gradient phonotactics in muna and optimality theory...

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Gradient phonotactics in Muna and Optimality Theory * Andries Coetzee and Joe Pater University of Michigan and UMass, Amherst October 7, 2005 1. Introduction Arabic verbal roots are subject to a well-known restriction on the co-occurrence of homorganic consonants (Greenberg 1950, McCarthy 1988). Frisch, Pierrehumbert and Broe (2004) draw attention to the fact that this restriction displays considerable gradience. For example, a coronal stop is very unlikely to appear with another coronal stop, is somewhat more likely to appear with a coronal fricative, and can appear freely with coronal sonorants and stops of other places of articulation. From this observed lexical distribution, we may reasonably infer that Arabic speakers recognize at least three degrees of well-formedness for roots with homorganic segments. A verbal root with a pair of coronal stops is ill-formed, one with a coronal stop- sonorant pair is well-formed, and one with a coronal stop-fricative pair is of an intermediate degree of well-formedness. While this particular example of intermediate well-formedness was recognized in earlier literature (McCarthy 1994), no fully formalized account of it was provided, and this general form of gradience remains unaccounted for in generative phonology, including Optimality Theory (Prince and Smolensky1993/2004). Frisch et al. (2004) refer to this type of gradience, in which phonological structures differ in the degree to which they are attested in the lexicon, as gradient phonotactics. This can be distinguished from another type of phonological gradience, variation, in which a single morpheme displays more than one output form in a given phonological environment. A simple hypothetical case of gradient phonotactics would be one in which words of a language typically lack codas, though a few words do have them. Codas in this language would neither be perfectly acceptable nor completely ruled out. This example highlights the relationship between gradient phonotactics and exceptionality: instances of gradient phonotactics can often be expressed in terms of a continuum between ill-formed, exceptional, and well-formed structures, though as we will see, this three-way distinction does not seem to be sufficient to capture the observed degrees of gradience in Arabic and elsewhere. Variation, on the other hand, is at work when the final consonant in a word is sometimes parsed as a coda, and sometimes deleted, in the same phonological context. This too is gradience, in that codas are neither completely acceptable nor unacceptable, but it is gradience observed in a single lexical item, rather than across the lexicon. Frisch et al. (2004) point out that extant accounts of variation in Optimality Theory (e.g. Anttila 1997, 2002, Boersma 1998, Boersma and Hayes 2001) cannot deal with gradient phonotactics, since in Arabic, and presumably many other such cases, a given lexical item has a fixed output * Special thanks to René van den Berg for sharing an electronic version of his Muna dictionary with us (Berg and Sidu 1996), and for his comments on parts of this research. Portions of this work were presented at the University of Victoria, New York University, the Manchester Phonology Meeting, the University of Edinburgh and at the Seoul Phonology Conference. We’d like to thank the participants for helpful discussion, and especially the following people at those events and elsewhere: Adam Albright, Lisa Davidson, Kathryn Flack, Stefan Frisch, Diamandis Gafos, Ben Gelbart, Greg Guy, Mike Hammond, Bruce Hayes, Shigeto Kawahara, John Kingston, John McCarthy, Elliot Moreton, Mits Ota, Steve Parker, Lisa Selkirk, Bruce Tesar, Anne-Michelle Tessier and Su Urbanczyk.

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  • Gradient phonotactics in Muna and Optimality Theory*

    Andries Coetzee and Joe PaterUniversity of Michigan and UMass, Amherst

    October 7, 20051. Introduction

    Arabic verbal roots are subject to a well-known restriction on the co-occurrence of homorganicconsonants (Greenberg 1950, McCarthy 1988). Frisch, Pierrehumbert and Broe (2004) drawattention to the fact that this restriction displays considerable gradience. For example, a coronalstop is very unlikely to appear with another coronal stop, is somewhat more likely to appear witha coronal fricative, and can appear freely with coronal sonorants and stops of other places ofarticulation. From this observed lexical distribution, we may reasonably infer that Arabicspeakers recognize at least three degrees of well-formedness for roots with homorganicsegments. A verbal root with a pair of coronal stops is ill-formed, one with a coronal stop-sonorant pair is well-formed, and one with a coronal stop-fricative pair is of an intermediatedegree of well-formedness. While this particular example of intermediate well-formedness wasrecognized in earlier literature (McCarthy 1994), no fully formalized account of it was provided,and this general form of gradience remains unaccounted for in generative phonology, includingOptimality Theory (Prince and Smolensky1993/2004).

    Frisch et al. (2004) refer to this type of gradience, in which phonological structures differ in thedegree to which they are attested in the lexicon, as gradient phonotactics. This can bedistinguished from another type of phonological gradience, variation, in which a singlemorpheme displays more than one output form in a given phonological environment. A simplehypothetical case of gradient phonotactics would be one in which words of a language typicallylack codas, though a few words do have them. Codas in this language would neither be perfectlyacceptable nor completely ruled out. This example highlights the relationship between gradientphonotactics and exceptionality: instances of gradient phonotactics can often be expressed interms of a continuum between ill-formed, exceptional, and well-formed structures, though as wewill see, this three-way distinction does not seem to be sufficient to capture the observed degreesof gradience in Arabic and elsewhere. Variation, on the other hand, is at work when the finalconsonant in a word is sometimes parsed as a coda, and sometimes deleted, in the samephonological context. This too is gradience, in that codas are neither completely acceptable norunacceptable, but it is gradience observed in a single lexical item, rather than across the lexicon.

    Frisch et al. (2004) point out that extant accounts of variation in Optimality Theory (e.g. Anttila1997, 2002, Boersma 1998, Boersma and Hayes 2001) cannot deal with gradient phonotactics,since in Arabic, and presumably many other such cases, a given lexical item has a fixed output * Special thanks to René van den Berg for sharing an electronic version of his Muna dictionary with us(Berg and Sidu 1996), and for his comments on parts of this research. Portions of this work werepresented at the University of Victoria, New York University, the Manchester Phonology Meeting, theUniversity of Edinburgh and at the Seoul Phonology Conference. We’d like to thank the participants forhelpful discussion, and especially the following people at those events and elsewhere: Adam Albright,Lisa Davidson, Kathryn Flack, Stefan Frisch, Diamandis Gafos, Ben Gelbart, Greg Guy, Mike Hammond,Bruce Hayes, Shigeto Kawahara, John Kingston, John McCarthy, Elliot Moreton, Mits Ota, Steve Parker,Lisa Selkirk, Bruce Tesar, Anne-Michelle Tessier and Su Urbanczyk.

  • Gradient phonotactics in Muna and OT p.2

    form – no variation is reported. Here we extend one OT approach to exceptionality to gradientphonotactics: that of indexed faithfulness constraints (Kraska-Szlenk 1997, Fukuzawa 1999, Itôand Mester 2000, 2001, Pater 2000). In this account, markedness constraints are rankedaccording to the degree to which they are obeyed in the lexicon, and lexically specificfaithfulness constraints are interspersed between them. We introduce this approach in section 2by analyzing Arabic data in terms of relativized OCP-PLACE constraints (Selkirk 1991,McCarthy 1994, Padgett 1995). For the example mentioned in the first paragraph, we show howranking an OCP constraint relativized to coronal obstruents agreeing in continuancy (OCP-COR[-SON][αCONT]) above a more general OCP constraint on coronals agreeing in sonorancy (OCP-COR[αSON]) expresses the greater ill-formedness of words with pairs of coronal stops (orfricatives) than words with coronal stop/fricative pairs.

    Frisch et al. (2004) propose an alternative to an OCP-based analysis of Arabic, in whichsimilarity between homorganic consonants is predicted to correlate with observed rates of co-occurrence. Besides the ability of this account to deal with gradient well-formedness, Frisch etal. (2004: 19) argue for it on the basis of its greater predictiveness. In the similarity metricaccount, pairs of consonants that are equivalent in terms of similarity should always patterntogether in co-occurrence restrictions. An account based on relativized OCP-PLACE constraintsincorporated into OT, however, does not make the same predictions: there is no reason whylanguages could not vary in terms the rankings of the various constraints. For example, thesimilarity metric might assign both the coronal stop-fricative pair /s-t/ and the labial stop pair /b-p/ a rating of .50 (as it in fact does in Muna – see 3.3), making a prediction that their rates of co-occurrence should be roughly the same. The relevant OCP constraints, OCP-COR[αSON] andOCP-LAB-[-SON][αCONT], however, need not be ranked together, and could in fact assume eitherdominance relation.

    In section 3, we introduce data from the Austronesian language Muna (Berg 1989) that show thatthe greater predictiveness of the similarity metric may be a liability, rather than an asset. As inArabic, homorganic consonants tend not to co-occur within roots, and the degree of under-representation of a homorganic pair of consonants negatively correlates with their featuralsimilarity. However, whereas in Arabic and other languages with documented place co-ocurrence restrictions similarity is primarily defined by sonorancy, in Muna it is voicing thatplays the dominant role. Thus, languages do vary in ways unexpected by the similarity metric. Inaddition, in Muna as in Arabic, coronals are relatively free to co-occur compared to labials anddorsals. However, unlike Arabic, the coronal inventory is not especially large in Muna, which isunexpected under Frisch et al.’s account of the Arabic coronal facts. We provide an analysis ofthe Muna data and its differences from Arabic in terms of lexicon-reponsive ranking ofrelativized OCP constraints. We also apply the similarity metric to Muna, and discuss the waysin which Muna supports, and challenges, Frisch et al.’s proposal.

    Since gradient phonotactics are not usually dealt with in generative phonology, it might beimagined that they could be excluded from its scope. In section 4, we argue against this position,drawing on experimental results indicating native speaker knowledge of gradient well-formedness. We then discuss some of the questions for empirical research opened up by theincorporation of gradient phonotactics, and related well-formedness judgments, intophonological theory. The learnability challenges that gradient phonotactics pose might provide a

  • Gradient phonotactics in Muna and OT p.3

    concrete reason to exclude them from phonology proper: we also use the fourth section of thepaper to address this issue.

    2. Arabic and the problem of lexical gradience

    In Arabic, there is a restriction against homorganic consonants in adjacent positions within theverbal root (Greenberg 1950, McCarthy 1988, 1994, Pierrehumbert 1993, Padgett 1995, Frisch etal. 2004). Given Arabic’s root-and-pattern morphological system, these consonants are oftenseparated by vowels supplied by other morphemes, so they are not necessarily adjacent in thephonological string. There are a number of exceptions to this general restriction, but thedistribution of these exceptions is not random. Frisch et al. (2004) examined the degree to whichparticular pairs of consonants are underrepresented in a list of 2,674 roots taken from adictionary of standard Arabic (Cowan 1979). For each pair, they calculated anObserved/Expected ratio, that is, the number of observed words with a particular pair ofconsonants divided by the number that would be expected if the consonants co-occurred freely.The lower the O/E value, the more underrepresented a pair is. Frisch et al.’s results, collapsedover place of articulation, are shown in Table 1. It should be noted that they omitted pairs withidentical consonants, which behave differently; we have also omitted the pharyngeals, sincethese are irrelevant to a comparison with Muna, the language we discuss in section 3.

    Labial Dorsal Coronal Sonorant Coronal Fricative CoronalPlosive

    b f m k g q l r n θ s z s z t d t d

    Labial 0.00Dorsal 1.15 0.02CoronalSonorant 1.18 1.48 0.06

    CoronalFricative 1.31 1.16 1.21 0.04

    CoronalPlosive 1.37 0.80 1.23 0.52 0.14

    Table 1 O/E for “adjacent” consonants in Arabic verbal roots

    O/E values for pairs of homorganic consonants in this table are generally near zero. However,within the coronals, there are several degrees of representation, as discussed in the introduction.Pairs of coronals that are both plosives, both fricatives, or both sonorants are highlyunderrepresented. Sonorants co-occur with plosives and fricatives at a rate slightly higher thanexpected. Fricative-plosive pairs co-occur at an intermediate rate.

    McCarthy (1988) accounts for the split between sonorants and obstruents by specifying that theconstraint against homorganic segments, the OCP for consonantal place, applies only within thesubclasses of coronals defined by the manner feature [+/-sonorant]. In Dresher (1989), Selkirk(1991), and Padgett (1995), the general OCP constraint is elaborated into a set of more specificconstraints that are violated only by segments that are identical in particular ways (see especiallyPadgett 1995 on this aspect of the proposal). The relativized OCP constraints that would

  • Gradient phonotactics in Muna and OT p.4

    correspond to McCarthy’s (1988) groupings appear in (1).1 In McCarthy’s analysis, theconsonants in question are assumed to be adjacent at a derivational level in which interveningvowels are absent.

    (1) OCP-LAB Adjacent labials are prohibitedOCP-DOR Adjacent dorsals are prohibitedOCP-PHAR Adjacent pharyngeals are prohibitedOCP-COR[αSON] Adjacent coronals agreeing in [+/-sonorant] are prohibited

    These constraints are categorical: the grammar bans pairs of consonants that fall under theirscope, and permits ones that do not. With OCP-COR relativized to [+/-sonorant],obstruent/sonorant pairs of coronals are permitted, while pairs of obstruents and pairs ofsonorants are banned.

    The difficulty is in creating a grammar compatible with the intermediate degree of representationof the fricative/stop pairs; given the constraints in (1), they should be ruled out. If the OCP-CORfor obstruents is further specified to apply only between segments that have the same value for[+/-continuant], as in Padgett (1995), then there is no restriction on stop/fricative pairs. Neitherof these seems correct. McCarthy (1994) states that continuancy restriction on the OCP-COR is“not absolute”, though this is not further formalized.

    The ranked and violable constraints of Optimality Theory offer a way out of this dilemma, butnot in their standard interpretation. In (2), a further elaborated set of OCP-COR constraints ispresented. We continue to use the term ‘adjacent’, but under the standard OT assumption thatmarkedness constraints apply at the surface, adjacency must be defined so as to ignoreintervening vowels (see Suzuki 1998, Rose 2000):

    (2) OCP-COR No adjacent coronalsOCP-COR[+SON] No adjacent coronal sonorantsOCP-COR[-SON] No adjacent coronal obstruentsOCP-COR[-SON][αCONT] No adjacent coronal obstruents agreeing in continuancy

    The ranking of these constraints that is appropriate for Arabic is as in (3):

    (3) OCP-COR[-SON][αCONT], OCP-COR[+SON] >> OCP-COR[-SON] >> OCP-COR

    Pairs of segments that meet the definition of the constraints in the top-most stratum are highlyunderrepresented, with O/E values approaching 0. Pairs of segments that fall outside the scope ofthose constraints, but that do meet the definition of the constraint in the middle stratum have anO/E value of 0.52. Pairs of segments that meet only the definition of the lowest ranked constrainthave an O/E value of above 1.

    1 McCarthy (1988) also divides the dorsals by sonority, classifying /w, j/ as the dorsal sonorants, thoughhe states that their lack of co-occurrence may have other explanations.

  • Gradient phonotactics in Muna and OT p.5

    The problem is that neither standard OT, nor the versions that have been proposed to handlevariation, allow the ranking in (3) to express an Arabic speaker’s knowledge of the observedlexical gradience. For a markedness constraint to be violated, a conflicting constraint mustoutrank it. Because we are not dealing with alternations, we will use the undifferentiatedfaithfulness constraint in (4):

    (4) FAITH The Input representation and the Output representation are identical

    FAITH must be ranked above OCP-COR, so that obstruent-sonorant pairs surface intact. It must beranked beneath the topmost stratum, so that sonorant pairs as well as obstruent pairs agreeing incontinuancy will be altered to fit the demands of the markedness constraints (we temporarilyabstract from the small set of exceptions). The issue is the ranking of FAITH with respect to OCP-COR[-SON]. Placed below it, stop-fricative pairs are ruled out. Placed above it, they are perfectlywell-formed. We again face the quandary that neither of these seems correct.

    If the ranking between these constraints is allowed to vary each time the grammar is employed,as in models like those of Anttila (1997) and Boersma (1998), then a word with a stop-fricativepair will vary between a faithful output, and one that is altered (for example by deleting, orchanging the place, of one of the segments). But lexical items in Arabic that have stop-fricativepairs are not reported to show variation. Hammond’s (2004) approach to lexically gradientacceptability does not distinguish between variation and exceptionality, and without furthermodification also leaves this issue unresolved. Zuraw (2000) does extend Boersma’s (1998)theory to patterned exceptionality by having a USE-LISTED constraint block variation, but thisaccount only covers cases involving alternation.

    In a theory with lexically specific constraints, we can resolve this dilemma by having a specificversion of FAITH that is indexed to words that contain stop-fricative pairs. This constraint FAITH-L ranks above OCP-COR[-SON], thus protecting them from its demands:

    (5) OCP-COR[-SON][αCONT], OCP-COR[+SON] >> FAITH-L >> OCP-COR[-SON] >> FAITH >> OCP-COR

    The next step is to provide a means by which a speaker could compute the relativegrammaticality of forms from the ranking in (5). So far, one might simply say that a speakerknows that forms with stop-fricative pairs must be lexically marked as exceptions, and that thisgives them an intermediate status between forms that are ruled out completely (for which therelevant markedness constraints dominate FAITH-L), and those that are perfectly acceptable (forwhich the relevant markedness constraints are dominated by FAITH).

    However, this would not be sufficient to deal with further degrees of gradience. In Arabic, formsthat violate OCP-COR[-SON][αCONT] and OCP-COR[+SON] are very rare, but are attested. Thismeans that faithfulness must rank above these constraints:

    (6) FAITH-L2 >> OCP-COR[-SON][αCONT], OCP-COR[+SON] >> FAITH-L1 >>OCP-COR[-SON] >> FAITH >> OCP-COR

  • Gradient phonotactics in Muna and OT p.6

    In the hierarchy in (6), another lexically specific faithfulness constraint, FAITH-L2, has beeninstalled to allow for the exceptional forms with pairs of coronal fricatives, coronal stops, andcoronal sonorants. Pairs of labials, on the other hand, are completely absent from the lexicon ofArabic roots. To rule these out, OCP-LAB must dominate faithfulness:

    (7) OCP-LAB >> FAITH-L2 >> OCP-COR[-SON][αCONT], OCP-COR[+SON] >>FAITH-L1 >> OCP-COR[-SON] >> FAITH >> OCP-COR

    We now have four grades of acceptability: ungrammatical (pairs of labials), marginallyacceptable (e.g. pairs of coronal obstruent stops), moderately acceptable (pairs of coronalobstruents disagreeing in continuancy) and acceptable (pairs of coronals disagreeing insonorancy). Ungrammaticality is expressed by the fact that a word with a pair of labials willnever surface intact, no matter which faithfulness constraint it is indexed to. Perfect acceptabilityis expressed by the fact that a word with an obstruent-sonorant pair of coronals will alwayssurface faithfully.

    One way to distinguish intermediate grades is by submitting a word to the grammar with eachlexical indexation. The more often it surfaces faithfully, the more acceptable it is (cf. Anttila’s1997 approach to variation). Given a word that contains a pair of coronal obstruent stops,indexing it to FAITH-L2 will allow it to surface faithfully, while indexing it to FAITH-L1, orleaving it unindexed, will force it to be altered to satisfy OCP-COR[-SON][αCONT]. That is, in 1/3of the possible indexations, a pair of coronal obstruent stops will surface faithfully (8b). On theother hand, a pair of coronal obstruents disagreeing in continuancy will surface faithfully with2/3 of the indexations: it will be altered only if it is left unindexed (8c). A pair of labials willnever surface faithfully (8a), while a pair of coronals disagreeing in sonorancy will survive intactregardless of indexation (8d). The ordering that thus emerges is shown in (8e).2

    (8) a. *p-m *p-mL1 *p-mL2 0/3b. *t-d *t-dL1 ✓t-dL2 1/3c. *t-s ✓t-sL1 ✓t-sL2 2/3d. ✓t-n ✓t-n L1 ✓t-n L2 3/3e. t-n > t-s > t-d > p-m

    The indexations shown in (8) are those that are considered when evaluating the well-formednessof a word, nonce or real. Under the learnability proposal discussed in section 4.2, an actual wordwill be indexed to the lowest ranked faithfulness constraint that will allow it to surface faithfully(this is a consequence of the proposal, rather than a description of it). Thus, a real word with a 2 This approach yields relative well-formedness of different structures depending on their lexicalfrequency, but does not directly mirror lexical frequency. For example, a language with only one wordwith a coda and a language with more exceptional coda-bearing words (say, three) could have the samegrammars, and the same ratings for well-formedness of codas. Whether they do or not would depend onother patterns of exceptionality. If these languages both had two words with a cluster, then the grammarfor the one coda language would be MAX-L1 >> NOCODA >> MAX-L2 >> *COMPLEX >> MAX, whereasthe three coda language would have MAX-L1 >> *COMPLEX >> MAX-L2 >> NOCODA >> MAX. Thanksto Mike Hammond, Bruce Hayes, and Mits Ota for raising this issue.

  • Gradient phonotactics in Muna and OT p.7

    pair of coronal stops will be indexed to FAITH-L2, while a real word with a coronal stop-fricativepair will be indexed only to FAITH-L3.

    Another possibility is to compute relative well-formedness by comparing tableaux for differentforms (as suggested in Everett and Berent 1998; see Coetzee 2004 for a formally explicitproposal). A pair of coronal stops violates a higher ranked constraint (OCP-COR[-SON][αCONT])than a pair of coronal obstruents disagreeing in continuancy (OCP-COR[-SON]). In Coetzee’srank-ordering model of OT, the grammar can use this information to place forms into a harmonicordering. Both of these approaches make use of the ranked and violable constraints of standardOT to generate gradient well-formedness. They extend the theory in different ways, but neither isinconsistent with its use for categorical patterns. For concreteness, we use the “possibleindexation” approach in our discussion of Muna.

    3. Gradient phonotactics in Muna3.1 The data

    Muna is a Western Austronesian language spoken on an island off Southern Sulawesi (van denBerg 1989). It has place co-occurrence restrictions that in interesting ways resemble, and differfrom, those in Arabic. In this section, we provide a description of these restrictions; section 2.2provides an analysis in terms of the approach just introduced in the discussion of Arabic, andsection 2.3 discusses the relevance of these data to Frisch et al.’s similarity metric account ofArabic.

    Muna’s consonantal inventory is presented in (9).3

    (9) labial coronal velar uvular glottalvoiceless p t kvoiced b d implosive nasal m n -vce, prenas mp nt k

    ns+vce, prenas mb nd -vce, fric f s h+vce, fric trill rlateral lglide w

    3 Muna also has a set of palatals recently borrowed from Indonesian, which are omitted from theinventory in (3), and from all other discussion in this paper. Van den Berg (1989: 16) states: “The palatalconsonants /c/, /j/, and /y/ are marginal loan phonemes. The number of words containing these recent loanphonemes is very low.” He further notes that they are replaced in all but very recent loans.

  • Gradient phonotactics in Muna and OT p.8

    In his grammar, van den Berg (1989) examined the consonantal co-occurrence patterns in a set of1100 CVCV roots. He found restrictions against multiple prenasalized obstruents (as in TimugonMurut; Prentice 1971, and Gurindji; McConvell 1988 and Evans 1995), and against pairs ofunlike liquids (as in Sundanese; Cohn 1992). Van den Berg also noted that homorganic stops thatdiffer in voicing do not co-occur, nor do nasals and homorganic obstruents. These last two gapsare suggestive of a broader generalization: a restriction on non-identical homorganic segments,as in Semitic (Greenberg 1950), Javanese (Uhlenbeck 1949) and other languages.

    To further investigate these co-occurrence patterns, we compiled a list of all of the (V)CVCVand (V)CVCVCV roots in an electronic version of van den Berg and Sidu’s (1996) dictionary,which yielded a total of 5854 roots. Our main focus here is on the patterns of co-occurrencefound between consonants in what Frisch et al. (2004) call “adjacent” positions – that is, onesseparated only by a vowel. The total number of such pairs of consonants is 7892; it is greaterthan the total number of roots, since (V)CVCVCV roots have two adjacent pairs. The followingtables present O/E values for consonants grouped according to place of articulation. The uvularfricative is classified as a dorsal since it behaves as such, and the glottal fricative is omitted, as itappears to co-occur freely with all segments. Table 2 presents these figures for non-identicalconsonants, with pairs of prenasalized segments omitted, since they are subject to anindependent, absolute co-occurrence restriction. As expected, co-occurrence of homorganicsegments is below expected rates, especially that of labial and dorsals. The table also presentsexamples of Muna words of each shape.

    Labial Dorsal CoronalObs Exp O/E Obs Exp O/E Obs Exp O/E156 477.8 0.33Labialbafu, mopi, mafaka875 770.9 1.14 63 210.6 0.30Dorsalmeko, bage, bugi kangia, kagala, kagundi

    2741 2179.0 1.26 1766 1522.5 1.16 1400 1751.5 0.80Coronalbida, budo, topina kona, kona, sikele lani, dato, detiki

    Table 2 O/E for “adjacent” non-identical consonants in Muna roots

    Identical consonants co-occur freely, as Table 3 indicates.

    Labial Dorsal CoronalObs Exp O/E Obs Exp O/E Obs Exp O/E

    103 59.8 1.72Labialbebe, kapopo, fefuna

    84 65.0 1.29Dorsalkakolo, gogoso, hakeka

    274 268.2 1.02Coronalkariri, adodo, sasi

    Table 3 O/E for “adjacent” identical consonants in Muna roots

  • Gradient phonotactics in Muna and OT p.9

    The identity exemption for place co-occurrence restrictions is also familiar from other languages,including Arabic, though the details in Muna are somewhat different, as we discuss in section2.2. One peculiarity is that the exemption also seems to apply between consonants that areidentical except that one is prenasalized (e.g. k-k): of the 63 attested non-identical dorsal pairs,34 fit this description. Table 4 shows the revised figures when these are omitted.

    Labial Dorsal CoronalObs Exp O/E Obs Exp O/E Obs Exp O/E

    Labial 132 441.9 0.30Dorsal 875 770.9 1.14 29 163.6 0.18Coronal 2741 2179.0 1.26 1766 1522.5 1.16 1338 1686.0 0.79Table 4 O/E for “adjacent” non-identical consonants in Muna roots, revised

    To facilitate a more detailed examination of the restrictions on homorganic consonants, thefollowing three tables present the O/E figures for consonant pairs within each place ofarticulation.

    k k k 0.82 0.07 4.40k 0.65 0.00 0.00 0.20 2.25 0.00 0.00 0.40 0.00 0.48 0.00 3.54 0.10 0.00 0.00 0.62 0.00 1.73Table 5: Observed/Expected frequencies of dorsal co-occurence

    p b mp mb f w mp 1.46b 0.10 2.79mp 0.79 0.20 0.00mb 0.31 0.52 0.00 0.00 0.11 0.28 0.34 0.69 1.70f 0.22 0.58 0.29 0.09 0.20 2.50w 0.16 0.00 0.29 0.74 0.40 0.65 2.04m 0.39 0.07 0.43 0.23 0.00 1.04 0.09 1.24Table 6: Observed/Expected frequencies of labial co-occurrence

  • Gradient phonotactics in Muna and OT p.10

    t d nt nd s ns l r nt 1.02d 0.60 2.54 0.37 0.18 2.94nt 0.74 0.92 0.10 0.00nd 1.22 1.31 0.45 0.00 0.00s 0.37 0.55 0.51 0.63 1.01 1.21ns 0.05 1.68 0.00 0.00 0.00 1.12 0.00l 0.78 0.79 0.99 1.07 1.45 1.13 1.37 0.89r 0.88 0.84 1.37 1.15 1.28 1.08 1.67 0.19 0.45n 0.70 0.25 0.39 1.28 0.57 1.17 1.51 0.32 0.56 2.94Table 7 Observed/Expected frequencies of coronal co-occurrence

    It is clear that there are many exceptions to a restriction against non-identical homorganicconsonants in Muna. However, it is also clear that as in Arabic, there are phonologicalgeneralizations about the patterning of these exceptions.

    One obvious factor in co-occurrence in Muna is the place of articulation: coronals co-occur morefreely than labials or dorsals. This can be confirmed by comparing similar pairs across places ofarticulation; for example, the coronal stops /t-d/ co-occur at a higher rate than /p-b/ or /k-g/.Table 8 presents the average values for the pairs that can be compared across all three places ofarticulation (voiced and voiceless stops, nasals, and prenasalized stops),4 omitting identical pairsand pairs of prenasalized segments, as well as pairs that are identical except for prenasalization(e.g. s-ns). This table shows that non-coronals are much more underrepresented than coronals,and that dorsals are somewhat less well represented than labials.

    Labial Dorsal CoronalObs Exp O/E Obs Exp O/E Obs Exp O/E31 143.9 0.22 8 93.5 0.09 146 186.3 0.78

    Table 8 Mean values: voiced and voiceless stops, nasals, prenasalized stops

    The role of voicing can be seen across the three places of articulation. In all cases, nasals aremore underrepresented with homorganic voiced stops than with voiceless ones (e.g. the O/E for/d-n/ is lower than for /t-n/). Particularly striking in view of the dominant role of sonorancy inother languages is the fact that voiced stops are even more restricted with nasals than with

    4 Fricatives differ across place in that the uvular is voiced, while the labial and coronal are voiceless;including these would introduce a confound, since the voiced uvular could be particularlyunderrepresented with the nasal because of its voicing, rather than its place. The inventory ofapproximants is also of course different amongst the three places.

  • Gradient phonotactics in Muna and OT p.11

    voiceless stops. Table 9 presents the O/E values for these three sets of pairs collapsed acrossplace of articulation.

    Nasals-voiced stops

    Nasals-voiceless stops

    Voiced stops-voiceless stops

    Obs Exp O/E Obs Exp O/E Obs Exp O/E6 41 0.15 42 110 0.38 30 94 0.32

    Table 9 Nasal and stop voicing interactions

    The voicing effect extends to fricatives. The voiceless fricatives /s/ and /f/ co-occur less freelywith the voiceless stops than with the voiced ones, while the voiced uvular fricative never occurswith the voiced dorsal stop, though it does appear with the voiceless one with an O/E of 0.40.5

    To examine the voicing effect statistically, we followed Frisch et al. (2004) in applying theWilcoxon Signed-Rank test to the O/E values of all of the pairs that shared a common segment,and differed only in whether the pairs agree in voicing, like those in (10). We omitted identicalpairs and pairs of prenasalized segments, as well as pairs that are identical except forprenasalization.

    (10) “Agree” “Disagree”m-b m-pp-f b-fl-d l-tns-t ns-d

    For the 21 such pairs of pairs, the Wilcoxon test indicated that the effect of voicing agreement ishighly statistically significant (signed rank sum S+ = 148, p < .005).

    The primacy of voicing in determining the strength of a restriction on non-adjacent homorganicconsonants is unique to Muna. While place co-occurrence restrictions are best known in Semiticlanguages (Greenberg 1950), there is a growing list of languages outside of that family that showthese patterns:

    (11) a. Javanese (Uhlenbeck 1949, Mester 1986, Yip 1989) b. English, French, Latin (Berkley 2000)

    c. Russian (Padgett 1995)d. Yamato Japanese (Kawahara et al. to appear)e. Rotuman (McCarthy 2003)

    5 The behavior of the implosives in terms of voicing is somewhat contradictory. They co-occur lessfrequently with the nasals than do the voiceless stops, in which way they pattern as [+voice]. However,they co-occur somewhat more frequently with voiced oral and prenasalized stops than with voicelessones; only the coronal oral stops buck this trend. The implosive labial co-occurs with /f/ at about the samerate as /p/ (with both more frequent than /b-f/), but the coronal implosive co-occurs with /s/ at about thesame rate as /d/ (with both more frequent than /t-s/). In sum, the implosives seem to be neutral withrespect to voicing.

  • Gradient phonotactics in Muna and OT p.12

    In all of these other languages, the strength of the co-occurrence restriction is mostly determinedby whether the segments agree in sonorancy, as in Arabic. Frisch et al. (2004) report effects ofvoicing similarity for Arabic, but they are much weaker (see also Kawahara et al. to appear forsimilar findings in Yamato Japanese). Within the class of coronal obstruents, pairs of segmentsthat agree for voicing are slightly less well represented than those that do not (O/E of 0.21 vs.0.36). Within the class of coronals as a whole, sonorants are more over-represented withvoiceless obstruents than with voiced ones (O/E of 1.31 vs. 1.15); this difference does not reachstatistical significance on the Wilcoxon test. The Muna pattern is not entirely unprecedentedhowever: voicing agreement seems to play a strong role in disfavoring sequences of homorganicconsonants in several languages, when the consonants are not separated by a vowel (Côté 2004;see also Shiels-Djouadi 1975, Guy and Boberg 1997).

    Along with voicing, sonorancy does play a role in determining the strength of the placerestriction in Muna. The sonorants /l/ and /r/ are more restricted with /n/ (O/E = 0.43) than theyare with the obstruent /d/ (O/E = 0.81). However, the labial sonorant /w/ is about equallyunderrepresented with /b/ (0.00) as it is with /m/ (0.07). When /w/ is paired with the segmentsthat are not [+voice] (/p/, // and /f/), its representation is somewhat higher (0.16, 0.40 and 0.65respectively). The absolute restriction against /b-w/, along with the stronger restriction against/d-n/ than /d-t/ (0.25 vs. 0.60) suggests that agreement in voicing, rather than agreement insonorancy, most strongly influences the restriction against homorganic segments in Muna.However, the shared voicing of the liquids with /d/ is not sufficient to force muchunderrepresentation, presumably because agreement in continuancy is also required amongst thecoronals.

    Other manner effects can be seen as well, and they are all subjugated to voicing. When aprenasalized segment is paired with a segment that is not identical to its oral portion, a differencein prenasalization does tend to mitigate the strength of the place restriction. Thus, pairs of contra-voiced oral stops (O/E {g-k, t-d, p-b} = 0.32) are rarer than pairs of contra-voiced oral andprenasalized stops (O/E {p-mb, b-mp, k-, -k, d-nt, t-nd} = 0.49). This is also evident in acomparison between s-d (0.55) and ns-d (1.68). However, when the oral portions agree invoicing, prenasalization has no effect: ns-t (0.05) is in fact somewhat less well represented than s-t (0.37). A difference in continuancy seems to have some effect in weakening the placerestriction: /p-b/ more restricted than /f-b/ (0.10 vs. 0.58), but this is again overridden by voicingsimilarity: /p-f/ is not well represented (0.22). Within the coronal obstruents, there is nonoticeable effect for continuancy (though see section 2.2.2 on effects across the sonorancydivide). When segments differ for sonorancy and continuancy, as well as voicing, they co-occurfreely: /n-s/, /m-f/, and /n-ns/ all have O/E values above 1. However, voicing similarity overrideseven this large manner difference; the voiced uvular fricative never occurs with //.

    2.2 Muna and the relativized OCP2.2.1 Core analysis

    In this section, we use ranked relativized OCP constraints to provide an analysis of one part ofthe Muna data. The data that we analyze here includes just those segment types that can be

  • Gradient phonotactics in Muna and OT p.13

    compared across place of articulation, and excludes prenasalized stops. Sections 2.2.2 and 2.2.3discuss how the analysis can be extended to other aspects of the data.

    Table 10 presents the O/E values for voiced and voiceless stops, fricatives, and nasals withineach of the three places of articulation, along with examples of words of each type. Again, pairsof identical segments are omitted.

    Coronal Labial Dorsald t 0.60 (3) b p 0.10 (1) k 0.07 (1)Voiced Stop + Voiceless Stop

    datu pabu kagalan d 0.25 (2) m b 0.07 (1) 0.00 (0)Nasal + Voiced Stop

    da:no bomut n 0.70 (3) m p 0.39 (3) k 0.10 (1)Nasal + Voiceless Stop

    tunani mopi kagian s 1.17 (4) m f 1.04 (4) 0.00 (0)Nasal + Fricative

    nasi mafakas d 0.55 (3) f b 0.58 (3) 0.00 (0)Fricative + Voiced Stop

    sida febunis t 0.37 (3) f p 0.07 (1) k 0.40 (3)Fricative + Voiceless Stop

    tisore fopanto kaaTable 10 Observed/Expected values for voiced and voiceless stops, fricatives,and nasals

    Unfortunately, without data on grammaticality judgments from native speakers of Muna, it is notclear what distinctions the analysis must encode. In absence of such data, we adopt the followingworking hypothesis about the mapping between O/E values and acceptability, where ‘0’ =unacceptable and ‘4’ = fully acceptable:

    (12) Hypothesized acceptability values0 → ‘0’0.01-0.10 → ‘1’0.11-0.30 → ‘2’0.31-0.70 → ‘3’> 0.70 → ‘4’

    These values appear in parentheses alongside the O/E values in Table 10. Since there are no O/Evalues in table 10 between 0.70 and 1, “the fully acceptable” value could have equally been set at“greater than 1” (though cf. Table 12).

    Under the assumptions laid out in section 2, with the hypothesized 5 levels of well-formednessthe basic structure of the Muna grammar will be as in (13), where “M-stratum” stands for a set ofMarkedness constraints, and “FAITH-L” is a lexically specific faithfulness constraint. Again,since we are not dealing with alternations, we use “Faith” rather than a specific faithfulnessconstraint.

  • Gradient phonotactics in Muna and OT p.14

    (13) M-stratum0 >> FAITH-L3 >> M-stratum1 >> FAITH-L2 >> M-stratum2 >> FAITH-L1 >>M-stratum3 >> FAITH >> M-stratum4

    Words that violate markedness constraints from M-stratum0 will be altered to fit the demands ofthose constraints, regardless of which lexically specific faithfulness constraint they are indexedto. If word types that get an acceptability score of ‘0’ violate a constraint in M-stratum0, they arecorrectly judged as ill-formed. Words that violate only the markedness constraints in M-stratum4,and no higher ones, will be parsed faithfully regardless of the faithfulness constraint they areindexed to. Word types that get an acceptability score of ‘4’ must therefore violate nomarkedness constraint in an M-stratum higher than M-stratum4. The intermediate acceptabilityvalues are similarly generated by ensuring that the relevant word-types violate at least onemarkedness constraint in the appropriate stratum, and no markedness constraint in any higherstratum. For instance, a word type ranked as ‘1’ must violate a constraint in M-stratum1, andnone in M-stratum0.

    In order to facilitate discussion, Table 11 groups the consonant pairs at each place of articulationfrom Table 10 according to the acceptability scores that each would be assigned.

    Acceptability score Coronal Labial Dorsal0 N-g, Â-g, N-Â1 b-p, f-p, m-b g-k, N-k2 n-d3 t-n, s-d, d-t, s-t m-p, f-b Â-k4 n-s m-f

    Table 11 Acceptability by place of articulation

    We will start by constructing the relativized OCP constraints for the dorsals in each acceptabilitygroup. The pairs [N-g], [Â-g] and [N-Â] are completely unacceptable. These three pairs areseparated from the others by the fact that they consist entirely of [+VOICE] segments. Thus, anOCP-DOR constraint relativized to shared voicing, OCP-DOR[αVOICE], will correctly pick themout. Since there is only one voiceless dorsal, [k], this constraint can apply to dorsals that sharevoicing, rather than just [+VOICE] dorsals.

    The pairs [g-k] and [N-k] receive an acceptability score of 1, and they should therefore violate amarkedness constraint ranked in the M-stratum1 in (13). These two pairs share the feature ofbeing non-continuants, and they therefore violate the constraint OCP-DOR[αCONT]. Since thereis only one dorsal continuant, [Â], no pair of dorsals that contain [Â] can violate OCP-DOR[αCONT]. We can therefore rank OCP-DOR[αCONT] in M-stratum1.

    The dorsal pair [Â-k] receives a rating of 3, and should therefore violate a markedness constraintfrom M-stratum3. Since we have already accounted for all other pairs of dorsal consonants, wecan use the general OCP-constraint for dorsals, OCP-DOR. The grammar necessary to accountfor the co-occurrence patterns of dorsals in Muna is then as shown in (14).

    (14) OCP-DOR[αVOICE] >> FAITH-L3 >> OCP-DOR[αCONT] >> FAITH-L2>> FAITH-L1 >> OCP-DOR >> FAITH

  • Gradient phonotactics in Muna and OT p.15

    Next we discuss the labials. The pairs [b-p], [f-p], and [m-b] all receive acceptability ratings of 1,and should therefore violate markedness constraints in M-stratum1 in (13). The pair [m-b] sharesthe feature [+voice] and the pair [f-p] shares the feature [-voice]. These two pairs will thereforeboth violate OCP-LAB[αVOICE]. Inspection of the labial pairs that receive acceptability ratingsother than 1, will show that none of these pairs share voicing. We can therefore rank OCP-LAB[αVOICE] in M-stratum1 without affecting the acceptability of the other labial pairs. The pair[p-b] share the features [-continuant] and [-sonorant]. We cannot use OCP-LAB[αSONORANT] orOCP-LAB[αCONTINUANT] for this pair, since OCP-LAB[αSONORANT] is also violated by the pair[f-b] that receives an acceptability score of 3, and OCP-LAB[αCONTINUANT] is also violated by[m-p] that also receives a score of 3. We therefore need the more specific constraint OCP-LAB[αCONTINUANT][βSONORANT].

    The pairs [m-p] and [f-b] both receive a score of 3, and should therefore both violate amarkedness constraint ranked in M-stratum3. The [m-p] pair shares only one feature, namely [-continuant]. The only pair with a better rating, [m-f], differ in continuancy. We can thereforesafely use OCP-LAB[αCONTINUANT] to account for the score that [m-p] receives. The [f-b] pairshares only the feature [-sonorant]. Again, since [m-f] does not share this feature, we can useOCP-LAB[αSONORANT] to account for the score that [m-p] receives.

    This leaves only [m-f], and since these two segments share no feature other than place, they willviolate only the general OCP-LAB, which should be ranked right at the bottom to account for theperfect acceptability of words that have this pair of labials. The grammar necessary to explain theco-occurrence of labials in Muna is given in (15).

    (15) FAITH-L3 >> OCP-LAB[αVOICE], OCP-LAB[αCONTINUANT][βSONORANT] >> FAITH-L2 >> FAITH-L1 >> OCP-LAB[αCONTINUANT], OCP-LAB[αSONORANT] >> FAITH >>OCP-LAB

    It now remains only to discuss the coronals. The pair [n-d] receives a score of 2, and this pairshould therefore violate a markedness constraint ranked in M-stratum2. This pair shares thefeatures [+voice] and [-continuant]. There are other coronal pairs that also have the samespecification for [voice] ([s-t]) or for continuancy ([t, n], [d, t]). We can therefore use neitherOCP-COR[αVOICE] nor OCP-COR[αCONTINUANT] to account for the relative well-formedness of[n-d], but need the more specific OCP-COR[αVOICE][βCONTINUANT] that uniquely selects thepair [n-d]. Ranking this constraint between FAITH-L2 and FAITH-L1 will account for theacceptability score of 2 that the words with the pair [n-d] receive.

    The pairs [t-n], [s-d], [d-t], and [s-t] all receive acceptability scores of 3, and should thereforeviolate markedness constraints in M-stratum3. The pair [t] and [n] share only the feature [-continuant]. Since the only pair that receives a better rating, [n-s], does not agree in continuancy,we can use OCP-COR[αCONTINUANT] to account for the score of 3 that [t-n] receives. Since thepair [d-t] also violates this constraint, this one constraint also takes care of this pair. This leavesthe pairs [s-d] and [s-t]. All the segments in these pairs share the feature [-sonorant]. Again, since[n-s] does not agree in sonorancy, we can use the constraint OCP-COR[αSONORANT] for the pairs[s-d] and [s-t].

  • Gradient phonotactics in Muna and OT p.16

    This leaves the pair [n-s] that are rated as perfectly well-formed. This pair should therefore onlyviolate markedness constraints that rank below all faithfulness constraints in M-stratum4. Asidefrom place [n-s] share no other features. The only OCP-constraint that this pair violates, is thenthe general OCP-COR constraint. In (16) we give the grammar necessary to account for therelative well-formedness of different coronal pairs.

    (16) FAITH-L3 >> FAITH-L2 >> OCP-COR[αVOICE][βCONTINUANT] >> FAITH-L1 >> OCP-COR[αCONTINUANT], OCP-COR[αSONORANT] >> FAITH >> OCP-COR

    The ranking in (17) combines the constraints for all three places of articulation, and indicates theacceptability of word-types targeted by the constraints. For reasons of space and readability,constraints in a single stratum are placed in a single column, and the domination symbol “>>” isomitted.

    (17) Muna consonantal co-occurrence grammarOCP-DOR[αVOI]

    OCP-LAB[αVOI]

    OCP-COR[αVOI][βCNT]

    OCP-COR[αCNT]

    OCP-COR

    OCP-LAB[αCNT][βSON]

    OCP-COR[αSON]

    OCP-LAB

    OCP-DOR[αCNT]

    OCP-LAB[αCNT]OCP-LAB[αSON]OCP-DOR

    Accept: 0

    FAIT

    H-L

    3

    Accept: 1

    FAIT

    H-L

    2

    Accept: 2

    FAIT

    H-L

    1

    Accept: 3FA

    ITHAccept: 4

    Most of the markedness constraints we have used have precedents in the analysis of otherlanguages. As discussed in section 2, OCP-PLACE constraints relativized to continuancy andsonorancy have been used to analyze the Arabic root constraints; see also Padgett (1995) onRussian and Javanese (as well as Mester 1986 and Yip 1989 on the latter). The novelty here isthe use of [voice] to further subdivide the sets of consonants that the OCP applies to, though asmentioned above, [voice]-specific OCP constraints have been posited for consonants that arestrictly adjacent. In addition, the division of OCP-PLACE into constraints specific to Labial,Dorsal and Coronal place, with OCP-COR ranked lowest, recapitulates Alderete’s (1997)proposal for Berber. The extension here is the combination of place-specificity and manner-specificity: for any manner-specific constraint (e.g. OCP-PLACE[CONT]), the Coronal-specificversion is never ranked above the Labial or Dorsal-specific version. In addition, the Dorsal-specific versions sometimes rank above, and never rank below, the Labial-specific ones (seesection 2.3 for further discussion).

  • Gradient phonotactics in Muna and OT p.17

    2.2.2 Other non-identical homorganic pairs

    While there are some ways in which this analysis remains incomplete, it does deal with the fullset of coronals. Table 12 presents the Observed/Expected values and hypothetical acceptabilityrankings for the voiced coronals, which includes the liquids /l/ and /r/.

    Nasal + Voiced Stop n d 0.25 (2)Nasal + Lateral n l 0.32 (3)Nasal + Rhotic n r 0.56 (3)Lateral + Rhotic l r 0.19 (2)Lateral + Voiced Stop l d 0.79 (4)Rhotic + Voiced Stop r d 0.84 (4)Table 12 Observed/Expected Values for voiced coronals

    The constraint OCP-COR[αCONT][αVOICE] targets /n-d/ and /l-r/, but none of the other pairs.The ranking of this constraint in M-stratum2 is consistent with their acceptability ranking of 2.The other division that needs to be made according to the hypothetical acceptability rankings isbetween the nasal/liquid pairs and the voiced stop/liquid pairs. As desired, the OCP-COR[αSON]constraint ranked in M-stratum3 is violated by /n-l/ and /n-r/, but not by /l-d/ and /r-d/.

    An analysis of the behavior of the labial approximant /w/ would require elaboration of the OCP-LABIAL constraints. The pair /b-w/ never occurs, whereas /b-m/ and /w-m/ both occur marginally(both 0.07). This suggests that OCP-LAB[VOICE] applies with more force between non-nasalsegments, and may thus be relativized to [-nasal]. The role of nasality in mitigating OCP-LABeffects is also seen in the free occurrence of /m-f/ versus the moderate restriction against /w-f/(0.65), and in the stricter ban against /w-p/ than /m-p/ (0.16 vs. 0.39). This would also entail anexpansion of the set of features that Padgett (1995) allows for relativized OCP constraints,though the evidence is less persuasive than for voicing. This is particularly true because there issome evidence that /w/ may not be a true sonorant. René van den Berg (p.c.) notes that though itis described as an approximant in van den Berg (1989), it is sometimes realized as a voicedbilabial fricative. With a classification of /w/ as an voiced obstruent continuant, nasality wouldnot be needed to explain these differences in co-occurrence rates.

    2.2.3 Identical pairs

    The OCP-PLACE constraints as formulated here and in previous work are violated by identicalconsonants. In Muna, identical consonants are permitted in all positions, as the following tablesshow.

  • Gradient phonotactics in Muna and OT p.18

    Labial Dorsal CoronalObs Exp O/E Obs Exp O/E Obs Exp O/E

    Non-IdenticalHomorganic 76 249.2 0.30 32 108.1 0.30 652 822.9 0.79

    Identical 54 32.2 1.68 39 27.7 1.41 105 113.7 0.92

    Table 13 Biconsonantal roots

    Labial Dorsal CoronalObs Exp O/E Obs Exp O/E Obs Exp O/E

    Non-IdenticalHomorganic 57 156.3 0.36 25 60.7 0.41 235 335.4 0.70

    Identical 35 18.8 1.86 36 26.3 1.37 83 45.8 1.81

    Table 14 C1/C2 of (V)C1VC2VC3V

    Labial Dorsal CoronalObs Exp O/E Obs Exp O/E Obs Exp O/E

    Non-IdenticalHomorganic 23 82.0 0.28 6 38.3 0.16 513 600.0 0.86

    Identical 14 9.4 1.50 9 9.2 0.98 86 110.6 0.78

    Table 15 C2/C3 of (V)C1VC2VC3V

    This identity effect is seen in Arabic and other Semitic languages, as well as in Javanese(Uhlenbeck 1949, Mester 1986, cf. Yip 1989). However, an interesting difference between Munaand these other languages can be seen in triconsonantal roots. In Arabic, identical segments areonly permitted in the second two positions (e.g. [s-m-m], *[s-s-m]), while in Javanese they areonly permitted in the first two (e.g. [s-s-m], *[s-m-m]; see also Gafos 1998 on Temiar). InMuna, the O/E values for identical segments in C1 and C2 position of (V)C1VC2VC3V (Table 14)are generally higher than for C2 and C3 (Table 15), as might be expected due to the closer geneticaffiliation of Muna with Javanese than with the Semitic languages. However, except for thecoronals, the O/E values remain above or just below 1.

    There is, as far as we are aware, no extant account of the identity exemption for the OCP-Placein Optimality Theory (cf. MacEachern 1999 on identity in laryngeal cooccurence, and see Frischet al. 2004: 189 for speculation on an OT-style account for Arabic). For Arabic, one might drawon the proposals in Gafos (1998) and Coetzee (2004) that the final consonant in a /s-m-m/ type‘root’ is in fact outside of the root, and that the OCP-Place, like the OCP for identical segments,applies only within the root (cf. Rose 1997, 2000, Ussishkin 1999). However, there is no reasonto propose such a structure for Muna, and one would have to further allow it to apply to either C1and C3 in the triconsonantal roots, as well as to one of the consonants in a biconsonantal root.

  • Gradient phonotactics in Muna and OT p.19

    Another complication is that as discussed in section 1, the identity effect appears to apply whenthe oral portion of the prenasalized stop is identical to the segment with which it co-occurs. Onecannot simply say that the nasal portion is ignored, since pairs of voiced and voiceless obstruentsare more frequent when prenasalization is present on one of the segments than when it is absent.

    It thus seems necessary to formulate OCP-PLACE constraints so that they only apply to segmentswhose ‘heads’ are identical, where the oral portion of a prenasalized segment is its head:

    (18) OCP-PLACE Adjacent consonants whose heads are non-identical cannot be homorganic

    Agreement for prenasalization is then another attribute that can be specified in relativized OCP-PLACE constraints, along with voicing, continuancy, and sonority. This approach can alsoaccount for the Japanese data in Kawahara et al. (2004), in which voicing disagreement weakensOCP effects, yet is irrelevant for the identity exemption. The ban against identical segments, asseen in Semitic and Javanese, would be imposed by a separate constraint, which is ranked low inMuna.

    The Muna identity effect also poses a challenge for Frisch et al.’s (2004) similarity metric,discussed in detail in the next section. This measure penalizes similarity, and judges pairs ofidentical segments as completely ill-formed. For Arabic, this fits with the absence of identicalsegments from C1/C2 position. For C2/C3 position, they suggest that the similarity metric might beoverridden by a separate constraint demanding identity (p. 189). Insofar as Muna does not allowfor that option, it would seem that the OCP-PLACE is not a constraint on similarity tout court, butrather on near identity.

    2.3 Muna and the natural classes similarity metric

    Frisch et al. (2004) provide an analysis of Arabic that predicts the relative rates of co-occurrenceof pairs of homorganic consonants using a similarity metric. Similarity is calculated for asegment pair by dividing the number of shared natural classes by the total number of naturalclasses to which each segment belongs within its place of articulation.

    Muna provides striking confirmation for some of Frisch et al.’s claims. As in Arabic, the Munaplace co-occurrence restrictions are clearly strengthened by similarity, and the effects ofsimilarity go well beyond the division of consonants into major classes on the basis of sonorancyand continuancy. Because voicing plays such a central role, Muna shows more robust evidenceof “cross-classification” than Arabic does. For example, the nasal [n] co-occurs less often with[d] than [t] due to its specification as [+voice], and co-occurs less often with [l] and [r] than [d]does because of its specification as [+sonorant]. In addition, the effects of voicing show that non-contrastive features can play a role in OCP-Place effects, as Frisch et al. argue on the basis of theless robust findings in Arabic (cf. Yip 1989, Padgett 1995). This is seen not only in the nasals,but also in the fricatives, in which voicing is non-contrastive and a factor in co-occurrence rates:voiceless [s] and [f] occur less frequently with [t] and [p] than with [d] and [b], while voiced []co-occurs less often with [g] than [k].

  • Gradient phonotactics in Muna and OT p.20

    As we have shown in our analysis of Muna, the effect of similarity can be captured by relativizedOCP constraints. Neither cross-classification, nor redundant feature activity poses a problem. Aswe discussed in the introduction, one difference between these analyses is that the similaritymetric is more predictive; there is no reason that a particular ranking of the relativized OCPconstraints should hold. To see how the similarity metric fares in predicting the relative rates ofco-occurrence for Muna, we calculated similarity values using the featural classifications in theAppendix. These were calculated as in Frisch et al. (2004): by dividing the number of naturalclasses that both segments belong to by the sum of the numbers that each belongs to. Wechecked our calculations by using Adam Albright’s segmental similarity calculator(http://web.mit.edu/albright/www/software/SimilarityCalculator.zip).

    Figure 1 plots the similarity values against Observed/Expected, for all of the homorganic pairs,except pairs of prenasalized segments, pairs of identical segments, and ones in which the oralportion of a prenasalized segment is identical to the other segment. We also fitted a regressionline to these data.

    0

    0.5

    1

    1.5

    2

    0 0.2 0.4 0.6 0.8 1

    Similarity

    O/E

    Figure 1 Similarity vs. Observed/Expected

    As expected, the general trend is that as similarity increases, the O/E value decreases. However,this correlation is far from perfect; pairs with low similarity have a wide range of O/E values.The r2-value for the regression analyses on these data is only .22, implying that roughly 80% ofthe observed variation is not accounted by the similarity metric.

    To show in detail where the similarity metric succeeds and fails, tables 16-18 present the resultsfor each place of articulation, with O/E values in parentheses.

  • Gradient phonotactics in Muna and OT p.21

    k k 0.44

    (0.07)

    k 0.42(0.65)

    0.21(0.00)

    0.25(0.20)

    0.44(2.25)

    0.42(0.00)

    0.29(0.40)

    0.47(0.00)

    0.14(0.48)

    0.27(0.00)

    0.27(0.10)

    0.47(0.00)

    0.14(0.00)

    0.27(0.62)

    0.29(0.00)

    Table 16: Similarity values for non-identical dorsals (with O/E)

    p b mp mb wb 0.50

    (0.10)mp 0.28

    (0.79)0.28(0.20)

    mb 0.29(0.31)

    0.48(0.52)

    0.62(0.00)

    0.65(0.11)

    0.59(0.28)

    0.39(0.34)

    0.35(0.69)

    f 0.55(0.22)

    0.36(0.58)

    0.33(0.29)

    0.24(0.09)

    0.50(0.20)

    w 0.17(0.16)

    0.35(0.00)

    0.10(0.29)

    0.20(0.74)

    0.19(0.40)

    0.26(0.65)

    m 0.29(0.39)

    0.48(0.07)

    0.20(0.43)

    0.30(0.23)

    0.35(0.00)

    0.24(1.04)

    0.26(0.09)

    Table 17: Similarity values for non-identical labials (with O/E)

  • Gradient phonotactics in Muna and OT p.22

    t d nt nd s ns l d 0.43

    (0.60)

    0.62(0.37)

    0.50(0.18)

    nt 0.38(0.74)

    0.22(0.92)

    0.27(0.10)

    nd 0.20(1.22)

    0.45(1.31)

    0.24(0.45)

    0.38(0.00)

    s 0.50(0.37)

    0.26(0.55)

    0.40(0.51)

    0.22(0.63)

    0.14(1.01)

    ns 0.24(0.05)

    0.13(1.68)

    0.20(0.00)

    0.46(0.00)

    0.22(0.00)

    0.40(1.12)

    l 0.19(0.78)

    0.36(0.79)

    0.22(0.99)

    0.10(1.07)

    0.19(1.45)

    0.32(1.13)

    0.16(1.37)

    r 0.19(0.88)

    0.36(0.84)

    0.22(1.37)

    0.10(1.15)

    0.19(1.28)

    0.32(1.08)

    0.16(1.67)

    0.86(0.19)

    n 0.11(0.70)

    0.32(0.25)

    0.13(0.39)

    0.06(1.28)

    0.18(0.57)

    0.11(1.17)

    0.06(1.51)

    0.31(0.32)

    0.31(0.56)

    Table 18: Similarity values for non-identical coronals (with O/E)

    By comparing corresponding pairs across the places of articulation, we can assess how well thesimilarity metric does at predicting the weakening of the co-occurrence restrictions amongstcoronals, as well as the more subtle difference between labials and dorsals. Looking at the voicedand voiceless stops in the top left corner of the tables, one would conclude that it does not dovery well: the similarity values are roughly equivalent, yet the coronals have a much higher O/Evalue. The average similarity and O/E values for the pairs that can be compared across all threeplaces of articulation (voiced and voiceless stops, nasals, and prenasalized stops), omitting thosethat may be subject to the identity effect or the ban on multiple prenasalized stops, are presentedin Table 19. The raw observed and expected values were presented in Table 8 above.

    Coronals Labials DorsalsO/E 0.78 0.22 0.09Similarity 0.22 0.33 0.29Table 19 O/E and average similarity values

    The differences amongst the similarity values are relatively small; these would all be groupedtogether in the table comparing O/E and similarity in Frisch et al. (2004: 203). The O/E values,however, fall dramatically from the coronals to the labials.

    The similarity metric derives the fact that OCP effects are diminished in coronals from the largesize of the Arabic coronal inventory, which increases the comparison space. As an inspection ofthe inventory in (9) shows, the coronal inventory size in Muna is only marginally larger than thatof the labials. McCarthy (2003b) finds a similar problem in Rotuman: like Arabic, co-occurrencebetween coronals is much freer across sonorancy classes than within them, but unlike Arabic, thecoronal inventory is not particularly large. The Rotuman and Muna facts suggest that the

  • Gradient phonotactics in Muna and OT p.23

    weakness of OCP effects between coronals is not simply a factor of inventory size. While noaccount of the coronal effect is offered in our own analysis (cf. Alderete 1997), it cannot beconsidered an advantage of the similarity metric that it derives it from the size of the coronalinventory.

    The other difficulty that the similarity metric has with Muna is the strength of the voicing effect.As shown in Table 20, the voiced stops are less similar to nasals than to voiceless stops, yet aremore restricted in their co-occurrence. The raw observed and expected values for these sets ofpairs are shown in Table 9.

    Nasals+Voiced Stops

    Voiced Stops+Voiceless Stops

    O/E 0.15 0.32Similarity 0.22 0.33Table 20 O/E and average similarity values

    Particularly dramatic instances of this difficulty are the pairs /-/ and /w-b/, which have little incommon but voicing, and thus have low similarity values, yet are unattested.

    Here the problem stems from the fact that languages weight features differently in how theyfunction in OCP effects, but the similarity metric has no featural weighting mechanism. Frisch etal. (2004: 204) find that for Arabic, the similarity metric results in values that are too high for /d-n/, but too low for /n-l/ and /n-r/, in comparison with the O/E values for Arabic. They suggest,following Bachra (2000), that this could be resolved by weighting [sonorant] more than otherfeatures, such as [voice]. In Muna, on the other hand, [voice] appears to be the feature in need ofa boost. Thus not only do features need to be weighted, as Frisch et al. (2004) suggest, but theweighting must be allowed to vary between languages. However, adding language-specificfeatural weighting weakens the theory considerably, and does not provide an answer to whylanguages should vary in this way.

    The similarity metric approach has different goals than the relativized OCP analysis presentedhere (predicting observed lexical patterns vs. expressing native speaker knowledge of well-formedness, which can be affected by lexical patterns), so it is difficult to directly compare them.Nonetheless, the advantages that Frisch et al. (2004) claim for their account over an OCP-basedshould be reconsidered. Since the similarity metric predicts neither the differences across placeof articulation nor the effects of voicing seen in Muna, it is not at all obvious that it is superior toan analysis based on relativized OCP constraints (cf. Frisch et al. 2004: 219). Besides itspredictive capabilities, the other argument in its favor is its built-in gradience. But as we haveshown in the last two sections, when relativized OCP constraints are ranked, they can alsoexpress lexically gradient well-formedness. In this case, non-conflicting constraints are placed ina ranking to express their relative strength. Of course, the original motivation for constraintranking is to negotiate the demands of conflicting constraints, which the similarity metric-basedapproach cannot accomplish (Frisch et al. 2004: 221).

  • Gradient phonotactics in Muna and OT p.24

    The similarity metric would also seem to have difficulty relating phonotactics to patterns ofalternation. Place co-occurrence restrictions are seen not only within underived words, but theyalso play a role in phonologically conditioned alternations (see Suzuki 1998 and especiallyFukuzawa 1999 for recent surveys; see also Tessier 2004). For example, in Muna, /um/infixation (19a,b), which forms the irrealis, is blocked when the initial consonant is a labial,resulting in either a nasalized initial segment (19c,d,h), or in deletion of the affix (19e,f,i) (vanden Berg 1989, Carter 2000, Pater 2001).

    (19) a. /um+dadi/ [dumadi] ‘live’b. /um+gaa/ [gumaa] ‘marry’c. /um+pili/ [mili] ‘choose’d. /um+futaa/ [mutaa] ‘laugh’e. /um+baru/ [baru] ‘happy’f. /um+bhala/ [bhala] ‘big’h. /um+waa/ [maa] ‘give’i. /um+wanu/ [wanu] ‘get up’

    These alternations always target natural classes, like the labials here. The Muna alternation canbe accounted for by ranking OCP-LABIAL above the relevant faithfulness constraints,6 thus usingthe same constraint to account for phonotactic well-formedness and alternation. The similaritymetric uses natural classes in its computations, but the output is numeric, and does notdistinguish between pairs at different places of articulation. Therefore, it is hard to see how itcould be used to create a constraint that would pick the right pairs – just labials, just coronals, orjust dorsals, as the case may be.

    It should also be emphasized that the relativized OCP account does make predictions about therange of cross-linguistic patterns. Because of the very nature of the constraints, they cannotexpress a pattern in which consonants that differ along some dimension are less well-formed thanones that are similar; they can only express the reverse, actually observed, pattern (Padgett1995). In addition, if as Alderete (1997) proposes, the OCP-CORONAL constraints are in a fixedranking beneath OCP-LABIAL and OCP-DORSAL, then a language that imposed a restriction oncoronals that is not enforced on the other places should be impossible. If a learner were presentedwith a lexicon that contained an impossible pattern, the lexicon would be learned, but thegrammar would not encode the pattern.7 Patterns that are encoded in the grammar would be morerobust over time, as they would affect processing more strongly than those that are not (Coetzee2004), and presumably ultimately shape the lexicon.

    6 Since the roots do sometimes have pairs of labials, while OCP-LABIAL violations are never tolerated in/um/ infixation, the lexically specific constraints must also be root specific, so that they do not allow for apotential case of /um/ infixation that creates an OCP-LABIAL violation.

    7 This prediction can and should be tested using an artificial language learning paradigm (Pater andTessier 2003, 2004, Pycha, Nowak, Shin and Shosted 2003, Wilson 2003, Carpenter 2005).

  • Gradient phonotactics in Muna and OT p.25

    3. Gradient phonotactics in phonological theory

    In this paper, we have shown that an OT grammar can capture gradient phonotactics byincorporating constraint rankings that are based on the degree to which the constraints areobeyed in the lexicon. In addition, we have used the Muna data to argue for some expansions tothe set of relativized OCP-Place constraints. However, if phonology is responsible only foralternations, and/or for categorical lexical generalizations, then neither this lexicon-responsiveranking, nor some parts of this expanded set of OCP-Place constraints would be necessary.8 Inthis part of the paper, we argue that phonological theory should, and can be responsible for thistype of data: ‘should’ because the arguments for the inclusion of phonotactics in general alsoapply to gradient phonotactics; ‘can’ because lexicon-responsive ranking is learnable with aminor elaboration to an existing learnability algorithm.

    3.1 What generalizations should a grammar encode?

    It might not be obvious that a grammar should encode static lexical generalizations, that is, onesthat do not induce alternations. Even though Muna does have alternations that seem to respond toan OCP-PLACE restriction (see 19), an account of these alternations requires only a single OCP-LABIAL constraint, not the full set of ranked relativized OCP constraints employed in section 3.2.However, ever since Chomsky and Halle (1968), generative phonological theory has aimed toaccount for static phonotactics using the same system that deals with alternations. One reason isthat alternations often serve to bring words in conformity with the patterns present in the lexicon.As Chomsky and Halle (1968: 382) note:

    (20)...regularities are observed within lexical items as well as across certain boundaries - therule governing voicing of obstruent sequences in Russian, for example - and to avoidduplication of such rules in the grammar it is necessary to regard them not asredundancy rules but as phonological rules that also happen to apply internally to alexical item (p. 382)

    Subsequent research cast doubt on the viability of a purely rule-based approach to thisduplication problem, and this became one of the early arguments for the introduction ofconstraints into phonological theory (see especially Kenstowicz and Kisseberth 1977, 1979). OTresolves the duplication problem by using the same ranking to produce alternations and filter outill-formed structures from a rich base (see McCarthy 2002 and Hayes 2004 for discussion). Paterand Tessier (2003) provide experimental evidence that speakers do use their knowledge of staticlexical generalizations in learning alternations, and Hayes (2004) and Tesar and Prince (2004)show that lexical patterns can play a role in the learnability of alternations.

    8 It is difficult to know exactly which portions of the Muna data presented in section 2 should be capturedby a purely categorical grammar. If phonology is only held to distinguish between possible andimpossible patterns, then one might claim that only the consonant pairs that are entirely absent from thelexicon need be ruled out. However, phonological theory does not typically restrict itself to exceptionlessgeneralizations. If highly underrepresented consonant pairs are ruled out by the grammar (see e.g.McCarthy 1988, 1994), then it remains to be specified what degree of underrepresentation corresponds toungrammaticality.

  • Gradient phonotactics in Muna and OT p.26

    The other argument for the incorporation of phonotactics in phonological grammars is thatspeakers demonstrate knowledge of the ill-formedness of structures that are absent in the lexicon.As Chomsky and Halle (1968) and Halle (1972) famously note, English speakers recognize that[blk] is a possible word of their language, while [bnk] is not.

    While phonotactics have long been considered within the purview of phonological theory, thesame cannot be said about gradient phonotactics. Though it is certainly uncontroversial to makea distinction between a regular, an exceptional, and an impossible pattern, that is, to have a three-way gradation in acceptability, further degrees of lexical gradience have not previously beenincorporated into phonological grammar. There does not seem to be a principled reason for this,beyond the inability of standard formalisms to express such further distinctions. If we appeal tonative speaker judgments to justify the need for a grammar to rule out structures that areunattested in a language, then if these judgments reveal that different structures are ranked alonga graded scale, the phonological grammar should reflect this gradience (see e.g. Zuraw 2000,Berent et al. 2001, Hayes and Boersma 2001, Frisch and Zawaydeh 2001, Albright and Hayes2003, Coetzee 2004, and Hammond 2004 on gradient well-formedness judgments, as well asPierrehumbert 2001 and references therein).

    Unfortunately, we do not have experimental data from native speakers of Muna, which coulddirectly inform the analysis above. However, English has a consonantal co-occurrence restrictionthat has some of the same key features as Muna and Arabic. In particular, its strength varies byplace of articulation, with coronals co-occurring more freely than dorsals, and dorsals morefreely than labials. The English restriction applies to consonants in words of the shapesC1V(C)C2: C1 and C2 are underrepresented if they are homorganic (see e.g. Fudge 1969, Davis1991, Lamontagne 1993). However, the degree of underrepresentation varies by place: pairs oflabial oral stops are unattested, dorsals are somewhat more common, and coronals are socommon that they are sometimes taken to co-occur freely (cf. Lamontagne 1993: 267). Examplesappear in (21).

    (21) sTVT e.g. stud, stood, stead, stat, state, staid, stilt, stunt, stand…sKVK e.g. skeg, skag, skunk, skank, skulksPVP e.g. ?

    Coetzee (2004) examined English native speakers’ judgments and lexical decision times onnonce words of the shape [sC1VC2], where C1 and C2 are identical stops, [p], [t], or [k]. Theresults show that the subjects ranked the words as in (22), where ‘>’ indicates highergrammaticality rating, and slower lexical decision time.

    (22) stVt > skVk > spVp

    In addition, Coetzee (to appear) shows that these restrictions also affect judgments of ambiguousstimuli: a segment ambiguous between [t] and [k] is more often judged as [t] in the coda positionof a word of the form [skVC] than [stVC]. Because the size of the boundary shift effect was as

  • Gradient phonotactics in Muna and OT p.27

    large in comparisons involving coronals ([skVC] vs. [stVC] and [spVC] vs. [stVC]) as it was incomparisons involving non-coronals ([skVC] vs. [spVC]), Coetzee concludes that speakers areaware of a restriction against [stVt]. The scale in (22) therefore represents three degrees of ill-formedness, which goes beyond the two-way scale “exceptional, unacceptable”.

    3.2 Questions for further research

    The incorporation of gradient phonotactics into phonological theory opens up a number ofquestions for further research. In this section, we discuss some of them.

    In our analysis of Muna, we posited three intermediate grades of well-formedness based onarbitrary distinctions between O/E values. Obviously, one question is whether these disctinctionscorrespond to those that a Muna speaker would make. This analysis is also based on an evenmore fundamental assumption that remains to be tested: that judgments of gradient well-formedness are based on O/E values, rather than on raw frequency of constraint violation. TheO/E measure is sensitive to the independent frequency of the segments involved. One occurrenceof a pair of segments whose overall frequency is high will result in a lower O/E value than thatof a pair of segments whose overall frequency is low. If these pairs of segments each violated asingle constraint, and no other structures in the language violated those constraints, then thefrequency of constraint violation would be equivalent. In accounts of gradient acceptability andvariation in stochastic OT (e.g. Boersma 1998, Boersma and Hayes 2001), as well as in thelearnability account for grammars encoding lexical gradience discussed in the next section, it israw frequency of violation that determines constraint ranking. Whether O/E, or frequency ofconstraint violation provides a better model of relative well-formedness remains to be tested.

    A general issue for any approach that uses a single system to capture well-formedness judgmentsand more standard phonological data like alternations is that while alternations do not seem toshow evidence of cumulative ill-formedness (see below), studies of well-formedness judgmentsindicate that a form with two unattested, or low probability structures are judged as worse than aform with one (Ohala and Ohala 1986, Coleman and Pierrehumbert 1997, Hay, Pierrehumbertand Beckman 2001, Pierrehumbert 2001). A promising aspect of the OT based model of gradientwell-formedness presented here is that it may resolve this apparent contradiction, as we will nowshow by using the possible indexation approach to analyze another simple hypothetical example.In this language, onsetless syllable and codas are generally banned, but there are a fewexceptional words containing instances of each. The grammar for this language would containrankings like those shown in (23):

    (23) C-MAX-L1 >> NOCODA >> C-MAXV-MAX-L2 >> ONSET >> V-MAX

    The repair for NOCODA violations is assumed to be consonant deletion (e.g. /bat/ -> [ba]), andfor ONSET vowel deletion (e.g. /uma/ -> [ma]). These violate MAX constraints relativized toconsonants (C-MAX) and vowels respectively (V-MAX). The exceptional words with codas andonsetless syllables are targeted by lexically specific versions of these constraints.

  • Gradient phonotactics in Muna and OT p.28

    A word could be specified as L1, as L2, as both L1 and L2, or as neither. Given this set ofpossible indexations, the outcomes for a nonce word containing just a coda, just an onsetlesssyllable, or both a coda and an onset syllable are shown in (24).

    (24) a. *bat ✓batL1 *batL2 ✓batL1,L2 2/4b. *aba *abaL1 ✓abaL2 ✓batL1,L2 2/4c. *abat *abatL1 *abatL2 ✓abatL1,L2 1/4d. bat, aba > abat

    A word with both a coda and an onsetless syllable (24c) will surface faithfully only if specifiedas both L1 and L2. It is thus rated as less well-formed than a word with just one of the markedstructures (24a, b), which will surface faithfully under two of the possible indexations.

    The cumulative effects occur as a by-product of how gradient acceptability is calculated, butcannot occur in alternations because of OT’s tenet of strict constraint domination. No ranking ofONSET, NOCODA, V-MAX and C-MAX will yield deletion of codas only from onsetless syllables,or vowels only from onsetless syllables with codas. This is in line with apparent absence of suchalternations cross-linguistically, despite the large number of languages that delete consonantsfrom coda position, and vowels in hiatus.9 Unrestricted cumulative constraint activity can createeven more bizarre results, such as vowel reduction in the presence of a complex onset anywherein the word, or cluster reduction in all syllables when one has a voiced coda. One of the moststriking results of the typological research that has been conducted in Optimality Theory is thatthere seems to be very little counter-evidence for strict domination. Local conjunction(Smolensky 1995) does create the effect of cumulative constraint activity, but the main objectionto this elaboration of OT is that it is overly powerful (see e.g. Padgett 2002, McCarthy 2003a,Kawahara 2005).

    Another important question for further research is to determine the extent to which thecumulative constraint activity observed in grammaticality judgments and other psycholinguistictasks matches that found in both in lexical restrictions and in phonological alternations. Theapproach to gradient well-formedness judgments proposed here provides one way of explainingtheir divergences from the more traditional data sources for phonological analysis.10

    3.3 Are gradient phonotactics learnable?

    The grammars that we have proposed for lexically gradient restrictions in Arabic and Muna raisethree learnability problems (see also Ota 2004): 9 Levelt and van de Vijver (2004) claim that a restriction against specifically VC syllables, and not CVCor V, holds in a stage of child language. However, this stage is derived from a statistical analysis of agroup of children’s productions, and they do not provide evidence of a stable stage in one child’sproductions in which only target VC syllables are altered. They also mention Central Sentani (Hartzler1976) as a possible example of a language that has this same restriction, but again, no examples of theapplication of a process affecting only VC syllables are provided, and Elenbaas (1999) notes that codasare in general rare.

    10 One type of cumulativity cannot be accounted for in this approach: multiple violations of single constraint.

  • Gradient phonotactics in Muna and OT p.29

    (25) i. How does a learner create lexically specific constraints for exceptions tophonotactics?

    ii. How do the markedness constraints get in the right order?iii. How do the faithfulness constraints get interspersed correctly?

    Itô and Mester (1999) propose a solution to the second two of these problems, but it requires thatthe learner encounter the data in a particular order, and it does not address the first problem.

    In Pater and Coetzee (2005), we address this issue by proposing that learners are initiallyconservative, in that when they encounter a word that requires an adjustment to the grammar,they first assume that this adjustment is specific that word. More formally, in terms of Tesar andSmolensky (1998) et seq., when Error-Driven Constraint Demotion produces a Mark-Data pair,faithfulness constraints preferring the winner are indexed to the lexical item in question. Whenthis proposal is incorporated into Prince and Tesar’s (2004) Biased Constraint DemotionAlgorithm, it automatically yields an answer to the second two problems. Here we offer just asimplified summary of the account so as to give some sense that the learnability problems are notinsuperable; see Pater and Coetzee (2005) for more details.

    In Error-driven learning, the grammar is used to parse the data presented to the learner. Whenthis parse results in an output that does not match the target data (an error), the grammar isrevised so that it does correctly generate the target form. For example, if a learner had NOCODA>> MAX, a piece of data of the form CVC would be incorrectly parsed as CV. NOCODA wouldthen be demoted beneath MAX, so that CVC is made correctly optimal. The amendment in Paterand Coetzee (2005) is that the faithfulness constraint is also indexed to the lexical item. Theresult is that instead of the grammar in (26a), presentation of CVC to a learner with NOCODA >>MAX produces in (26b).

    (26) a. MAX >> NOCODAb. MAX-L >> NOCODA >> MAX

    Presentation of further words with codas results in further lexically specific MAX constraints,which coalesce into the general constraint once a threshold of constraints in the same stratum isreached. A learner of a language with a small set of codas will wind up with the grammar in(26b), which encodes the marginality of the structure, and a learner of a language with a largerset will end up with (26a).

    Intermediate grades of well-formedness are achieved as a by-product of the relative sizes of thesets of lexically specific constraints. For example, a language with two codas, and one complexonset, would have the following lexicon and set of constraints:

    (27) Lexicon: /pa/ /ti/ /la/ /me/ /go/ /ra/ /matL1/ /netL2/ /fleL3/Constraints: NOCODA *COMPLEX MAX-L1 MAX-L2 MAX-L3

    When choosing amongst faithfulness constraints to rank in the current stratum, Prince andTesar’s (2004) Biased Constraint Demotion Algorithm (BCDA) seeks the smallest set that will

  • Gradient phonotactics in Muna and OT p.30

    free up a markedness constraint. This was proposed to ensure a maximally restrictive grammar,but it has the benefit here of leading to an ordering of markedness constraints that reflects lexicalfrequency. When applied to (27), the BCDA first installs MAX-L3, which allows *COMPLEX tobe ranked, and then installs MAX-L2 and MAX-L3, followed by NOCODA:

    (28) MAX-L3 >> *COMPLEX >> MAX-L1, MAX-L2 >> NOCODA

    As desired for our account of gradient phonotactics, the less frequently violated *COMPLEX endsup ranked higher than the more frequently violated NOCODA.

    Because it is sensitive to frequency of constraint violation, Boersma’s (1998) Gradual LearningAlgorithm (GLA) might also be adapted to acquire rankings consistent with gradientphonotactics. Though we leave the full exploration of this possibility for further research, eachalgorithm would appear to have its own advantage related to this domain. The ConstraintDemotion Algorithm detects inconsistency, which seems crucial in learning some cases ofexceptionality (Tesar et al. 2003, Tesar 2004, Pater 2005), as well as for learning underlyingforms (Tesar and Prince 2004, McCarthy 2004) and metrical structure (Tesar 1998; cf.Apoussidou and Boersma 2004). The Gradual Learning Algorithm does not detect inconsistency,but it does handle variation, and has been applied to gradient exceptionality in alternations(Zuraw 2000, Hayes and Londe 2005).

    4. Conclusions

    Muna provides a novel case of lexically gradient phonotactics, which adds to our understandingof the cross-linguistic range of place co-occurrence restrictions. We have analyzed the Muna datain terms of relativized OCP-Place constraints, including constraints relativized to [voice], whichMuna uniquely motivates. By ranking these constraints with interspersed lexically specificfaithfulness constraints the gradience in their application across the lexicon can be dealt with.Frisch et al.’s (2004) critique of an OT analysis of place co-occurrence loses force in light of thepossibility of accounting for gradient phonotactics in OT, and also in view of the difficulties thattheir alternative analysis has in accounting for the place co-occurrence patterns in Muna.

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