Paradigm Function Morphology

1 Introduction

In realization-based morphologies inflectional affixes are not classical morphemes, that is, lex-ical entries which contribute a meaning of their own. Realizational models take as their start-ing point the full set of features or morphosyntactic properties which characterize a cell in theparadigm of a lexeme, and then provide a set of instructions for constructing or accepting theword form which occupies that cell, and which hence realizes those morphosyntactic proper-ties. In Paradigm Function Morphology this is achieved by means of the paradigm functionfor the language. Stump (2001:32) characterizes the paradigm function as “... a function which,when applied to the root of a lexeme L paired with a set of morphosyntactic properties appro-priate to L, determines the word form occupying the corresponding cell in L’s paradigm.” Theparadigm function itself is defined by a set of realization rules, which determine the way thatspecific morphosyntactic properties are realized by stem selection, affixation and so on.

2 Brief overview of PFM

2.1 Realization rules

In PFM inflected forms are derived by the successive application of blocks of realization rules.IN the most straightforward instances, each rule introduces an affix, triggered by some setof feature specifications. The order in which the rule blocks apply corresponds to the linearorder of affixation. A simple example will illustrate. The Finnish noun form talo-i-ssa-ni ‘in myhouses’ consists of the root talo, followed by plural number, inessive case and 1SG possessoraffixes. These can be introduced by the rules shown in (1)1:

(1) a. RRI, {NUM:plural}, N(< X,σ>) = < X,σ>

b. RRII, {CASE:iness}, N(< X,σ>) = < Xssa,σ>

c. RRIII, {POSS:1sg}, N(< X,σ>) = < Xni,σ>

Formally speaking these rules are functions which map an ordered pair consisting of set offeatures, σ, and a form to another ordered pair consisting of a (possibly distinct) form and thesame set of features. The feature set σ is a complete characterization of the feature content ofthe cell in the paradigm, in this case the plural inessive 1sg possessed form. The ‘X’ representsthe output of the previous block of rules. For the first block it represents the stem dictated bythat particular feature set. By default, ‘X’ denotes the root of the lexeme, in this case talo.

The subscripts on the rule name ‘RR’ denote successively (i) the rule block in which the ruleapplies, (ii) the set of morphosyntactic properties (feature values) the rule realizes (which wecan refer to as τ) and (iii) the class of lexemes to which the rule applies, for example ‘verbs’ or‘Class IIIa nouns’. The convention for determining whether a given realization rule can applyis this: we inspect the subscripted feature set τ. If τ is a subset of the complete feature set σ and

1Stump uses the abbreviation ‘RR’ for ‘realization rule’, noting that he used ‘RR’ in earlier works to mean ‘rule of referral’.A slightly more perspicuous notation for PFM is developed inAckerman and Stump (2004).

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the lexeme is of the appropriate class then the rule can apply in that block. The complete fea-ture set σ is repeated on the right hand side of the realization for essentially technical reasons.For most purposes, however, the repeated feature set in the output can be ignored.

The nominative singular unpossessed form of ‘house’ is just the root, talo. In a strict morph-eme based theory this would require a string of zero morphemes meaning respectively ‘singu-lar’, ‘nominative’ and ‘unpossessed’. This, however, completely fails to capture the intuitionthat in Finnish nouns the root form is the default form, used to express default meanings. Ina paradigm-based theory the grammar contains a set of features and their permissible values.This will include the specifications [NUM:sg], [CASE:nom] and [POSSESSOR:none]. Hence, anyFinnish noun is necessarily associated with a cell labelled ‘nominative singular unpossessed’,which must be filled by some appropriate expression (provided the paradigm is not defect-ive). The PFM model appeals to an important principle, that of the Identity Function Default.An identify function is a function, f , which applies to some value, x, and delivers the sameelement: f (x) = x. In PFM it is assumed that in any block of realization rules there is onerealization rule which has exactly the format of the identity function. This is a realization rulewhich takes any feature set for any category and maps X to X, as shown in (2):

(2) Identity Function Default

RRn,{any},any(<X,σ>) = <X,σ>

For Stump, this is a universal default which applies in any rule block where no explicit rulehas applied. In the case of the word form talo ‘house’, we would find that Finnish grammarlacks specific realization rules in Blocks I, II, II for [NUM:sg], [CASE:nom] and [POSSESSOR:none]respectively, and so the Identity Function Default would apply. Since no special form of theroot is required the form talo serves as the ‘X’ in the rule set and this is the output of BlockI. This form then serves as the input to the Block II realization rules, where again there is noFinnish-specific rule to apply and the Identity Function Default is invoked. Similarly, talo isthe output of Block III.

In the specification of the form talo-ssa-ni‘in my house’, where the property ‘singular’ re-ceives no overt realization, the Identity Function Default applies in Block I and the two overtaffixation rules apply in Blocks II, III. In the specification of the unpossessed form talo-i-ssa‘in(the) houses’, the Identity Function Default would apply solely in Block III.

The Identity Function Default is formalized as the most general rule imaginable: ‘for anyset of features, X = X’. Other things being equal, the Identity Function Default would guaranteethat no word would ever be overtly inflected. Where we have an explicit realization rule, suchas that for [NUM:pl], however, the default is pre-empted by the more specific or narrow rule.This illustrates another important feature of PFM. Rule block organization is governed by aprinciple known under various names but referred to by Stump as ‘Pan. inian Determinism’:2

where two rules are in competition the narrowest applicable rule applies. For instance, imaginethat OX is the only noun in English with an irregular plural. Then, we can state plural formationby saying ‘(i) for OX the plural is oxen, (ii) for any noun with root X the plural is X-z’. WithoutPan. inian Determinism the regular plural rule (ii) would derive *oxes but this application ispre-empted by the more specific rule (i). The fact that rules (i) and (ii) are in paradigmaticopposition within the same block is captured by Pan. inian Determinism.

In models such as PFM, which are based on the logic of default inheritance and in whichthe whole grammar can be thought of as a set of nested defaults, Pan. inian Determinism is

2The reference, of course, is to the great Sanskrit grammarian, P an. in ı, whose grammatical description of Vedic Sanskrit,the As.t. adhy ay ı or ‘Eight Books’ is widely regarded as the first, as well as being one of the greatest works in formal linguistics.P an. in ı’s grammar makes crucial use of the default logic deployed in PFM and other inferential models of linguistics.

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the principal organizing factor. For example, consider the Finnish nominative plural formtalot ‘houses’. This has an unexpected (and unique) desinence -t, signalling simultaneouslythe properties ‘nominative’ and ‘plural’, what is sometimes known as cumulation. Classicalmorpheme theory has problems with cumulation and other deviations from a strict one-onerelationship between form and content. Is -t the nominative case ending used with the pluralor is it the plural ending used in conjunction with the nominative case ending? In other words,is the form ‘really’ (3a) or (3b)?

(3) a. talohouse

∅

pl

tnom

b. talohouse

tpl

∅

nom

In the case of (3a) we would have to explain how the grammar ‘knows’ that the exceptionalzero plural marker has to be selected, while in the case of (3b) it would have to ‘know’ how theexceptional -t plural marker was selected. In each case we would have sensitivity to an ‘outer’affix. In point of fact, a strict morphemic approach would probably have to opt for the analysisin (3b), because if (a) were adopted it is unclear what would prevent the regular plural affix ifrom being inserted to give the ungrammatical *talo-i-t. In addition, the analysis in (3b) wouldbe regarded as a little more elegant because it would only require one exceptional allomorph,for the plural. Nonetheless, the technical problems with such an example remain: assumingthe analysis in (3b) some way has to be found to ensure that the regular plural suffix is notaccepted: *talo-i-Ø and some way has to be found to ensure that case suffixes other than thenominative suffix Ø are not suffixed to the -t form: *talo-t-ssa etc.3

Even more problematic are cases in which the two affix positions are separated by otheraffixes. Stump (2001: 162f) exemplifies precisely that situation with the Swahili past negat-ive. The normal past tense prefix in Swahili is li and the normal negative prefix is ha. Insimple cases the order of prefixes is ha-SUBJECT.MARKER-TENSE-VERB.ROOT. However, just inthe past tense there is a special prefix found when the verb is in the negative form: ku. Thus,a negative past tense verb has the form ha-SUBJECT.MARKER-ku-VERB.ROOT . Clearly, meas-ures have to be taken on a strictly morpheme-based theory to ensure that the incorrect string*ha-SUBJECT.MARKER-li-VERB.ROOT isn’t accepted as a grammatical word form.

In PFM this Finnish example could be handled very simply by adding a rule to the Block Irule set to accommodate the unexpected nominative plural form, as in (4):

(4) a. RRI, {NUM:pl, CASE:Nom},N(<X,σ>) = <Xt,σ>

b. RRI, {NUM:pl},N(<X,σ>) = <Xi,σ>

Rule (4a) expresses cumulation by allowing one affix to be the realization of two featurespecifications. (Extended exponence occurs when a single feature specification is mentioned

3Roark and Sproat (2007), referring to class notes of mine taken from my website, are surprised by my arguments here.They claim that analysis (3b) is clearly correct and, moreover, that this causes no problems to a morpheme-based account.All we need to say is that the zero nominative morpheme is marked to select thet-allomorph of the plural morpheme|i| (inother words, we need to add a statement of the form “if the leftadjacent affix is thenum:plural morpheme then it must bethe t allomorph”. However, this presupposes some kind of theory of (inwards) allomorph selection. Specifically, some waymust still be found in the classical approach of preventing the default forms from being wrongly selected, here,*taloi for thenominative plural, and to ensure that the non-default plural allomorph is incompatible with the other cases. In the classicalapproach, before the advent of formal or generative ways of thinking, these matters were not made explicit. As Roark andSproat would have learnt had they attended the relevant lectures, making such assumptions explicit will often lead to preciselythe kind of realizational model proposed by Stump and others. This discussion illustrates the importance of the advice we giveto our undergraduate students about the dangers of surfing websites and quoting their contents without checking the precisecontext.

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in rules from two distinct rule blocks). Note that both rules (4a) and (4b) could in principleapply to a form bearing the feature set [NUM:Pl], [CASE:Nom]. However, rule (4a) pre-emptsrule (4b) because it is the more specific. Another way of putting this is to say that rule (4b)subsumes rule (4b). Moreover, this fact can be readily computed by simple feature counting: arule A is more specific than rule B if its feature set properly contains that of rule B. Thus, wesee how Pan. inian Determinism captures the idea of disjunctive sets of affixes within a singleposition class (in structuralist terms, paradigmatic organization as opposed to syntagmaticorganization).

An alternative solution to the Finnish nominative plural problem would be to say thatthere was a single portmanteau suffix which simultaneously realizes the properties ‘plural’and ‘nominative’, as shown in (3c):

(3) c. talohouse

tpl.nom

This, indeed, is the kind of solution often proposed for such data in the classical approach.However, it’s important to realize that a solution of this sort is represents an important weak-ening of the principles of the classical morphemic approach. The portmanteau type of solutionoften has much to recommend it and we will see below in §3.2 how such an analysis is codedin PFM.

One could imagine a language in which every affix was distinct from every other and everyfeature specification was found just once, associated with a single rule in a single rule block. Alanguage which exhibited such ‘rule block coherence’ would be a perfectly agglutinating lan-guage. However, there are no known languages with this property and all the logically pos-sible deviations from the canonical one-one mapping are common. A particularly widespreaddeviation is underdetermination, when a set of morphosyntactic feature values receives noovert expression in the inflected word form. In classical morphemics this is handled by pos-tulating zero morphemes. Thus, on a strict morpheme-based analysis the Finnish word formtalo ‘house-nominative-singular-unpossessed’ would receive the analysis talo-∅-∅-∅. However,in the great majority of cases where such zero morphemes appear to be needed, the zero ex-presses the default feature specification for that block and is therefore handled in PFM by theIdentity Function Default.

Occasionally, we find genuinely ‘significative’ zeros. An instance is provided by the aoristtense forms of Bulgarian verbs. This is signalled by a suffix o: krad-o-x ‘I stole’, krad-o-xme‘we stole’, igra-o-x, ‘I played’, igra-o-xte ‘you (pl.) played’, dava-o-xme ‘we gave’ dava-o-xa ‘theygave’. However, in the 3sg forms the o is ellided before the 3sg agreement suffix e: krade ‘s/hestole’, igra-e ‘s/he played’, dava-e ‘s/he gave’. Stump (2001: 45) overrides the o-suffixation rulein the first suffix block with a rule of the form shown in (5):

(5) RRI, {TNS:Aor, AGR:3sg},V(<X,σ>) =def <X,σ>

Again, it is not that we add a zero here, rather rule (5) stipulates that no affixation occurs eventhough this is not the default situation for this property.

Finally, none of the affixes is a lexical entry with its own meaning. An inflectional affix issimply a marker providing (partial) information about the set of feature specifications associ-ated with the cell in the paradigm occupied by the completed word form.

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2.2 Paradigm functions

Stump (2001: 43) gives (6) as the general characterization of the paradigm function:

(6) PF(<X,σ>) = <Y,σ>

Thus, the paradigm function for Finnish applied to the lexeme HOUSE, root talo to specify theinessive singular non-possessed form talossa ‘in the house’ would be (7):

(7) PF(<talo, { NUM:sg, CASE:iness, POSS:no}>) = <talossa, {NUM:sg, CASE:iness, POSS:no}>

What this function does is to take a lexeme’s root paired with a complete set of features re-quired to fully specify a cell in the paradigm and it delivers a pairing of that cell’s features to-gether with the inflected word form that occupies that cell. In other words, the right hand sideof the function enumerates a paradigm in the sense of ‘form-property paradigm’ as defined inChapter ??.

Where a word form is defined by the successive application of rule blocks the order ofapplication is part of the definition of the paradigm function. Assuming three rule blocksfor Finnish the paradigm function in (7) can therefore be thought of as a concrete instanti-ation of the paradigm function shown in (8), where X is the root of any (nominal) lexeme andσ = {NUM:α, CASE:β, POSS:γ}:

(8) PF(<X, σ>) = RRIII (RRII (RRI(<X, σ>)

The paradigm function is defined over the root of the lexeme, and instructs us how to formcompleted words from that root. In effect, the root form of the word is being used as an indexfor the lexeme of which it is a root. This leads to immediate problems, of course, wherever wehave root homophony. Stump (2001: 43) allows for this by assuming that each root carries alexemic index (‘L-index’). In order to reflect the fact that an inflected form remains a form ofone and the same lexeme, Stump adds principle (9), the ‘persistence of L-indexing’:

(9) For any realization rule, RR(<X,σ>) = <Y,σ>, L-index(Y) = L-index(X)

3 Affix ordering

3.1 Three types of deviation

Affixes do not always line up in the way expected and there are several sets of deviations fromthe agglutinative ideal presupposed in classical structuralist morphotactics. There are threemain types of deviation. First, a given affix may appear to straddle a sequence of slots, thatis, it may appear to belong simultaneously to a sequence of two or more consecutive slots(‘portmanteau position classes’). Second, we may find that one and the same set of affixes mayappear in distinct positions depending on their grammatical function. A common situation isfor a single set of pronominal affixes to be found in different positions when realizing subject,respectively object agreement features. This is the problem of ‘parallel position classes’. Third,we may find that the relative ordering of affixes changes depending on the exact set of featuresassociated with a word form. Again, subject/object markers provide a common scenario, andwe may find that a set of markers (not necessarily parallel) may occur in one order when real-izing one feature set and the opposite order when realizing a different feature set (‘reversibleposition classes’).

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3.2 Portmanteau position classes

Portmanteau position classes are handled in PFM by portmanteau rule blocks. To describesuch phenomena we suspend the assumption that the blocks of rules are necessarily appliedsequentially. We can illustrate this situation by returning to the problem of the Finnish nom-inative plural. An alternative analysis of the Finnish case can be given if we suppose that thet nominative plural suffix occupies not Slot I, but Slots I, II simultaneously. In PFM we wouldthen posit a realization rule defined over the sequence of slots, notated by the composed blockindex [II,I] as shown in (10):

(10) RR[II,I] {NUM:pl, CASE:nom},N(<X,σ>) = <Xt,σ>

In effect, the rule (10) is outside the rule block system of Finnish inflection, in that rule (10) isin paradigmatic opposition simultaneously with the rules of Block I and of Block II.

In order to ensure that rule (10) can apply, we have to ensure that the paradigm functionfor Finnish nouns can be realized by such a rule. This means that we must revise the paradigmfunction shown in (8), as in (11):

(11) Revised paradigm function for Finnish nouns

Where σ = {NUM:α, CASE:β, POSS:γ}

PF(<X,σ>) =def RR[II,I] (RRI(<X, σ>))

But now we must ensure that the standard Block I, II rules can realize the paradigm function.Therefore, Stump (2001: 142) introduces the Function Composition Default (FCD):

(12) RR[n,m] (<X,σ>) =def RRn(RRm(<X,σ>))

The composed rule (10) will always be more specific than any individual rule in Block I, II, sothat (10) will pre-empt the default plural rule and any other case rule. Where σ is other thannominative plural, the FCD, (12), applies and the normal realization rule sequence is calledinto play.

3.3 Parallel position classes

Parallel blocks occur when the same set of affixes occupy different position classes in orderto express slightly different functions, as when identical subject and object markers occupydifferent positions depending on the function. For the sake of exposition let us consider anidealized Bantu language whose verbs inflect according to the schema in (13) (where ‘SM/OM’mean ‘Subject/Object Marker’ respectively and ‘TAM’ means ‘Tense/Aspect/Mood Marker’):

(13) Bantu prefixes

SM TAM OM Verb stem

III II I 0

Suppose further that the SM, OM cross-reference person and number and are identical in form.If we write independent realization rules for Slots I, III then we would effectively be stating sixidentical rules twice, but with different rule block indices, thus missing a clear generalizationabout the language. Stump therefore modifies the rule block model by permitting realization

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rules which effectively have no block index (Stump 2001: 147). The rules of Block I, III areconflated as ‘Block Agr’. When the paradigm function comes to evaluate a feature set in BlockI, III it is referred to the corresponding realization rule in Block Agr.4 If there is an incompleteoverlap between SM and OM (as in Lingala) then Blocks I, III will contain their own specificrules which will pre-empt the Block Agr rules because they will make reference specifically tosubject or object agreement.

3.4 Reversible position classes

Reversible rule blocks are found when we have cases of affixal metathesis. Stump (2001: 149f)discusses cases from Fula subject/object agreement and Stump (1993) discusses similar phe-nomena in Swahili. In Fula in certain tense forms the default affix order is Verb stem SM OM.However, for certain person/number combinations we find the opposite order. This can beseen from the forms shown in (14) (cf Stump 2001: 151):

(14) a. máall-u-Pon-mo

help-past-2pl-3sg

‘you(pl) helped him’V-SM-OM

b. máall-u-mi-Pe

help-past-1sg-3pl

‘I helped them’V-SM-OM

c. máall-u-moo-mi

help-past-3sg-1sg

‘I helped him’V-OM-SM

The order of application of realization rules is defined as part of the paradigm function (gen-erally using iconically labelled block indices such as ‘I, II, III, . . . ’ or ‘A, B, C, . . . ’). In Stump’sanalysis of the Fula verb the SM, OM slots are labelled III, IV. He therefore sets up realiz-ation rules for SM in Block III and rules for OM in Block IV, but adds a portmanteau ruleblock [IV,III]. By the FCD, (12), this is normally realized by the sequence of realization rulesRRIV (RRIII (. . . ))) to give the order V-SM-OM. However, for certain feature combinations theFCD is pre-empted by rule (15) (adapted from Stump 2001: 154):

(15) Where σ = {certain feature combinations}

RR[IV,III], σ,V(<X,σ>) =def RRIII (RRIV (<X,σ>))

4 Rules of referral

We often find that forms occupying cells in one part of a paradigm are systematically identicalto those of other cells. This is inflectional homonymy or syncretism. This arises for a vari-ety of reasons, as detailed minutely, and with a wealth of examples in Baerman et al. (2005).

4Technically the way this is achieved is by means of a rule of referral, discussed below in §4.

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In some cases it’s not actually appropriate to think in terms of homonymy at all. For in-stance, in Russian there are three genders, masculine, feminine, neuter, but this distinctionis completely neutralized for all nominals in the plural. The simplest (i.e. best) way of de-scribing this is to define a dependency between gender and number, such that the plural sub-paradigm simply doesn’t make any gender distinctions, i.e. the property ‘gender’ is undefinedfor [NUMBER:plural]. Alternatively, and perhaps equivalently, we can think of plural numberas a kind of fourth gender. In other cases the homonymy can be explained in terms of an un-derspecification of properties For instance, in Latin it is clearly necessary to distinguish fivecase forms, including the dative and the ablative. However, there are no nominals (nouns,adjectives, pronouns or whatever) that distinguish the dative and ablative case in the plural.One possible way of describing this situation is to set up a special ‘dative/ablative’ case whichsplits into dative and ablative in the singular but remains one case in the plural, fulfilling allthe morphosyntactic functions of both the dative and ablative. A number of other situationsare discussed by Baerman et al., together with the various logically possible ways of analysingthem.

There is one set of syncretisms, however, that are of importance for paradigm-based real-izational models. These are instances in which two featurally distinct cells are associated sys-tematically with exactly the same forms but in which one of those form∼feature pairings can(or must) be taken as prior, and the other form∼feature pairing defined as being identical tothe first. A rule which encapsulates such an equivalence statement is a rule of referral (Zwicky,1985). Stump provides an interesting case from Bulgarian (and Macedonian) conjugation. Bul-garian has one present and two past tenses, aorist and imperfect. Verb endings consist of atheme vowel, a tense marker and an agreement marker, however there is no simple corres-pondence between form and function: the 3sg aorist of RABOTJA ‘work’ is rabot-i while the 3sgimperfect of IMAM ‘have’ is im-a-se. Nonetheless, there is an exceptionless generalization inthe conjugation system: for any verb, including even the highly irregular verb BE, the 2sg aor-ist/imperfect forms are identical to the corresponding 3sg aorist/imperfective forms. Stumpargues that this syncretism should be expressed by means of a rule of referral, taking the 3sgforms as the basic ones and referring the 2sg forms to the 3sg in either of the two past tenses.

In PFM a rule of referral for such a syncretism is defined by referring each realization rulefor 2sg forms to the corresponding realization rule for 3sg forms on a block-by-block (effect-ively, affix-by-affix) basis. In principle, it would be possible to refer the entire word formexpressing 2sg features to the entire word form expressing 3sg features, but Stump argues (p.217f) that there are instances in which only some of the affixes of a form need to be subject to areferral. He therefore treats all referrals as block-by-block referrals, with whole-word syncret-ism being simply the limiting case in which all rule blocks are subject to the syncretism. For theBulgarian example, Stump (2001:55f) proposes a rule which in prose states the following: letτ be a feature set containing the features {TENSE:past,AGR:2sg}; let n be any of the rule blocksneeded for describing Bulgarian conjugation. Then, for any realization rule RRn,τ,V(<X,σ>)= <Y,σ> serving to (partially) realize the features {TENSE:past, AGR:2sg}, apply instead thecorresponding rule with AGR:3sg substituted for AGR:2sg.

5 Allomorphy in PFM: morphological metageneralizations

The formulation of realization rules given thus far would be sufficient for purely concatenativemorphology. However, there are instances of inflection in which some kind of morphophon-ological process applies to a stem in addition to or instead of affixation. An affixation processitself may involve more than just concatenation and may trigger such processes as haplologyor other types of truncation. In addition, we may find that the affix is an infix. Other processes

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include ablaut, stress/tone/accent shift, consonant mutation, truncation and, very commonly,reduplication.

Many of these effects would normally be subsumed under the operation of the morpholo-gical metageneralizations argued for by Stump (2001: 47f). These metageneralizations capturethe traditional intuition that a morphophonological (non-automatic) alternation might be apart of the morphological process itself. Stump generalizes the format of the realization rule toaccommodate morphophonological alternations. Suppose a realization rule introduces a suf-fix, Z, so that we have RRn,τ,C(< X,σ>) = < XZ,σ>. If we designate the output XZ as Y, then thegeneralized realization rule takes the form RRn,τ,C(< X,σ>) = < Y′,σ>. The expression Y′ de-faults to Y (i.e. XZ), but for certain rules in certain rule blocks Y′ might be some phonologicalalternant of Y. For instance, Y′ might be X′Z, where X′ is a palatalized variant of X. This altern-ation would be captured by means of a morphophonological redundancy rule with roughlythe form of (16):

(16) Where RRn,τ,C(< X,σ>) = < Y′,σ>, if X = WC, where C is a palatalizable consonantwhose palatalized alternant is C′, and Y = WCZ, then Y′ = WC′Z

In prose, (16) states that result of affixing Z to X is to palatalize C, the last consonant of X, C′.

Stump (2001: 47) proposes that “. . . for each realization rule R, there is an unordered set ΦR

of morphophonological rules constraining the evaluation of R in any instance of its applica-tion.” If the palatalization rule is the only morphophonological rule relevant to applicationsof R, then Stump would assume a morphological metageneralization of the form “Morpho-phonological rule (16) applies to realization rule R”. In some cases a morphophonological rulewould be applicable to just one realization rule, capturing the idea that a single affix triggersthat alternation, while in other cases every rule in a given block might be subject to the meta-generalization. Since a single block often realizes values of a single morphosyntactic category(such as ‘non-past tense’ or ‘subjunctive mood’), this would capture the idea that the morpho-phonological alternation is a partial exponent of that property. To varying degrees it is possiblefor the morphophonological rules to capture phonological invariants. For instance, if all andonly front vowel initial suffixes trigger a class of palatalizations this fact can be written intothe rule. On the other hand, if a language has completely regular [ATR] harmony, such that anaffix with a [+ATR] vowel causes all [−ATR] vowels elsewhere in the word to become [+ATR],this can in principle be handled by underspecifying the [−ATR] vowels for the harmonic fea-ture and by assuming a default rule which specifies all vowels underspecified for [ATR] afterthe application of all realization rules and morphophonological rules as [−ATR]5.

6 Stems in PFM

In this section I briefly summarize the role of stems in PFM. The stem notion will be discussedin more detail in Chapter ??.

Following Aronoff (1992, 1994) Stump argues for the importance of stems and stem selec-tion. Stems may be listed lexically for a lexeme or they may be the result of a completelygeneral word formation rule. For instance, in Romance languages we find that the verb inthe default conjugation has a root but most inflected forms are built on a stem formed from theroot together with a theme vowel (e.g. Latin amo ‘love’ root am-, stem ama:-). There is no needto assume that the theme vowel has any meaning or featural content. Indeed, Aronoff argues

5For arguments that the morphological metageneralizationsmodel is superior to the rather similar system of co-phonologiesproposed by Inkelas and Orgun (1998), see Stump (1998).

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that there are cases in which it would be entirely wrong to assume that a stem form expressed ameaning. He discusses the Latin ‘third stem’, illustrated by the form ama:t(um). The stem formama:t- is the basis for the passive perfective participle ama:tus ‘(having been) loved’, as wellas the supine form ama:tum. However, the third stem is itself the basis for the active voice fu-ture participle ama:tu:r(us) ’about to love’. Aronoff outlines a variety of other formations frominflection and derivation which also appeal to this stem form. He points out that we knowthat we are dealing with a specific stem form because many verbs have an irregular third stembut this behaves in exactly the same way as the regular forms. For instance, the verb FERO ‘Icarry’ has a suppletive third stem la:t- which forms both the passive perfective and the activefuture participles: la:tus ‘carried’ and la:tu:rus ’about to carry’. Aronoff concludes from suchcases that the Latin third stem is just a form devoid of any feature content or meaning overand beyond the lexical meaning associated with the lexeme itself. He argues that morphologyhas to be couched in terms of processes and representations that appeal just to forms and notto meanings. Such asemantic processes and representations he calls ‘morphomes’. Thus, theLatin third stem is an example of a morphomic stem.

6.1 The nature of stems

Stump (2001: Chapter 6) provides a very detailed demonstration of the need for morphomicstems, and an exhaustive illustration of the way that a complex set of stem alternations mayoperate, basing himself on Sanskrit.

We often find that stems come in groups or sets (the ‘stem sets’ of Anderson, 1992), whichmay be associated with each other by means of regular rules of stem formation. A particu-larly common instantiation of this is the phenomenon of the ‘theme extension’ to a verb root.This is found throughout Indo-European languages, for instance. In Latin, verb fall into fourtraditional conjugations defined by theme vowels: 1st conjugation in -a/a: (am-a:-re ‘to love’),2nd conjugation in -e: (mon-e:-re ‘to advise’) 3rd conjugation in -e/i (reg-e-re/reg-i-t ‘to rule, s/herules’), and 4th conjugation in -i: (aud-i:-re ‘to hear’), but similar phenomena are found throughthe world’s languages. In other cases, stems may be associated with each other by means ofmorphophonological generalizations which don’t, nevertheless, have the status of morpholo-gical rules proper, because they are idiosyncratic and lexically conditioned. In many languagesverb stems undergo vowel alternations (ablaut, apophony, largyngealization and so on), or al-ternations in tone, accent, length. We frequently find that consonants at the edge of verb stemssystematically undergo changes such as (de)voicing, palatalization, spirantization and so on.

Stump shows that in Sanskrit there is a class on lexemes for which it is possible to definestem sets in terms of their distribution as ‘Strong’ or ‘Middle’ and there is another set of lex-emes for which the ‘Middle’ class can be divided into ‘Middle’ and ‘Weakest’. For example, thepossessive adjective BHAGAVANT ‘fortunate’ belongs to the class which has two stem forms,Strong and Middle, while the perfecti active participle TASTHIVANS‘having stood’ has thethree-way three stem alternation, Strong, Middle and Weakest:

(17) a. Strong(BHAGAVANT) = bhagavant-Middle(BHAGAVANT) = bhagavat- (morphophonologically bhagavn

"t)

b. Strong(TASTHIVANS) = tasthiv´ans-Middle(TASTHIVANS) = tasthivat-Weakest(TASTHIVANS) = tasthivus.-

In the declension of BHAGAVANT in the masculine the Strong stem is used for the nominat-ive/accusative forms, singular and plural together with the nominative plural form. In the

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neuter gender declension on the nominative plural uses the Strong stem. Elsewhere bothgenders use the Middle stem. This is an instance of paradigmatic stem selection, which isdealt with by reference to an abstract morphomic stem furnished with an arbitrary index. Inthe declension of TASTHIVANSthe Middle stem is divided into a Middle and Weakest stem.The Middle/Weakest distinction is effectively allomorphic in the sense that the Weakest stemis selected with the following suffix is vowel-initial and the Middle stem is selected elsewhere(Stump 2001: 174f), i.e we have phonologically conditioned suppletion. This is syntagmaticstem selection, handled by reference to the morphophonological form of the stems and affixesas well as by reference to morphosyntactic and morpholexical properties. We will briefly con-sider both types, starting with the paradigmatic type of stem selection.

The three-way characterization of stems into Strong, Middle, Weakest corresponds in gen-eral to their morphophonological characterizations, the traditional Zero Grade, Gun. a Gradeand and Vr.ddhi Grades (Stump, 2001: 186). We might imagine that there is only need for oneof the two sets of labels: by knowing that a stem is, say, Zero Grade we can usually predict thatit has the distribution of a Weak stem and vice versa, while the ‘Strong’ stem generally appearsin the Vr.ddhi Grade. However, Stump demonstrates at great length that the correspondenceis not perfect: the default mapping can be overridden. For instance, there are occasions whenthe Strong stem is expressed by the Gun. a Grade rather than the Vr.ddhi Grade. An exampleis the vocative singular of a certain class of nouns including RAJAN ‘king’. Similarly, there areoccasions when the Middle stem is expressed by the Zero Grade rather than the Gun. a Grade,among other mismatches. At the same time, however we identify a stem, whether by defaultfrom its form, or by stipulated labelling, we cannot in general predict how that stem will beused in the paradigm. In fact, the distribution of the three stem types is very complex and hasto be stated as part of the morphology of Sanskrit, sometimes on a lexeme-by-lexeme basis.Moreover, if we examine the actual forms of lexemes such as BHAGAVANT we find that oneand the same suffix may be associated with different stems. For instance, in the declension oflexemes such as BHAGAVANT the masc accusative plural is based on the Middle stem, whilethe masc nominative plural is based on the Strong stem. Yet the suffix is -as in both cases: mascnominative plural bhagavant-as masc accusative plural bhagavat-as. In other words, Sanskritstems are paradigm examples of morphomic stems in Aronoff’s sense.

In some cases the selection of stems can be written into the realization rule which introducesthe affixes attached to those stems. Stump provides three compelling reasons why this is notsufficient in the general case to account for stem distribution. He provides two such reasonson the basis of the Breton partial paradigm shown in (18):

(18) Breton conjugation SKRIVAN ‘write’

Present Imperfect Future ImperativeIndicative

1sg skriv-a-n skriv-e-n skriv-i-n —2sg skriv-e-z skriv-e-s skriv-i skriv3sg skriv skriv-e skriv-o skriv-e-t1pl skriv-o-m skriv-e-m skriv-i-m skriv-o-m2pl skriv-i-t skriv-e-c’h skriv-int skriv-e-nt3pl skriv-e-r skriv-e-d skriv-o-r —

Stump assumes that the forms skriv, skriv-e, skriv-i and skriv-o are all stem forms. The first pointis illustrated by the Future forms skriv-i and skriv-o. Both of these are uninflected stem forms(on Stump’s analysis) and so they don’t involve any (non-trivial) application of a realizationrule. Therefore, we can’t link the selection of the two distinct stems to such a realization rule.The second point is illustrated by the 1pl forms skriv-o-m, skriv-e-m and skriv-i-m. In each case

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these are the result of the (default) realization rule for the 1pl agreement inflection, but ineach case the stem is distinct (the imperative form is syncretic with the present indicative formso there are, in fact, only three stem forms here). The third argument comes from Bulgarianconjugation. The verb JAM ‘eat’ has the stem form jad- for most of the present tense paradigm,and this reflects the fact that it belongs to the so-called ‘non-truncating consonantal inflectionalclass, whose 1sg form is regularly -@ as in krad@ ‘I steal’. However, but the 1sg form of JAM

is not *jad@, as would be expected but ja-m. This form is regular on the assumption that the1sg form is built on a stem belonging to the non-truncating, non-consonantal class. But by thisreasoning we have to assume that it is the stem selection which determines the nature of thesuffix and not the other way around. In other words, stem selection is prior to the operation ofany realization rules effecting inflection.

Phonologically conditioned stem allomorphy is illustrated by the selection of the Middle/Weakeststems of the TASTHIVANS-class of nominals. Consider the masculine accusative and instru-mental plural forms of the relevant classes of adjectives. The forms for BHAGAVANT are re-spectively {bhagavat-as, bhagavad-bhis} (where the t/d alternation is purely phonological)but the forms for TASTHIVANS are {tasthus.-as, tasthivad-bhis}. The two case forms of BHAGAV-ANT are built on the same stem form (modulo regular phonological voicing assimilation), butthe accusative plural form of TASTHIVANS differs from the instrumental plural form in that theaccusative form is built on the Weakest stem while the instrumental form is built on the Middlestem. This is because the accusative ending is vowel-initial while the instrumental ending isconsonant-initial. Stump appeals to a morphological metageneralization which states, in effect“select the Weakest stem form when the stem comes before a vowel” (see his rules (8, 9), p.181).Interestingly, the stem selection rule for tasthus. - can’t be attributed solely to the phonology ofthe resulting word form. In particular, the Weakest stem is not found prevocalically in com-pound formation (rather, the default Middle stem is selected in such cases). For this reason,Stump argues that the morphological metageneralization is relativized to Block I suffixation.In this sense the stem selection is governed both by phonological form and by morphologicalstructure.

Stump (2001: 183) provides the set of rules shown in (19) for determining the relevant formsof the three stems of an alternating lexeme:

(19) Stem-formation rules for L = perfect active participle

Where L is a perfect active participle, properties (a) and (b) imply each other and bothimply (c):

a. L’s Strong stem is X iv´ans-

b. L’s Middle stem is X ivat-

c. L’s Weakest stem is X ivus˙-

Parallel to the determination of morphologically distributed Strong/Middle/Weakest stemsstudents of Sanskrit provide a phonological characterization of stem types or grades. The firsttwo are generally referred to by their Sanskrit names, Vr.ddhi, Gun. a and the third is the Zerograde. These grades are essentially a type of moraically-defined ablaut root vowels, showingrespectively the alternations long-a, short-a and no vowel. The basic definition is provided byStump (2001: 186) in (20):

(20) Sanskrit grades

For any gradational nominal L, each of (a)-(c) implies the other two:

a. The Vr.dhi-grade stem of L has the form Xa(R)C0

b. The Gun. a-grade stem of L has the form Xa(R)C0

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c. The Zero-grade stem of L has the form X(R")C0

In an ideal world these phonological definitions would correspond exactly to the morphologic-ally defined stem types, but this is not the case for Sanskrit. We find, for instance, the followingcorrespondence between grade type and stem type:

(21) BHAGAVANT, Strong stem = Gun. a grade, Middle stem = Zero-gradeRAJAN ‘king’: Strong stem = Vr.ddhiPAD ‘foot’: Strong stem = Vr.ddhi, Middle stem = Gun. aATMAN ‘soul’: Strong stem = Vr.ddhi, Middle stem = Zero, Weakest = Gun. a

Moreover, what correspondences there are only apply to gradating nominals. Many words failto show gradation at all, so that their morphological stem classes differ from their phonologic-ally defined stem classes by definition. To be sure we can identify a default mapping, as shownin (22) but even this rather complex default statement is frequently overridden:

(22) Sanskrit stem defaults

Where L is a gradational nominal

a. by default, L’s Strong stem is its Gun. a-grade stem.

b. by default, L’s Middle stem is its Zero-grade stem.

c. if L belongs to the Weakest class, then by default, L’s Weakest stem is its Zero-gradestem

d. if L ∈ {n-stem nominals, perfective active participles, comparative adjectives in-yam. s, MAHANT, . . . }, then L’s Strong stem is its Vr.ddhi-grade stem.

Such deviations from default mappings between the phonological and morphological char-acterizations of stems lead Stump (2001: 199f) to conclude that morphological theory requiresus to distinguish stem forms and stem indices. The stem index is an arbitrary integer or otherlabel which uniquely identifies a given stem for a given class of lexemes, for instance‘Strong’,‘Middle’ ‘Weak’. Stump (2001:184, 188f) summarizes these conclusions in (23), as his IndexingAutonomy Hypothesis:

(23) The Indexing Autonomy HypothesisThe determination of a stem’s index is in principle independent of the determination ofits form.

Finally, we illustrate stem selection by seeing how it interacts with the notion of port-manteau position class introduced in §3.2. Consider the situation in which an irregular stemserves not as the basis for affixation but as the complete inflected word form itself. For instance,the comparative form worse of the lexeme BAD is an irregular stem which doesn’t accept thenormal comparative suffix -er: *wors-er. In other words, we must ensure that in such casesthe word form-cum-stem doesn’t feed into the normal affixation rules. By contrast, one mightwish to analyse the irregular comparative better as consisting of an irregular (suppletive) stembett- followed by the regular -er suffix.

We shall assume that the comparative is an inflectional morphosyntactic category governedby the feature DEG:{positive, comparative, superlative}. Here I shall simplify Stump’s ruleschemata in obvious ways to make the discussion more perspicious. The analysis of worse andbetter appeals to the notion of portmanteau position class and defines worse as the result ofapplying a stem selection rule to the class [I,0], which in English defines an entire inflectedword form. Thus, we define rule (24) where BAD is the label for the lexical class containingBAD as its sole member (Stump 2001: 208f):

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(24) RR[I,0],{comparative}.{BAD}, (X) = worse

The Function Composition Default (12) will apply unless pre-empted by rules such as (24), forexample to define taller as the comparative of TALL:

(25) PF(tall, comparative) =RR[I,0],{comparative},ADJ(tall) = (by FCD)RRI (RR0(tall) =RRI(tall) = taller

The Block 0 realization rule selects the root tall as the stem and the Block I realization rule isthe regular -er suffixation rule.

Now consider better, which, for the sake of argument we are assuming consists of the sup-pletive stem bett- with the regular -er affix. The stem selection rule for better takes the form(26):

(26) RR0,{comparative}, {GOOD}(X) = bett

This differs from the stem selection rule for worse in that it refers only to Block 0. It thusdefines an irregular stem to which the regular suffix is attached in Block 1. The irregular stemselection rule (26) pre-empts the default stem selection rule which would have selected theroot form good.

6.1.1 Stems - summary

In sum, we require the following system of rule-types and principles:

• Stem-formation rules, which specify the phonological shape of a stem or set of stems. Indefault cases the stem-formation rule will also permit us to predict the stem index andvice versa, but not always.

• Stem-indexing rules, overriding the default specifications given by the stem-formationrules or other default principles.

• Stem-selection rules, which specify which stem is to be used in a given cell of theparadigm. Such rules are the first rules in the paradigm function of the lexeme andthe first block of inflectional realizational rules proper takes this stem as its input. Wherethere is no stem-selection rule, stem-selection proceeds by default (in which case the in-put to the realization rules is typically the lexical root).

6.2 Paradigm linkage in PFM

6.2.1 Form-paradigms and content-paradigms

In a number of works (Stump, 2002, 2005, 2006; Stewart and Stump, 2007) Stump argues foran enriched conception of the notion ‘morphosyntactic feature’, which does justice to the syn-tactic functions of features as well as to their morphological functions. He argues that eachlexeme is associated not only with a set of form-function pairings in the morphology, but alsowith a set of pairings between the lexemic index of the lexeme and those properties which

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govern the behaviour of that lexeme in the syntax. For instance, an English count noun suchas cat has singular and plural forms, but these forms correspond to syntactic terminals whereappropriate singular, resp. plural forms can appear. This means that, in addition to the formparadigm of the lexeme cat, given in (27) we also have a content paradigm, as shown in (28):

(27) Form paradigm for cat

a. <|kat|, sg> realized as /kat/

b. <|kat|, pl> realized as /katz/

(28) Content paradigm for cat

a. <cat, SG>

b. <cat, PL>

An example such as this is trivial, of course, because in the default case the morphologicallyrelevant form paradigm is isomorphic to the content paradigm. Needless to say, however,there are interesting cases of mismatch in which the default isomorphism is subverted.

There are several types of mismatch between morphological form and syntactic function. Aclassical example is deponency (Stewart and Stump, 2007:393f) such as that found in Latin con-jugation. A whole host of verbs in Latin have passive morphology but are active in meaning.For instance, the verb rego ‘rule’ has an active form regit ‘rules (3sg, present)’ and a passiveform regitur ‘is ruled (3sg, present)’, while the verb loquor ‘speak’ has just the passive formloquitur which, however, has active meaning ’speaks’. There is no form *loquit. Therefore, wehave to say that their form paradigms are defined over whatever features distinguish activeverb forms from passive forms, but their content paradigms contain only the active voice fea-ture, as illustrated in (29):

(29) Deponency as an instance of form-content mismatch

Form cells Content cells Realizationrego <reg, 3sg, pres, act> <rego, 3SG, PRES, ACT> regitrego <reg, 3sg, pres, pass> <rego, 3SG, PRES, PASS> regiturloquor <lokw, 3sg, pres, pass> <loquor, 3SG, PRES, ACT> loquitur(loquor <lokw, 3sg, pres, act> <loquor, 3SG, PRES, ACT> —)(loquor <lokw, 3sg, pres, pass> <loquor, 3SG, PRES, PASS> loquitur)

The mappings for loquor in brackets in (29) are undefined for this lexeme. Other types ofmismatch include syncretisms, heteroclisis (Stump, 2002, 2006), periphrasis (Ackerman andStump, 2004) and principal parts phenomena of various kinds (Stewart and Stump, 2007).

The (default and non-default) relations between form and content paradigms are specifiedby rules of paradigm linkage. The default case is represented by the universal rule of paradigmlinkage given in (30) (Stewart and Stump, 2007: 392; see also Stump, 2006: 286):

(30) The universal default rule of paradigm linkage

Given a lexeme L, where R is L’s root, <L, σ>⇒ <R, σ>

The binary connective⇒ is to be interpreted as expressing the relation between correspondingfeature specifications in the obvious way.

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6.2.2 Heteroclisis

One particularly clear instance of the need for a distinction between form and content paradigmsis the phenomenon of heteroclisis, in which a lexeme inflects according to one inflectional classfor one part of its paradigm but according to a distinct inflectional class for the other partStump (2002, 2006). Heteroclisis also illustrates the need for an articulated theory of stem se-lection. We will consider the example of the Czech noun pramen‘spring, source’. This declinesas a ‘soft’ (palatalized) noun in the singular, like pokoj ‘room’ and as a ‘hard’ (non-palatalized)noun in the plural, like most‘bridge’, as shown in Table 1 (adapted from Stump 2006:xxx):

Declension soft heteroclite hardpokoj ‘room’ pramen ‘source’ most ‘bridge’

SingularNom pokoj pramen mostVoc pokoji prameni mosteAcc pokoj pramen mostGen pokoje pramene mostuDat pokoji prameni mostuInstr pokojem pramenem mostemLoc pokoji prameni moste

PluralNom pokoje prameny mostyVoc pokoje prameny mostyAcc pokoje prameny mostyGen pokoju pramenu mostuDat pokojum pramenum mostumInstr pokoji prameny mostyLoc pokojıch pramenech mostech

Table 1: Heteroclite declension of Czechpramen ‘source’

However, although the ‘soft/hard’ declension pattern in Czech has its historical origins inphonologically defined stem types, this phonological motivation has been obscured, so thatthere is no way of telling from the form of the root that PRAMEN takes anything other than the‘hard’ set of endings. What this means is that the lexical entry of PRAMEN has to be furnishedwith a root with two distinct labels, say, PRAMENSOFT and PRAMENHARD. The lexeme is thengiven a class feature indicating that the ‘hard’ root is to be used with plural forms.

The paradigm function for a heteroclitic word now has to made sensitive to the distinctionbetween the two roots. The way that Stump (2002, 2006) achieves this is to distinguish twosorts of ‘paradigm’, a ‘syntactic/content paradigm’ and a ‘morphological/form paradigm’.The form paradigm is defined over a pair <root, features>, while the content paradigm isdefined over a pair <L, features>, where ‘L’ is the lexemic index of the lexeme. In the normalstate of affairs, the two paradigms are homomorphic, and there is a trivial mapping betweenthem. This is illustrated schematically for the non-heteroclite nouns POKOJ ‘room’ and MOST

‘bridge’ (with obvious abbreviations):

(31) Form-content mappings for POKOJ, MOST

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a. < pokoj, gen sg> �⇒ < POKOJ, GEN SG> = pokoje< pokoj, gen pl> �⇒ < POKOJ, GEN PL> = pokoju. . .

b. < most, gen sg> �⇒ < MOST, GEN SG> = mostu< most, gen pl> �⇒ < MOST, GEN PL> = mostu. . .

However, for heteroclite nouns such as PRAMEN this default linkage is subverted. Takingthe ‘soft’ root to be the default, the ‘hard’ root form is then a co-radical. Stump then defines aspecial linkage rule, (32), stating that the hard co-radical is selected for the plural number partof the paradigm.

(32) Czech rule of stem licensing:

If lexeme L belongs to the PRAMEN class, then {NUM:pl} licenses L’s coradical stem.

6.3 Stems and the English verb

English provides a simple example of how stem formation and indexing works6. A regu-lar transitive verb can express the morphosyntactic features past tense, perfect participle andpassive participle. However, the form is the same for all three features, e.g. walked. We can callthis Stem1. This stem is derived by regular affixation from the root and on its own can realizeeach of the three features. However, some verbs have an irregular Stem1, such as BUY: rootbuy, Stem1 bough-(/bO:/) (or perhaps Stem1 = bought). This listed Stem1 form overrides thedefault stem formation rule, but it behaves in other respects exactly like Stem1. In other verbs,the past tense and perfect/passive participle features are realized by different stem forms, asin WRITE, root write, past wrote, participle stem writt- (/rIt/). What we can say here is that thereis a Stem3 which is by default identical to Stem1 but which in some verbs has a form distinctfrom Stem1. In all verbs the perfect and passive participles are realized by the same stem form(Stem2). This can be pictured as in (35), where the definition of the different stems is madeexplicit in (34):

(33) English verb stem system

Stem0 (=root) Stem1 Stem2 example

X X-ed = Stem1 WALK (regular)X Y Y BUY

X Y Z WRITE, SING

X Y X TAKE

X X X PUT

etc.

(34) walk walk-ed walk-edbuy bough-t bough-twrite wrote writt-entake took take-nput put put

(35) Stem-to-feature mapping for English

6For a detailed discussion of stems in English and West Germanic generally see Blevins (2003).

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By default Stem2 = Stem1

Stem2⇒ [VFORM:perfpart]

Stem2⇒ [VFORM:passpart]

Stem1⇒ [TENSE:past]

Rules of morphology define which stem is used for realizing which set of features. For instance,the realization of [VFORM:perfpart] appeals to Stem2 (by default set equal to Stem1). In the caseof verbs of the class[WRITE] this stem serves as the basis for -ensuffixation. In the case of verbsof the class[SING] Stem2 on its own realizes that property set, and hence the stem form occupiesa portmanteau position class (Slot[1,0]; cf the discussion of portmanteau stem-selection rules,Stump 2001:208f).

7 Derivational morphology in PFM

7.1 Derivational paradigms

A number of authors have argued that derivational relationships can in some cases exhibitparadigmatic structure, though in some instances different authors may mean slightly differentthings by ‘paradigm’ (or indeed ‘derivation’) (Bauer, 1997, Booij, 1997, 2002, (Spencer, 1988)).Consider the set of words in (36):

(36) Subject nominalizations in English

drive driverwalk walkeract actorreside residentstudy studentclaim claimantapply applicantchair chairman/chairpersonguide guidecook cheffly pilot

Clearly, the English lexicon is structured in such a way as to warrant us defining a notion of‘subject nominalization’, under which for any given verb there is (usually) some noun whichdenotes the subject argument of that verb. The morphological means used to realize this cor-respondence are varied, though it’s also clear that the suffixation of -er (which may also include-or as a graphemic variant) is in some sense the default morphology.

To see these correspondences as a paradigm we only need to compare the list in (36) with asimilar list of regular and irregular plurals. In each case we have a systematic relationship, ex-pressed by means of generally affixal morphology, but with exceptions, including conversion(guide), stem suppletion (applicant) and whole word suppletion (chef, pilot). The only differencein the formal means of realization between the list of plurals and the list of subject nominals isillustrated by chairperson, which is a compound (and which many morphologists, no doubt,would omit from the list of subject nominals for that reason).

To describe singular/plural inflection we set up a feature [NUMBER] with two values {sg, pl}.To describe subject nominalization we cannot deploy a binary feature in this way, however,

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because the base verb and its subject nominalization are not in an equipollent relation to eachother. Rather, the subject nominalization process is determined by a privative (single-valued)feature ‘subject nominalization’.

On this understanding, the subject nominalization paradigm is a very simple paradigm,consisting of exactly two cells per verb lexeme, one occupied by the base verb and the other byits nominalization. The individual morphological means for realizing the nominalization arein paradigmatic opposition to each other, hence, the application of the paradigm metaphor.7

There is a second notion of ‘paradigm’ that is of some interest to models of morphology.In Spencer (1988) I discuss so-called ‘bracketing paradoxes’ of the type generative grammarianor bass guitarist. These are instances of morphosemantic mismatches. Morphologically the ex-pressions are clearly segmented as written: [[generative] grammarian], [[bass] guitarist]. How-ever, semantically they deserve the segmentation [[generative grammar]-ian], [[bass guitar]-ist]. There are a great many expressions in English which exhibit this kind of morphosemanticmismatch, some of them systematically. Of particular interest to paradigmatic approaches toword formation are specifically the personal nouns of the kind generative grammarian. Thereason is that these represent a highly productive pattern, though one which can only bedefined in terms of a structured lexicon. Spencer (1988) discusses cases of the form (37) insome detail:

(37) generative grammarian

criminal lawyer

baroque flautist

moral philosopher

modern linguist

plastic surgeon

electrical engineer

organic chemist

theoretical linguist

monumental mason

North American

East German

Southern Dane

What these examples have in common is that they are all personal nouns derived fromnominal expressions of the form Adjective + Noun. In each case, the base expression has tobe lexicalized. Thus, for afficionados of pre-classical music, the term baroque flutedenotes aspecific type of (pre-Bohm) instrument, almost certainly made out of wood and with at mostone key. It is a fixed expression with a fixed denotation, and for that reason can serve as thebase for derivation.

7There is in the literature another interpretation of the notion of paradigm. Bauer (1997) has argued for the need toinclude derivational paradigms in morphological theory, where by ‘paradigm’ he means something more akin to a syntagmaticnotion. Thus, from, say, the noun ‘nation’ he would derive the paradigm consisting of the words{nation, national, nationalize,re-nationalize, nationalization, . . .}. This notion corresonds, if anything, to the notion of ‘wordnest’ sometimes used bySoviet morphologists (@Uluxanov 1996?? other refs - check). Although such a notion is potentially of lexicographic andpsycholinguistic interest, I don’t really see how it has anyrole to play in a theory of morphology, so I shall ignore thisinterpretation.

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The fact that baroque flautist is the personal noun form can be deduced from the fact thatflautist is the personal noun form of the head noun flute. In other words, the relationshipbetween the base expression baroque flute and the personal noun baroque flautist is cruciallydefined with respect to the head of the expression, flute. A derivational way of picturing this isto deploy what Hoeksema (1985, 1989) has called a ‘head operation’. We first form the personalnoun from the head, to get flautist. Then we take the phrasal base baroque flute, ‘circumscribeout’ the modifier, baroque, apply the personal noun forming process to the remaining head, andreplace the modifier:

(38) Derivation of baroque flautistbaroque flute ⇒ ‘circumscription’ of head nounflute ⇒ personal noun formationflautist ⇒ re-instatement of modifierbaroque flautist

Another way of picturing this is as in (39):

(39) baroque flute⇒ (baroque) fluteist

==⇒ (baroque) flautist

and in Spencer (1988) I present the process as a kind of Latin Square:

(40) Latin Square representation of baroque flautist

flute ⇒ flautist⇓ ⇓

baroque flute ⇒ baroque flautist

However we choose to picture it, the crucial facts are that (i) the base has to be a lexicalizedexpression and (iii) the process is entirely productive.

Point (i) is evident when we look at minimal pairs which involve ordinary phrases ratherthan lexicalized phrases. In (41) we see some examples of failure of the personal noun forma-tion process:

(41) wooden flute ; wooden flautistmodern linguistics ; modern linguist

Wooden flautist can only mean ‘flautist who is wooden’ and modern linguist, if the out-put of personal noun formation, can only mean ‘specialist in/student of Modern Languages’,and thus has to be derived from the (fixed) expression modern languages, not the syntacticallyformed modern linguistics.

A further salient feature of personal noun formation is that it often involves suppletiveor subtractive morphology. For this reason it can’t sensibly be treated in terms of ordinarymorphemic analysis8.

As I point out in Spencer (1988), personal noun formation is paradigmatic, though not inquite the sense that inflection is paradigmatic. The grammar of English has to include somefeature, label or whatever which encodes the fact that personal noun formation from nounsand lexicalized nominal phrases is (in principle always) possible. It must also specify that the

8Ackema and Neeleman (2004) develop a very interesting analysis of these constructions in terms of an abstract type ofmorpheme, their AFFIX, which circumvents some of the problems raised for a classical morphemic approach.

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morphological form of a phrase-based derivation is computed from the morphological formobtained by applying that process to the noun head of the phrase. In this respect, we havea derivational paradigm, just as we do for deverbal subject nominalizations, though not onewhich can easily be defined in terms of a default affixation process.

7.2 Derivational paradigms in PFM

The notion of derivational paradigm illustrated by 37 is the second of the two interpretationsmentioned by Stump (2001:255). We can think of it as a meaning-, feature-, or content-drivennotion of paradigm, in which formal relationships are secondary. The first is that of Stump(1991), devoted to morphosemantic mismatches of the ‘baroque flautist’ variety, in which hetreats a derivational paradigm as being defined by the (usually affixational) process whichderives the new lexeme. On this interpretation the examples in (??) and (??) would all rep-resent distinct paradigms, that is, there would be an -∼er/or paradigm, an -∼ent/ant paradigmand so on. This is a form-driven notion of paradigm. One consequence of Stump’s (1991) wayinterpreting this type of paradigm is that the semantic relationship between the derived lex-eme and the base lexeme can be very (in principle, completely) different. In fact, these twonotions of paradigm have been current in the East European structuralist tradition for sometime. The meaning-driven notion corresponds to the notion of ‘derivational category’, whilethe form-driven notion corresponds to the notion of ‘derivational type’ (see Szymanek, 1988,1989 for detailed discussion of these distinctions). I will take the crucial notion here to be thatof derivational category, i.e. that which appeals to the notion of content-paradigm.

Stump (2001:257) illustrates the application of PFM to derivation by considering the case offriendlessfrom friend. Since we are assuming a derivational paradigm there must be a paradigmfunction which delivers the derived lexeme. This means that the paradigm function (in itsmost general sense) for English must include an application of the form (42), in which δ is asyntacticosemantic (i.e. derivational) category:

(42) PF(<X,δ>) =def <Y,δ>

PF(<friend, privative adjective>) = <friendless, privative adjective>

Notice that the paradigm function is defined as usual over a pairing of root and property toderive a new root.

8 Head Marking and the Head Application principle

In morpheme-based models of morphology, on one interpretation of the notion of ‘morphemeconcatenation’, it is natural to suppose that morphology gives rise to branching structures.Indeed, this will be the case if we regard morphemes as lexical entries in their own right, sothat morpheme concatenation is homologous with compound formation. This is the essence ofso-called ‘Word Syntax’ (see Selkirk, 1982, for an early model and Toman, 1998 for an overviewof the issues). In clear cases of endocentric compounding the head is that element which de-termines the overall syntactic category of the compound, which determines the meaning of thecompound (by defining a denotation which is then delimited in some way by the non-head)and which receives the inflections of the compound as a whole. Thus, mousetrapis headed bytrap because it is a kind of trap and because more than one of them are called mousetrapsratherthan *micetrap. Similarly, a blackbird is a bird and the word blackbird is a noun, just like bird(but unlike black). Given this background, morphologists have asked whether affixed words

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are headed in the same way. For instance, are the word forms walked, re-write or walkerheadedand if so what is the head?

The most extreme answer to the question is that given by Williams (1981), who arguesthat for all languages the head is the right-most element. I and many other observers havebeen mystified by this claim so I will leave it to one side. Another possibility is that the mostrecently added affix is the head, mimicking compounding. This would make -ed, re- and -er respectively the heads in our examples. For this to respect the putative homology withcompounding this would mean that the affixes would have to have a syntactic category whichis the category of the whole word, and a meaning which is modified by the non-head (thelexical root in this case). While this may make some sense for walker, it’s less obvious that itcan be applied to examples other than highly canonical derivational morphology. For re-writewe would have to say that the basic meaning was that of a repeated event, further delimitedby the concept ‘write’. For walkedwe would have to say that the meaning is that of ‘pastevent’, modified by the concept ‘walk’. Not surprisingly, some theorists have balked at thisway of analysing inflection. Selkirk (1982) proposed a notion of ‘relativized head’, under whichdifferent parts of a complex word can contribute head properties. For instance, we could arguethat the wordform walkedhas two heads. The lexical head walk provides the lexical semantics(and syntactic class, perhaps) to the word as a whole while the -ed affix provides the feature[TENSE:past]. In a sense, this is equivalent to treating an inflected word form as though itwere a periphrastic expression such as has walked. In that expression the auxiliary verb is theinflectional head (in that it takes tense and agreement inflections) while the verb form walkedis the lexical head. The inflected word form as a whole inherits the properties of its parts by aprocess of ‘feature percolation’ under which morphosyntactic and morphosemantic propertiespass from a lower node to a higher node. In languages which permit several inflections perword form, each inflection is a head in its own right. The natural critique of the relativizedhead notion is that it evacuates the notion of ‘head’ of its crucial meaning.

In realizational models the question of headedness doesn’t arise in this form, because thereare no affixal morphemes as such to serve as pseudo-syntactic heads and morphology is notidentical to (endocentric) compounding. However, there do arise situations in which the no-tion of ‘head’ seems to be warranted even in realizational theories. Consider English pre-fixed verbs of the type undertake, understand, withstand, withhold, uphold. These verbs inflectin the same way as their unprefixed bases, whether the prefixes are unproductive and non-compositional or productive and semantically transparent (such as stressed re-). This meansthat whatever lexical property it is that verbs such as take, stand, hold may have which determ-ines their conjugation that property is preserved under prefixation. A popular way of thinkingof such situations is to say that the prefixed words are headed by their verb bases and that itis the heads that determine inflection. This way of looking at things is particularly attractivewhen the inflections are also prefixes and they appear closer to the root than the derivationalprefixes. This is a common situation, being found in classical Indo-European languages, aswell as Modern Greek, German and a whole host of other languages. For instance, in Germanwe have the verb nehmen‘to take’, past participle ge-nommen. A prefixed form of this verb, suchas mit-nehmen‘to take with (one)’ has the past participle mit-ge-nommen, in which the prefixalpart of the lexical root is added to the form inflected for past participle.

Stump (1991, 2001:Chapter 4) argues that a necessary (though not, of course, sufficient) con-dition for analysing complex words as headed structures of this type is that they are the resultof derivation or compounding which preserves word category, as in the examples cited above.If in addition such a process is transparent with respect to some property of the base thenwe can speak of a headed structure. Stump offers a number of examples of such transparencyfrom diminutives in various languages (more generally, evaluative morphology, encompassingperjoratives, augmentatives and so on as well as diminutives sensu stricto). Perhaps the com-

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monest use of evaluative morphology is found with diminutives of nouns. In some languagesthe diminutive morphology is no different from straightforward derivation. For instance, inGerman the diminutive suffix -chencreates a neuter gender noun, irrespective of the gram-matical (or natural) gender of the base (masculine, feminine or neuter). However, a propertyof diminutive processes in many languages is that they preserve the gender of the base noun,even where this is at variance with the default gender assignment for the inflectional classof the output. For example, Russian is rich in diminutive suffixes, all of which preserve thegender of their bases. Thus, the affectionate/diminutive suffix -ulja creates a feminine gendernoun mamuljafrom mama‘Mummy (feminine)’ and a masculine gender noun, papulja, frompapa‘Daddy (masculine)’. In this case the affix determines the inflectional class of the output,but the gender is transparent. In other cases the gender and also the inflectional class are trans-parent. Thus, the suffix -ecek∼-ecka∼-ecko is added to consonant-final (masc.), -a final (fem.)and -o final (neuter) lexemes, as in celovek∼celov-ecek‘person (masc.)’, doska∼dosc-ecka‘board(fem.)’, slov-o∼slov-ecko‘word (neut.)’ preserving both gender and inflectional class (thoughit can be added to Class III nouns ending in a palatalized consonant, such as doc ∼doc-ecka‘daughter’, in which case it imposes Class II membership while preserving gender). Stump(p. 99f) cites further examples from Southern Barasano and Breton, in which the diminutiveformation rule preserves syntactic category (noun, adjective, adverb).

The Russian diminutives, while headed in Stump’s technical sense, inflect in a way that tar-gets the suffix, not the base noun. In this respect the Russian examples are not head marking,and Stump refers to this type of (standard) inflection as external marking (EM). However, theSouthern Barasano diminutives do exhibit head marking. The suffix is -aka. When attachedto a noun such as wi ‘house’ it gives wiaka ‘little house’ but the plural of the diminutive isformed by suffixing -aka to the plural inflected form of the base, wi-ri , to give wiriaka. Thisis head-marking (HM). Diminutive formation in Breton is, if anything, even less canonical:the diminutive suffix -ig gives rise to double plural marking when attached to a noun: bag‘boat’, bag-ig ‘little boat’, bag-ou‘boats’, bag-ou-ig-ou‘little boats’. Thus, Breton exhibits doublemarking (2M). The property of being head-marking or not is a property of the derivational orcompounding construction itself: either all the outputs of the given construction (‘coderivat-ives’) exhibit head-marking or none do (the ‘Coderivative Uniformity Generalization’, p. 98,108). Moreover, if an output exhibits head-marking in some part of its inflectional paradigmit exhibits head-marking throughout the whole of the paradigm (the ‘Paradigm UniformityGeneralization’ p. 98, 109).

This means that there are three types of category-preserving derivational or compound-ing construction. Those constructions that exhibit EM are called root-to-root rules, those con-structions that exhibit HM are called word-to-word rules and those that exhibit 2M are calledword-to-stem rules. The logic of the terminology is this. In inflecting a Russian diminutivethe realization rules apply to the derived word in exactly the same way they would apply toa simplex word. Thus, the base form of the derived word behaves itself exactly like a rootwith respect to the operation of the realization rules of the inflectional component. However,when a HM word such as the Southern Barasano diminutivized noun is inflected, the effect isto take an inflected word (the plural form wi-ri ‘houses’) and apply the diminutive process todeliver another inflected word (perhaps ‘word form-to-word form’ would be a more accuratedescription). In the case of a doubly marked Breton diminutive, the -ig suffixation applies toan already inflected word form, as in Southern Barasano:[bag-ou] + -ig. However, the output,bagouigis not a completed word form, rather it is the stem to which a second round of pluralaffixation applies, to give bagouigou. Hence, the -ig suffixation creates a stem from a word.

The behaviour of headed constructions produced by word-to-word rules is governed bythe Head Application Principle (HAP) (p. 115). In simple terms the HAP states that for anyword Y that is headed by Z, every inflected word form of Y is headed by the corresponding

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word form of Z. For instance, the prefixed verb lexeme UNDERTAKE is headed by TAKE. Thismeans that each inflected form of UNDERTAKE (i.e. undertake, undertakes, undertaking, undertook,undertaken) is headed by the corresponding forms of TAKE.

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