forbade which are discussed below) 61 irregular ordoublets verbs (eg forgondashforwentforgoed interweavendashinterwoveinterweaved) 18 consistentregulars (eg devourndashdevoured overlook-overlooked) and 41 inconsistent regulars (egaccostndashaccostaccosted decidendashdeciddecided) These verbs were excluded from analysisbecause this study focuses on monosyllabic verbs

4 There were four past-tense forms which can take the role of auxiliary or modal (bendashwasbendashwere havendashhad dondashdid) These were treated separately because they may have a distinctlinguistic and psychological status (eg Stromswold 1990)

5 There were 11 irregular past-tense forms belonging to ve verbs with more than oneirregular past as determined by the authorrsquos dialect or by FK and AP frequency countsgreater than 0 for more than one of the irregular past-tense forms spitndashspitspat bidndashbidbadeforbidndashforbidforbadforbade drinkndashdrankdrunk and stinkndashstankstunk

6 There were 18 verbs which the author judged to be possible de-nominals de-adjectivalsor of onomatopoeic origin 8 consistent regulars (eg placendashplaced) and 10 inconsistentregulars (eg trustndashtrusttrusted) These forms were excluded because their computation maydiffer from that of forms not derived from another grammatical category (Kim PinkerPrince amp Prasada 1991)

7 There were four verbs whose stems or past-tense forms seemed to be easilyconfoundable with another word (eg with the consistent regular foundndashfounded the stemcan be confused with the irregular past tense found)

8 There were 18 no-change irregulars 13 irregulars (eg hitndashhit) and 5 doublets (eg wetndashwet) These were eliminated because their stem and past-tense forms can be confounded andbecause the FK and AP frequency counts may not have reliably distinguished betweenpresent and past-tense uses of these verbs

9 There were ve verbs whose irregular past-tense forms are marginally acceptable inAmerican English learnndashlearntlearned spellndashspeltspelled smellndashsmeltsmelled spoilndashspoiltspoiled and cleavendashcleftcleaved

10 There were seven verbs which were not originally classed as doublets but whose lowirregular ratings and high regular ratings suggested doublethood (eg smitendashsmotesmitedweavendashwoveweaved) They were classied neither as doublet nor as non-doublet irregulars

11 There were 11 verbs whose stems have a nal t or d and are thus similar to the stemsof many irregulars but were originally categorised as consistent regulars (eg chatndashchattedboastndashboasted shoutndashshouted) They were analysed neither as inconsistent regulars nor asconsistent regulars

12 There were six verbs with accidental errors in their presentation or apparent errors intheir frequency counts

PAST-TENSE FREQUENCY AND NEIGHBOURHOOD EFFECTS 67

APPENDIX 2 EXCLUDED STIMULIThe full questionnaires contained not only the 89 irregular and 48 regular past-tense formswhose ratings are analysed in this paper but the past-tense forms of an additional 335 verbs aswell These verbs comprised several categories which were omitted for a variety of reasons

1 There were 20 monosyllabic lsquolsquodoubletrsquorsquo verbs like divendashdovedived which take both anirregular and a regular past-tense form

2 There were 111 monosyllabic lsquolsquoinconsistent regularrsquorsquo verbs whose stems are phonolo-gically similar to the stems of irregular verbs (eg glidendashglided cf ridendashrode hidendashhid) Unlikelsquolsquoconsistent regularsrsquorsquo whose stems are phonologically dissimilar to the stems of regular verbsinconsistent regular verbs are predicted by a dual-system view to be memorised if they werenot people would utter forms like glid or glode which does not appear to occur They will bediscussed in a future paper

3 There were 120 prexed or other multisyllabic verbs (these 120 verbs do not include thethree past-tense forms forbid forbad forbade which are discussed below) 61 irregular ordoublets verbs (eg forgondashforwentforgoed interweavendashinterwoveinterweaved) 18 consistentregulars (eg devourndashdevoured overlook-overlooked) and 41 inconsistent regulars (egaccostndashaccostaccosted decidendashdeciddecided) These verbs were excluded from analysisbecause this study focuses on monosyllabic verbs

4 There were four past-tense forms which can take the role of auxiliary or modal (bendashwasbendashwere havendashhad dondashdid) These were treated separately because they may have a distinctlinguistic and psychological status (eg Stromswold 1990)

5 There were 11 irregular past-tense forms belonging to ve verbs with more than oneirregular past as determined by the authorrsquos dialect or by FK and AP frequency countsgreater than 0 for more than one of the irregular past-tense forms spitndashspitspat bidndashbidbadeforbidndashforbidforbadforbade drinkndashdrankdrunk and stinkndashstankstunk

6 There were 18 verbs which the author judged to be possible de-nominals de-adjectivalsor of onomatopoeic origin 8 consistent regulars (eg placendashplaced) and 10 inconsistentregulars (eg trustndashtrusttrusted) These forms were excluded because their computation maydiffer from that of forms not derived from another grammatical category (Kim PinkerPrince amp Prasada 1991)

7 There were four verbs whose stems or past-tense forms seemed to be easilyconfoundable with another word (eg with the consistent regular foundndashfounded the stemcan be confused with the irregular past tense found)

8 There were 18 no-change irregulars 13 irregulars (eg hitndashhit) and 5 doublets (eg wetndashwet) These were eliminated because their stem and past-tense forms can be confounded andbecause the FK and AP frequency counts may not have reliably distinguished betweenpresent and past-tense uses of these verbs

9 There were ve verbs whose irregular past-tense forms are marginally acceptable inAmerican English learnndashlearntlearned spellndashspeltspelled smellndashsmeltsmelled spoilndashspoiltspoiled and cleavendashcleftcleaved

10 There were seven verbs which were not originally classed as doublets but whose lowirregular ratings and high regular ratings suggested doublethood (eg smitendashsmotesmitedweavendashwoveweaved) They were classied neither as doublet nor as non-doublet irregulars

11 There were 11 verbs whose stems have a nal t or d and are thus similar to the stemsof many irregulars but were originally categorised as consistent regulars (eg chatndashchattedboastndashboasted shoutndashshouted) They were analysed neither as inconsistent regulars nor asconsistent regulars

12 There were six verbs with accidental errors in their presentation or apparent errors intheir frequency counts