paradigm gaps in whole word morphology

LUC BARONIAN (BOSTON/USA) & ELENA KULINICH (MONTRÉAL/CANADA) Paradigm gaps in Whole Word Morphology∗

Abstract

The authors present an account of paradigm gaps of defective verbs taken from French, Spanish, English and Russian, couched in Whole Word Morphology (WWM). After locating paradigm gaps within defective verbs in general, they first show how theories relying on general defaults are by definition incapable of accounting for such phenomena and how two participation conditions among morphological choices (Word-Formation Strategies–WFS–in WWM) are independently motivated. Under the present analysis, defective verbs end up “caught” between WFS, because they partially behave like one WFS and partially like another, without ever satisfying both participation conditions. The uncovered similarity across the languages analyzed is striking. The case of Russian gaps is partic-ularly enlightening, as it has almost systematically been analyzed as one of “lexical gaps” in previous analyses. With original data and an experimental survey on recent borrowings from English, the au-thors demonstrate the “productivity” of Russian gaps and their essentially grammatical nature.

1. Background

Defective verbs are verbs lacking forms for one or more exponents. For example, native French speakers typically cannot generate imperfect, present participle or plural present forms for the verb frire ‘fry’:

∗ The article follows Baronian’s research and theoretical proposals first established in Baronian

(2005, 2009). Kulinich’s contribution consists in her original investigation of Russian neological verbs and the analysis of the results that came from said investigation, which is the bulk of her 2010 MA thesis at the Université du Québec à Chicoutimi. For discussion on these matters over the years, the authors thank Adam Albright, Lev Blumenfeld, Jean Dolbec, Paul Kiparsky, Will Leben, Yves Charles Morin, Ivan Sag, Rajendra Singh, Arnold Zwicky, as well as Marc Fredette for help with the statistical analysis. All final responsability remains the authors’. Elena Kulinich acknowl-edges financial support from the Social Sciences and Humanities Research Council (SSHRC) of Canada and the Fonds québécois de recherche sur la société et la culture (FQRSC) in the form of graduate fellowships.

Luc Baronian & Elena Kulinich 2

(1) 1SG: je fris 2SG: tu fris 3SG: il frit 1PL: nous *frissons, *frisons, *frions, *frivons, *fritons... cf. nous finissons ‘we finish’ nous conduisons ‘we drive’ nous marions ‘we marry’ nous écrivons ‘we write’

Defective verbs are hence irregular in that speakers fail to use their language’s mor-phology to generate certain forms.

1.1. A typology

In a loose acceptance of the term, impersonal verbs requiring an expletive subject are defective for lacking all NON-3SG forms. However, notice that speakers have no prob-lem in predicting that the 1SG present form of English rain would be I rain, or that the 1PL of its French equivalent pleuvoir would be nous pleuvons. It is the meaning that would be unclear, but one could be imagined in a creative context, e.g. a speaking cloud in a children’s book, or a poem, similar to Émile Nelligan’s non-impersonal use of neiger ‘to snow’: (2) Ah! Comme la neige a neigé

‘Oh! how the snow has snowed’ Impersonal verbs are then not a theoretical problem for the word-generating component of grammar we take morphology to be and will not be discussed further in this paper. We will also put aside a second type of defective verbs, which, however, do pose a theoretical problem for morphology: paradigmless verbs. Fodor (1972) cites English beware, which has an infinitive (to beware of this dog is a good idea), an imperative (beware of the dog!) and a subjunctive (he asks that you beware of the dog), but no present or past: (3) *I/You beware of the dog.

*He bewares/bewore of the dog. It is intriguing why such forms aren’t used, but as with, for example, the French verb douer ‘endow’, which only has infinitive and participial forms, speakers don’t seem to question what the missing forms would be (je doue, tu doues, il doue, etc. in the latter case). While further research may prove us wrong, we currently hold the position that the explanation behind the lacking forms of paradigmless verbs must be of a different nature than the one behind the paradigm gaps of defective verbs, which is the topic of this paper. At the very least, we know of no successful attempt at explaining paradigm-less and paradigm gap verbs together. The French verb frire cited in (1) falls in the paradigm gap category, though there are also distinctions within the said category.

(4a) Impersonal verbs: only an expletive subject is allowed e.g. English rain (*I rain, *you rain)

Paradigm gaps in Whole Word Morphology 3

(4b) Paradigmless verbs: no finite forms exist e.g. English beware, French douer ‘endow’

(4c) Paradigm gap verbs: verbs that lack only some finite forms, or some non finite forms i Potential non-automatic alternation involved

e.g. French frire (above), English stride (stridden, strided or strode?), Russian dudet' (duzhu or dudu?), recent borrowing apgreydit' (‘upgrade’, apgreyzhu or apgreydu?)

ii Prefix and suppletion e.g. English forgoed or forwent?, French re-naître: rené or renu? iii Phonologically marked forms e.g. French colorier: je color[j]?

By far the most discussed type of paradigm gap involves a non automatic (i.e., morpho-phonological) alternation. In fact, it is this type that was first discussed in the generative literature by Halle (1973), who mentions the 100 Russian verbs (or so) that lack a 1SG NON-PAST form. These defective Russian verbs contain a stem ending in a dental conso-nant which could palatalize in the 1SG NON-PAST like the non-defective “dental” verbs of the second conjugation, or maintain their dental consonant like non alternating verbs. Such a morphonological choice is the hallmark of most reported cases of paradigm gaps. For example, the French verbs whose infinitive ends in /-ir/ have a phonologically non predictable consonant linking the stem to some person-number suffixes of certain tenses: (5) Cons: /s/ /z/ /v/

je fini-ss-ais / condui-s-ais / écri-v-ais ‘I was finishing / driving / writing’

When trying to conjugate the verb frire, speakers are thus confronted with a choice between consonants to link the stem to the suffix, as illustrated by the rejected possi-bilities in (1). Likewise, the English verb stride, for which some speakers have difficul-ties in generating a past participle, offers at least three possibilities: ablaut identity with the past (I have strode, as in I have won/bled); raising+suffix (I have stridden, as in I have written); regular suffixation (I have strided, as in I have loved).

A second type of paradigm gap involves a prefixed root, which, when unprefixed, normally undergoes suppletion. For example, many English speakers cannot decide between forgoed and forwent as the past tense of forgo, while French speakers can usually not generate the past participle of renaître ‘to be reborn’: the past participle of naître is partially suppletive (né), but other verbs ending in -naître follow a different strategy (connaître/connu, méconnaître/méconnu, reconnaître/reconnu). Of course, one could consider suppletion as an extreme type of morphonological alternation, making the distinction a pedagogical one more than a substantive one.

Finally, the third type we have identified would yield an underlying form with no analog in the language. Morin (1987) gives the example of French colorier, which is being replaced in the language by the alternative colorer. According to Morin, speakers


analyze the underlying form of the infinitive to be /kɔlɔrje/, which would regularly yield a PRES SG form /kɔlɔrj/, if one is unaware of the traditional PRES SG form /kɔlɔri/. However, as Morin points out, there is no other French word ending in /-rj/. Whether this unusual underlying form is truly the reason for the speakers’ discomfort remains an open question. Once again, this type of gap could be considered morphonological if we consider the potential alternation between /j/ to /i/ to be a non automatic one.

1.2. The problem with default theories

Paradigm gaps are an important problem for theories of morphology because so many of them rely on default rules. By definition, a default rule will always allow the speak-ers to generate a form. Therefore, the only way to prevent a gap from being filled by a form rejected by speakers is to state an ad hoc constraint forbidding the form.

The problem with default rules is clear when we compare the accounts of two theories at the opposite end of the root/lexeme spectrum: Paradigm Function Morphology (PFM) and Distributed Morphology (DM). In (6), we see that PFM accounts for irregular verbs by ordering a lexically specified realizational rule before a more general (regular) one. (6) The English Past Participle in Paradigm Function Morphology

(adapted from Blevins 2003: 751) R([see, verb, dent, part]) = seen R([past]) = Xd

In (6) above, the (past or passive) participle realization of the verb see R([see, verb, dent, part]) is thus lexicalized as seen (dent is a lexical marker used by Blevins to iden-tify “dental” stems). Other past verb forms use R([past]), unless another specific rule tells the speaker otherwise, and a /-d/ is simply added: Xd. So in the case of stride, either a specific (irregular) rule deriving stridden is learned, or stride is forced into the second realization rule (strided) and no gap is ever possible.

Although apparently very different in nature, DM has a surprisingly similar architec-ture. A series of verbs are lexically marked for using the specific /n/-suffixing rule to form their past participle. Other special cases (not shown in 7) exist, but, crucially, the remaining verbs will end up using the general /d/-suffixing default rule. (7) The English Past Participle in Distributed Morphology

(adapted from Halle & Marantz 1993) [+participle, +past] ↔ /-n/ / X+__, where X = see, go, beat, ... [+past] ↔ /-d/

Hence, once again, either stride is added to the irregular list or it is forced into the second rule (strided) and no gap is ever possible. Paradigm gaps then constitute a se-rious challenge for most contemporary theories of morphology that make use of the notion of default.


1.3. Previous accounts

In order to prevent gaps from being filled by default rules, Halle (1973) stipulates that Russian gapped forms are marked [-lexical insertion]. As Albright (2003) points out, this approach lacked a principled account of which Russian verbs show gaps (a subset of the second conjugation “dental” stems) or where (1SG NON PAST). Under Halle’s view, there would be no reason why a random first conjugation verb would not random-ly be gapped, or why some verbs aren’t gapped in the 2PL or 3SG. Baronian (2009) further points out that such a mechanism would require negative evidence in the acqui-sition process. Indeed, if the initial setting of the feature were [+lexical insertion], then the child would never receive any positive evidence contradicting such a setting (be-cause adults don’t produce the gapped form). But if the initial setting were [-lexical insertion], then this would entail that children must learn all verb forms before being able to use them, negating the generative capacity of morphology. Not only is the latter item clearly not on Halle’s agenda, but that new verbs can be inflected in various lan-guages is not a matter of debate.

Morin (1987, 1995) proposes a directional stem suppletion account of French gaps. He proposes an implicational hierarchy of stems among verbal person-numbers.

(8) 2PL stem is used as a 1PL stem 1PL stem is used as a 3PL stem 3PL stem is used as a SG stem

Morin’s implicational hierarchy described in (8) is to be understood as a set of default “filler” rules. For example, the French singular (present) verb /fini/ is lexicalized as such; therefore the implicational statements of (8) are not relevant. But the stem of the French 3PL (present) verb /efas/ ‘erase’ is also used as a singular, because no singular form is lexicalized. Thus, if a verb is missing a SG form, it can always be “filled in” by the 3PL stem combined with the SG suffix. However, if it is missing a 2PL form, no other stem of the system can be used to “fill” it in. This hierarchy seems to work well for general suppletion facts. The verb faire ‘do/make’ changes stem at each step, the verb dire ‘say’ changes twice (and the 1PL is carried over to the 3PL as predicted), while second group verbs such as finir ‘finish’ only change their stem for the SG forms.

(9) 2PL fait-es dit-es finiss-ez 1PL fais-ons dis-ons finiss-ons 3PL fon-t dis-ent finiss-ent SG fai-s/t di-s/t fini-s/t

However, it is difficult to justify the directionality of the hierarchy. Morin is careful to state that his model is one of the adult language, but diachronic and L1 acquisition facts suggest that the use of a stem for a different person-number in the other direction is not at all impossible. For example, children often use a 2PL disez (based on the 1PL or 3PL


form), some dialects have leveled the SG stem of the verb tenir ‘hold’ to the entire pa-radigm. Further, like Halle’s account, Morin’s has a large part of arbitrariness in that any verb at some point could be lacking a 2PL stem and have a gap for it, but the fact that gaps typically occur when a morphophonological alternation is involved bears no weight in Morin’s account. Morin also recognizes some problematic gaps, which should be filled in by the plural stem: the missing SG forms of colorier for some speak-ers, as mentioned above, and the missing SG form of vaincre ‘win’ for some speakers. In spite of its problems, Morin’s account explores an interesting avenue of a potential relationship between gaps and how verbs forms are built one on another.

Dell (1970) and Plénat (1981) propose that gaps arise from the speakers’ inability to pick one morphological possibility over another. Plénat goes a little further in claiming that the reason why frire is defective is because speakers cannot choose the correct linking consonant. While the existence of a choice in and of itself cannot be a sufficient condition for the existence of a gap, it certainly appears to be a necessary one.

Albright (2003, in press) proposes a statistical approach linking Spanish and Russian gaps to low frequency, lack of familiarity and fragmentation of verb classes. While his approach is more reliant on statistical factors than ours, and less systematically on the fragmentation of various word classes, it is probably the closest to ours.

Some OT accounts of paradigm gaps have also been proposed (Orgun & Sprouse 1999, Hansson 1999, Rice 2005). Like default theories, OT accounts are designed to always generate an output (a winning candidate). They must therefore rely on a filter mechanism to eliminate the winning candidate. Besides the approach being ad hoc, Albright (in press) argues that these approaches undergenerate (yield many more gaps than typically attested).

Finally, the recent studies on Russian gaps all propose that gaps are lexically speci-fied as such, as Halle had nearly forty years ago. The analyses of Baerman (2008), Dal-and et al. (2007) and Sims (2006) all share this feature. Daland et al. (2007) provide a tentative account of how the extremely low frequency of certain forms provide learners with implicit negative evidence that they do not exist. It remains to be shown however that such an account does not overgenerate gaps (so to speak, i.e. undergenerate forms).

2. Whole Word Morphology

In this paper, we propose an account of paradigm gaps based on the theory of Whole Word Morphology (WWM), which, unlike many current theories, does not provide general defaults. WWM was previously known as Projection Morphology, and, in un-ion with Lexicase, Seamless Morphology (Singh & Starosta 2003). Ford & Sing (1991), and Ford et al. (1997) are its founding texts, with Singh (2006) providing a list of im-portant references and a recent summary adapted in (10) below.


(10) Word-Formation Strategies (WFS) have the following shape and requirements: /X/a ↔ /X'/b

(10a) /X/a and /X'/b are words; X and X' are abbreviations of the forms of classes of words belonging to categories a and b (with which specific words belonging to the right category can be unified or onto which they can be mapped).

ex.: English: /X/NOUN.SG ↔ /Xz/NOUN.PL (10b) ' represents (all the) form-related differences between /X/ and /X'/ that fall out-

side of automatic phonology. Devoicing of the plural suffix in cats is handled by automatic phonology, there-

fore is not a form-related difference to be noted in a WFS. (10c) a and b are categories that may be represented as feature bundles. VERB-PRESENT-3SG (10d) The ↔ represents a bidirectional implication (if /X/a, then /X'/b, and if /X'/b,

then /X/a). (10e) The interpretation of /X/a is a semantic function of /X'/b and vice versa. (10f) ' can be null if a ≠ b. /X/VERB ↔ /X/NOUN (love, light...) but polysemy is excluded from the realm of morphology: * /X/VERB ↔ /X/VERB (run a marathon vs. run a script)

It is important to note that WWM is a truly word-based theory of morphology, where roots, stems and affixes are at best pedagogical categories, but have no primitive status in the theory. Also, nothing in (10) prevents the use of (non binary) network strategies (Singh & Agnihotri 1997), e.g.:

(11) /XaɪC/PRES-NON3SG ↔ /XoʊC/PAST ↔ /XɪCn/PAST.PART

stride, ride, write, rise, drive, strive (Present-NON3SG) ↔ strode, rode, wrote, rose, drove, strove (Past) ↔ stridden, ridden, written, risen, driven, striven (Past Participle)

Singh & Neuvel (2003) also stress the point that WFS should be only as general as the learned data licenses. Hence, (11) should preferably be written as (12), because all the concerned verbs have an r-final onset before the relevant vowel.

(12) /XɹaɪC/PRES-NON3SG ↔ /XɹoʊC/PAST ↔ /XɹɪCn/PAST.PART

stride, ride, write, rise, drive, strive ↔ strode, rode, wrote, rose, drove, strove ↔ stridden, ridden, written, risen, driven, striven

This requirement prevents WFS from overgenerating, since any verb with the vowel /aɪ/ could otherwise form its past by ablaut (e.g., fight). Note however that WWM does not aim to account only for the attested words, but for any word potentially created by speakers. That is, even if goed is not the standard past form of go, WWM holds that it is


licensed by the grammar. As in all theories, learned forms are preferred, so it will take exceptional circumstances for goed to override went.

3. Our proposal

Our account of paradigm gaps involves two reinforcements of WWM and two partici-pation conditions in the WFS. First, we assume that speakers are able to make phonem-ic subgeneralizations about the data that are significant in some way or another. The second reinforcement is to assume that speakers favor network representations over binary ones, when this leads to an economy of representation. With this in mind, (12) becomes (13) before stride is learned:

(13) /ɹaɪT/PRES-NON3SG ↔ /ɹoʊT/PAST ↔ /ɹɪTn/PAST.PART (T is a dental consonant) e.g. ride, rise, write /Xɹaɪv/PRES-NON3SG ↔ /Xɹoʊv/PAST ↔ /Xɹɪvn/PAST.PART e.g. strive, drive

We admit that there is an open question as to what are the correct subgeneralizations to be made, but as we will see in the next sections, there are good reasons to believe that speakers make subgeneralizations similar to the ones in (13).

3.1. WFS participation conditions

The participation conditions impose limits on which verbs may be inserted in which WFS. They were proposed in Baronian (2005, 2009), but they are here adapted to the framework of WWM. The first condition prevents the learning of a new word (e.g. stride) to undo the subgeneralizations made in (13) until it is confirmed (by learning each form) that stride/strode/stridden are the paradigm’s forms.

(14) Generalization Preservation (GP): Do not force a word into a WFS that would change the previously established generalization.

Nothing of course would prevent a word such as thrive from generating throve and thriven, but dive could never generate *diven, because it is lacking the onset-final /r/. Notice that GP makes correct predictions outside the problem of defective verbs. The examples in (15) suggest that a plural hice for house and meese for moose are possible, while similar ablaut plurals for couch and proof are impossible.

(15a) /Xaʊs/NOUN.SG ↔ /Xaɪs/NOUN.PL (mouse, louse ↔mice, lice) house/hice, but couch/*c[aɪ]ch


(15b) /XuːS/NOUN.SG ↔ /XiːS/NOUN.PL (S is a dental fricative) (goose, tooth ↔geese, teeth) moose/meese, but proof/*preef

A simple search on google.com allows us to confirm this. Indeed, while few native speakers would make those “mistakes”, discussions about why the plural of moose is not meese are much more common than why the plural of root is not reet by a factor greater than 200.

(16) Words rhyming with mouse, louse, goose or tooth “plural of moose” meese 99,600 “plural of booth” beeth 67,500 “plural of mongoose” mongeese 47,900 “plural of house” hice 40,500 Words not rhyming with mouse, louse, goose or tooth “plural of root” reet 200 “plural of proof” preef 9 “plural of mouth” mithe 7 “plural of flute” fleet 1 (Google.com searches retrieved July 1, 2010)

Once the WFS are set up, the second participation condition prevents words from hop-ping from one series of WFS to another.

(17) Counterevidence Respect (CR): Do not insert a word in a WFS if a related word it generates contradicts a learned word.

For example, we do not expect a new French verb in /-ir/ to hop from a WFS inserting a linking consonant /s/ in the 1PL to one inserting /z/ in the 2PL. So if a French speaker knows or has decided that the 1PL of the fictive verb cautrir is cautrissons, she will not generate 2PL *cautrisez, *cautrivez or *cautriez, but will stick with cautrissez.

(18a) /X/PRES-NON3SG ↔ /Xd/PAST e.g. like/liked, but go/*goed because of went and CR

(18b) /Xi/PRES.SG ↔ /Xisɔ̃/PRES1PL ↔ /Xise/PRES2PL /Xi/PRES.SG ↔ /Xizɔ̃/PRES1PL ↔ /Xize/PRES2PL e.g. /li/ /lizɔ̃/ ⇒ lize/*lise ‘read’

In a sense, CR yields a generalized blocking effect, in that it prevents any learned form from being overridden, directly or indirectly (i.e., through WFS hopping). However, this alternative kind of blocking requires no default architecture.


3.2. French

As we saw in (1), French verbs in /-ir/ are fragmented according to the consonant they use to link the stem to the suffix. In (19), we can see that GP and CR prevent frire from being inserted in any of them. The SG forms je fris, tu fris, il frit are easily obtained, because they require no linking consonant, and indeed they are not gapped. The SG /fri/ however cannot be inserted in (19a), because of its special FEM.PAST.PART frite and CR. The WFS in (19b) and (19c) do have similar FEM.PAST.PART, but frire’s phonemic make-up diverges from these verbs’ significantly (they all start by either /Xkr/ or /Xɥi/), so GP prevents its participation in those WFS. (19a) /Xi/PRES.SG ↔ /Xisɔ̃/PRES1PL ↔/Xi/PAST.PART e.g. finis/finissons/fini(e), rugis/rugissons/rugi(e), etc. (19b) /Xɥi/PRES.SG ↔ /Xɥizɔ̃/PRES1PL ↔ /Xɥi/MASC.PAST.PART ↔ /Xɥit/FEM.PAST.PART e.g. conduis/conduisons/conduit/conduite, cuis/cuisons/cuit/cuite... (19c) /Xkri/PRES.SG↔/Xkrivɔ̃/PRES1PL↔/Xkri/MASC.PAST.PART↔/Xkrit/FEM.PAST.PART e.g. écris/écrivons/écrit/écrite, proscris/proscrivons/proscrit/proscrite... Therefore, the verb frire is incapable of participating in any of the WFS. As we will see in the following sections, very similar situations arise in other languages.

3.3. Spanish

We will illustrate the Spanish gaps with two verbs, abolir and balbucir, which represent the two types of gaps reported by Albright (2003). The first type, represented here by abolir, seems to have two candidate forms for the PRES1SG: *abolo or *abuelo, the latter with the same morphophonological vowel change as verbs like dor-mir/duermo. (20a) /XoCir/INFINITIVE ↔ /XweCo/PRES1SG ↔ /XuCjendo/PRES.PART

(C is a cluster) e.g. dormir/duermo/durmiendo, morir/muero/muriendo...

The verb abolir cannot participate in the WFS in (20a), because its PRES.PART, abolien-do, already diverges from the form that this WFS would generate (abuliendo), so this insertion is prevented by CR. In (20b) below, we see that Spanish verbs with a PRES-PART similar to abolir’s all have either /a/, /i/ or /e/ as the vowel preceding /-ir/.

(20b) /XaCir/INFINITIVE ↔ /XaCo/PRES1SG ↔ /XaCjendo/PRES.PART /XuCir/INFINITIVE ↔ /XuCo/PRES1SG ↔ /XuCjendo/PRES.PART /XiCir/INFINITIVE ↔ /XiCo/PRES1SG ↔ /XiCjendo/PRES.PART (C is a cluster) e.g. batir/bato/batiendo, partir/parto/partiendo...


sumir/sumo/sumiendo, surtir/surto/surtiendo... vivir/vivo/viviendo, incidir/incido/incidiendo...

The verb abolir having a vowel /o/ in this position, it therefore cannot be inserted in (20b) either, because of GP. The second type of Spanish gap consists of defective verbs with an infinitive ending in /-usir/, as in balbucir. This type requires a little more atten-tion. Here, it cannot be inserted in (20b) because no verb in /-usir/ participates in (20b). The second WFS in (20b) should thus be rewritten as (20c)

(20c) /XuCir/INFINITIVE ↔ /XuCo/PRES1SG ↔ /XuCjendo/PRES.PART (C is a cluster that is not an /s/)

As we did earlier, we acknowledge that it is not obvious how speakers “catch” a gene-ralization such as the one in (20c). It does seem to be significant though that all other verbs in /-usir/ either end in /-lusir/ or /-dusir/, as we can see in (20d).

(20d) /Xlusir/INFINITIVE ↔ /Xlusko/PRES1SG /Xdusir/INFINITIVE ↔ /Xdusko/PRES1SG

The WFS in (20d) must be stated separately from (20c) because of the special morpho-phonological insertion of a /k/ in the PRES1SG. Verbs like balbucir thus cannot be in-serted in (20d) either for GP reasons.

3.4. English

We mentioned earlier that some English speakers have a PAST.PART gap for the verb stride and saw how part of the English WFS forming the PAST.PART is split according to patterns observed in the lexicon. We repeat (13) as (21) below for convenience:

(21) /ɹaɪT/PRES-NON3SG ↔ /ɹoʊT/PAST ↔ /ɹɪTn/PAST.PART (T is a dental consonant) e.g. ride, rise, write /Xɹaɪv/PRES-NON3SG ↔ /Xɹoʊv/PAST ↔ /Xɹɪvn/PAST.PART e.g. strive, drive

Once a speaker knows the forms stride/strode, she cannot insert either form in either WFS in (21), because of GP. Indeed, the first WFS requires a verb to be /r/-initial and end in a dental (coronal) consonant in the PAST and PRES.NON-3SG, while the second one requires the latter forms to end in /v/. Note that the form *strided cannot be gener-ated either, CR preventing this once the irregular PAST form strode is learned. If how-ever the form strode were never to be learned by a speaker, we predict that the verb would simply get regularized to stride/strided/strided.

Albright (in press) also cites dive, smite and strive as sometimes gapped in English. A speaker who never learns the PAST.PART dived, but has dive and the innovative PAST


dove is likewise predicted to have a PAST.PART gap under our account, for the same reasons as stride. What we are claiming then is that the PAST.PART dived must be learned by English speakers who have dove. This is yet another difference between our account and general default accounts: for the latter, -ed PAST.PART are always regular and predictable; for us, it depends on the rest of the forms participating in the WFS. The case of smite/smote is identical to that of stride. The case of strive requires a little more attention: if the form striven is lost, then the second WFS (21) is never part of the grammar. In such a case, drive/drove/driven would behave as a hapax legomenon and not yield a WFS.

Our proposal for analyzing gaps within WWM thus works well for English, although it makes two predictions that yet need to be confirmed empirically: 1) speakers who have regularized the PAST of a verb like stride, smite, strive (to strided, smited or strived) would not have a PAST.PART gap; 2) the PAST.PART dived is learned by speak-ers, even if it has what other theories call a “regular” shape. A third prediction concern-ing strive is also possible, depending on the particular implementation one would even-tually adopt of the generalization-making algorithm. The issue is whether knowing the forms of stride and drive would be sufficient to posit (22):

(22) /XɹaɪC/PRES-NON3SG ↔ /XɹoʊC/PAST ↔ /XɹɪCn/PAST.PART e.g. stride, drive

If so, then we predict that is it impossible for such speakers (who know the forms of both stride and drive) to have a gap for strive. Baronian (2005), while unaware of the possible gaps of strive, did show that the ratio of striven forms over other forms of strive was much higher than that of stridden over its other forms, indicating that striven gaps are at least more common than stridden ones. Because drive/drove/driven has such a high frequency, its forms are unlikely to get lost, so learning stridden could have the automatic effect of yielding (22). Whether there are speakers with a stridden gap among those with a striven gap remains, however, an (empirically) open question.

3.5. Russian

Russian gaps are famous at least since Halle (1973) who brought to the attention of generative grammarians that 1SG.NON-PAST forms are lacking for some verbs of the second conjugation that could potentially undergo a palatalization process in this per-son. Recently, the problem has attracted the attention of Baerman (2008), Daland et al. (2007) and Sims (2006). What is striking to us is that all these accounts of Russian gaps end up stating, one way or another, that the said gaps are learned. This could not possi-bly mean that unheard forms are never generated, as new forms would then never arise diachronically. It could mean however (as Daland et al. 2007 most explicitly state) that speakers hear the other forms of these verbs enough to know that statistically the miss-


ing ones are less common than they should be. Our skepticism towards this approach is twofold. First, we find it odd that gaps would then typically occur with rare verbs. It seems to us that under this approach, gaps should be more common with frequent verbs for which speakers can make more reliable predictions about the lower relative occur-rence of a form, but as pointed out by Albright (2003), this does not appear to be the case. Second, as pointed out by Albright (2003, in press), the problem of why gaps occur when a morphophonological or suppletive alternation is potentially involved is evacuated, not to mention the cases of diverging participles in French (frite) and Span-ish (aboliendo), which, as we will see, have close analogues in Russian. Under the lexi-cal approach, it would appear that gaps could occur under any circumstance. For exam-ple, why are there no reported PAST.PART gaps for English stick, dig, sting, string, swing? It seems to us that the available verbs in the lexicon are simply diverse enough to yield the WFS in (23):

(23) /XɪK/PRES-NON3SG ↔ /XʌK/PAST ↔ /XʌK/PAST.PART K is a velar consonant

Perhaps the generalization made by speakers is even looser to include the verb spin, but this would only strengthen our point: if one of the PAST.PART were to be not learned (or, in Daland et al.’s terms, be relatively infrequent enough for speakers to notice) speakers could always use (23).

In the specific case of Russian, a lexical analysis of gaps has to explain what appears to be a strikingly coincidental fact: neological verbs originating in borrowings from English computer terms display gaps. How then can these gaps have been learned, since there were no preexisting corpora for speakers to infer them? Here is an example of a blogger pondering about the correct 1SG of the verb ‘to friend’:

(24) Friending policies: новых френдов я очень всячески приветствую и коплю, но ради одной только взаимности не френдю (или не френжу?). А зато френдю (-жу) тех, кого приятно и/или интересно читать.

http://mashaaaa.livejournal.com

Friending policies: I accept new friends, but I don’t make friends [frend'u] (or frenžu?) only for reciprocity. However, I make friends [frend'u] (-žu) whom [I find] interesting and pleasant to read. (authors’ translation)

Below is a list of similar verbs, which have a similar coronal-ending stem that palatal-ize in non defective verbs of the second conjugation:

(25) Verb Transliteration Gloss Флудить fludit’ to flood чатить(-ся) čatit’(-sja) to chat (за-), (о-) бутить (za-), (o-) butit’ to boot Перебутиться perebutit’sja to boot


Гейтиться gejtit’sja to gate Коннектиться konnektit’sja to connect (от-) роутить (ot-) routit’ to route Френдить frendit’ to friend Апгрейдить apgrejdit’ to upgrade (за-) холдить (za-) holdit’ to hold (за-) фитить (za-) fitit’ to fit (по-) фиксить (po-) fiksit’ to fix Фоксить foksit’ to use FoxPro Факсить faksit’ to fax

In order to verify whether these words truly behave like traditional Russian defective verbs, we conducted a survey with 23 native Russian speakers, mostly students at a technological university in Moscow. We selected 37 verbs (10 verbs known to be de-fective, 9 neological verbs borrowed from English, 10 low frequency verbs and 8 non defective distractor verbs). In a written survey inspired by Albright (2003), subjects were asked to produce the 1SG NON-PAST of these verbs to complete a sentence and rate their confidence from 1 to 4 (4 being the most confident), for example:

(26) Я (апгрейдить) мой компьютер. (Confidence 1-2-3-4)

Admittedly, the weak point of this method is that speakers feel compelled to provide an answer. In the case of defective verbs, this is potentially problematic as the expected answer is “no form”, but speaker rarely expressed this option. This kind of problem is unavoidable for all researchers who try to quantify what is in the end a qualitative an-swer. Our assumption then is that, to the extent that Russian defective verbs are a valid category, we should expect a close behavior between the verbs known to be defective in traditional grammars and the recent English borrowings. Our global results are shown in Table 1.

Verb type Alternating Non alternating Other responses Confidence Known defective 48.70 % 39.57 % 11.74 % 2.50 Neological 48.30 % 45.89 % 05.79 % 2.05 Low frequency 66.08 % 25.65 % 08.26 % 2.26 Distractors 91.85 % 05.98 % 02.17 % 3.72

Table 1: Global results of the survey

As expected, the two main types of responses were alternating (with palatalization) and non alternating, although other responses were sometimes given. The confidence index showed no significant difference between the known defective, neological and rare verbs, which is in line with Albright’s (2003) analysis of defective verbs as some kind of extreme uncertainty. On the other hand, we found a significant difference between low frequency verbs on one hand and what we take to be the defective verbs (known or


neological) on the other, as well as between the low frequency verbs and the distractor verbs. While the distractor verbs have a palatalization rate of over 90%, about 2/3 of the low frequency ones behave the same way, while only half of the other two types of verbs palatalized. In order to determine the significance of this apparent three-way grouping of the four verb types, two statistical methods were used (Genmod and Glim-mix procedures of SAS), which gave near-identical results.

(27) The % of palatalized known defective and neological verbs were indistinct (p=86.3%).

The % of palatalized low frequency verbs was distinct from the neological verbs (p=0.02%).

The % of palatalized distractor verbs was distinct from the neological verbs (p<0.01%).

The % of non palatalized known defective and neological verbs was distinct (p=18.19%), but the difference was small (6.32%).

The % of non palatalized low frequency verbs was distinct from the neological verbs (p<0.01%).

The % of non palatalized distractor verbs was distinct from the neological verbs (p<0.01%).

Thus overall, we note only a small difference between the non-alternating responses of known defective and neological verbs with not a very high significance. Note in passing that for a significant number of low frequency verbs (over 25%) and even for over 5% of distractor verbs, answers without palatalization were possible. This stands in contrast to Baerman’s (2008) observation that palatalization is exceptionless in (Standard) Russian, which is his justification for dismissing the possibility that gaps are the result of competi-tion between morphological options. Even if we ignore the fact that there are two ways of palatalizing verbs in /-t/ (č or šč), the contrast between our results and Baerman’s observa-tion highlights the problems of confronting a phenomenon based on speakers’ varying intuitions with the (sometimes) leveled out standard of a language.

The key to our analyses of gaps in different languages so far has been to show that what are traditionally referred to as paradigms stem from WFS that are fragmented ac-cording to subgeneralizations of their form. In the case of Russian, can we hope to find such a fragmentation? Albright (in press) brings the beginning of a positive answer, as can be seen in Table 2 below. It turn out that when Russian verbs are grouped by traditional roots, the second conjugation is extremely fragmented, especially the dental-final roots:

Final C Fixed stress alternating stress Total p 12 2 14 b 10 0 10 m 9 2 11 v 12 2 14


Final C Fixed stress alternating stress Total t 19 10 29 d 19 7 26 s 7 3 10 z 9 1 10

Table 2: Fragmentation of Russian verbal roots, from Albright (in press)

WWM does not have roots as a concept, but the Russian cases of prefixed roots are similar to English latinate formations, such as conduce/conduction, induce/induction, reduce/reduction, etc. (Neuvel & Singh 2002):

(28) /Xduːs/VERB ↔ /Xdʌkʃn/NOUN

Therefore, it could be the case that each set of Russian root would yield a separate WFS, though some groupings may also be possible. Further, we observed that the Rus-sian conjugation is even more fragmented when the past participle is taken into ac-count, as illustrated by the following verbs:

INFINITIVE PAST.PART 1SG.NON.PAST rodit' rozhd'onnyj (alt 1) rozhu (alt 2) obgorodit' obgorozhennyj (alt 2) obgorozhu (alt 2) pronzit' pronz'onnyj (no alt) pronzhu (alt 2) zapretit' zapreshtshonnyj (alt 1) zapreshtshu (alt 1)

Table 3: Fragmentation of Russian verbal alternation patterns

Hence the fragmentation shown in Table 2 and the one in Table 3 could give ample room, respectively, for GP and CR to operate. Because of the vast number of Russian defective verbs and the tentative status of what counts as a generalization in our ap-proach, a case-by-case explanation would leave too many open questions for this paper (though see Baronian 2005 for such an attempt). However, we view the general align-ment of the Russian facts with those of French, Spanish and English as very encourag-ing for our approach.

4. Conclusion and reflections on irregularity and paradigms

As we have seen, we offer an account of paradigm gaps that resist analysis by definition in default-type frameworks of morphology. In sum, WWM can account for paradigm gaps of defective verbs without the following pitfalls of other accounts: no arbitrary feature (Halle 1973); no assumption that word-formation is arbitrarily directional (Mo-rin 1987, 1995); no false assumption that Russian palatalization is automatic (Daland et al. 2007, Baerman 2008). Albright (2003, in press), with who this analysis shares a lot, also avoids these pitfalls, but contra his analysis, we take into account complete mor-


phological network results. We also acknowledge his argument that competition be-tween morphological options normally leads to variation (and not gaps), but our use of independently justified WFS participation conditions allows us to make a stronger statement than he does: paradigm gaps are the result of having no acceptable morpho-logical option. The general problem seems to be that they behave or look partially like one set of verbs and partially like another set. We thus suggest the metaphor that they are “caught” between classes of verbs.

The (defective) verbs examined in this paper that exhibit gaps in their set of finite forms display competition between more than one strategy in the formation of the rele-vant forms and, for pedagogical reasons, involve a (non automatic) morphophonologi-cal alternation (type 3.1). It should not be too difficult however to extend our analysis to any gap of types 3.2 or 3.3. As an example of 3.2, English forgo somewhat behaves like go, as it has the PAST.PART forgone, akin to gone, but for the more rarely occurring PAST of this verb, speakers cannot use the hapax legomenon strategy:

(29) /goʊ/PRES-NON3SG ↔ /wɛnt/PAST ↔ /ɡɔn/PAST.PART

As an example of 3.3, if we assume with Morin (1987) that French colorier is analyzed by speakers as having an underlying /j/, then the alternation between /j/ and /i/ in simi-lar French verbs is a morphophonological one. This is in fact not unlikely, given that there is a contrast between the pronunciations of words like paye [pɛj] and pays [pɛi], or carillon [kaʁijɔ̃] and marions [maʁjɔ̃]. The [j] in the latter could be analyzed as ei-ther /i/ or /j/. If /j/, then, in WWM, this yields a special WFS form words such as carier ‘decay (of teeth)’, marier ‘marry’, varier ‘vary’, parier ‘bet’:

(30a) /Xaʁje/iNFINITIVE ↔ /Xaʁi/PRES-NON3SG

By GP, colorier could not participate in (30a). And while we found other verbs in -orier, they all actually ended in -torier (inventorier, répertorier). Given Singh & Neu-vel’s (2003) principle that WFS must only be as general as the data licenses, it does not seem out of line with the preceding examples to state the following WFS for inventori-er and répertorier, which colorier cannot integrate for GP purposes:

(30b) /Xtɔʁje/INFINITIVE ↔ /Xtɔʁi/PRES-NON3SG

It may seem ad hoc to posit (30a) and (30b) as separate WFS, but notice that we have used the same strategy throughout this paper: small classes of exceptional verbs divided into sub-generalizations according to their phonological shape. Although we can’t claim to yet fully understand when this type of sub-grouping occurs, its recurring use-fulness in the analysis of paradigm gaps allows us to think we are on the right track. Further, the assumption that an underlying form is unacceptable runs against the RICH-NESS OF THE BASE principle of Prince & Smolensky (1993), which has gained wide-spread acceptance in contemporary phonology.


However, so far, we have nothing to say about paradigmless verbs (our type 2 defec-tive verbs), such as English beware and French douer. We hope to have made our point general enough, so that it is clear it does not depend specifically on adopting WWM as one’s theory of morphology. We do hope however that the reader will appreciate that the lack of general defaults in WWM is what made it originally attractive to us as a theory for implementing the ideas outlined in Baronian (2005, 2009).

The absence of a regular/irregular distinction in WWM (all WFS having the same potential) falls in the same line of advantages of the theory. Productivity in WWM is a factor of the generalizations speakers make from the data and their usage habits (fre-quency of lexicalized words, size of lexicalized classes of words, desire for innovation), but WWM has no such notion as a primitive. Likewise, WWM has no pre-established paradigms; they emerge from the networks of WFS, yet, without irregularity or para-digms as a priori concepts, WWM can account for the irregularity of paradigm gaps better than previous accounts and other theories. In order to hope to achieve similar results, theories such as Distributed morphology and Paradigm Function Morphology must abandon the notion of default rules and the regular/irregular distinction. Further, while abandoning the notion of paradigm is not necessary to account for paradigm gaps, doing so would yield a simpler theory.

Finally, a word should be said about the relationship between our view of WWM (enriched by the two participation conditions) and the issue of rules vs. analogy. First, while there is some pattern analogy involved in the model, it is a very constrained one (one could never for example create a plural for couch by raising its diphthong as one does with mouse). Second, in our view, the rule/analogy distinction of Pinker (1999) corresponds to a continuum between fully specified suppletive lexical relations and completely unrestricted regular WFS.

It remains an open question whether the lexical suppletive relations should be consi-dered morphological or where one should draw the line. For example, is the relation-ship between heat and hot, or wet and water, simply lexical? They obviously cannot be used for production, because they are too specific, but are they actively used in recog-nizing words? The issue, of course, is linked to the precise algorithm WWM should eventually adopt for making the same phonic generalization about the data that speak-ers make. Our observations about gaps and discussions of potential plurals such as hice (and the absence of such discussions for words such as couch) strongly suggest that speakers make such generalizations, but what they are exactly remains to be shown.

suppletive English go: /goʊ/PRES-NON3SG ↔ /wɛnt/PAST English hapax: /hiːt/NOUN ↔/hɔt/ADJ (cf. seat/*sot) irregular /XVmidlowC/NOUN.SG ↔ /XVmidhigh/NOUN.PL (partially restricted) French irregular plural: boeuf/boeufs, oeuf/oeufs, os/os /XɪCvelar/PRES-NON3SG ↔ /XʌCvelar/PAST.PART English ablaut: dig/dug, ring/rung, sing/sung


irregular /XVC/NOUN.SG ↔ /X¨VCer/NOUN.PL German umlaut: Buch/Bücher (partially restricted) /CX/VERB ↔ /rəCX/VERB French repetitive: prendre/reprendre /VX/VERB ↔ /reVX/VERB French repetitive: apprendre/réapprendre regular /X/PRES-NON3SG ↔ /Xd/PAST (unrestricted) English regular past: love/loved

Table 4: WWM as a single-route model (with stops along the way)

Abbreviations

DENT dental PRES present FEM feminine SG singular MASC masculine WFS Word-Formation Strategy PART participle WWM Whole-Word Morphology PL plural

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