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. Gradient phonotactics in Muna and OT p.2 form – no variation is reported. Here we extend one OT approach to exceptionality to gradient phonotactics: that of indexed faithfulness constraints (Kraska-Szlenk 1997, Fukuzawa 1999, Itô and Mester 2000, 2001, Pater 2000). In this account, markedness constraints are ranked according to the degree to which they are obeyed in the lexicon, and lexically specific faithfulness constraints are interspersed between them. We introduce this approach in section 2 by 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 how ranking 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 (or fricatives) than words with coronal stop/fricative pairs.
Frisch et al. (2004) propose an alternative to an OCP-based analysis of Arabic, in which similarity 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 et al. (2004: 19) argue for it on the basis of its greater predictiveness. In the similarity metric account, pairs of consonants that are equivalent in terms of similarity should always pattern together in co-occurrence restrictions. An account based on relativized OCP-PLACE constraints incorporated into OT, however, does not make the same predictions: there is no reason why languages could not vary in terms the rankings of the various constraints. For example, the similarity 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] and OCP-LAB-[-SON][αCONT], however, need not be ranked together, and could in fact assume either dominance relation.
In section 3, we introduce data from the Austronesian language Muna (Berg 1989) that show that the greater predictiveness of the similarity metric may be a liability, rather than an asset. As in Arabic, 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 featural similarity. However, whereas in Arabic and other languages with documented place co- ocurrence restrictions similarity is primarily defined by sonorancy, in Muna it is voicing that plays the dominant role. Thus, languages do vary in ways unexpected by the similarity metric. In addition, in Muna as in Arabic, coronals are relatively free to co-occur compared to labials and dorsals. However, unlike Arabic, the coronal inventory is not especially large in Muna, which is unexpected under Frisch et al.’s account of the Arabic coronal facts. We provide an analysis of the Muna data and its differences from Arabic in terms of lexicon-reponsive ranking of relativized OCP constraints. We also apply the similarity metric to Muna, and discuss the ways in which Muna supports, and challenges, Frisch et al.’s proposal.
Since gradient phonotactics are not usually dealt with in generative phonology, it might be imagined 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 the incorporation of gradient phonotactics, and related well-formedness judgments, into phonological 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 the paper 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 the verbal root (Greenberg 1950, McCarthy 1988, 1994, Pierrehumbert 1993, Padgett 1995, Frisch et al. 2004). Given Arabic’s root-and-pattern morphological system, these consonants are often separated by vowels supplied by other morphemes, so they are not necessarily adjacent in the phonological string. There are a number of exceptions to this general restriction, but the distribution of these exceptions is not random. Frisch et al. (2004) examined the degree to which particular pairs of consonants are underrepresented in a list of 2,674 roots taken from a dictionary of standard Arabic (Cowan 1979). For each pair, they calculated an Observed/Expected ratio, that is, the number of observed words with a particular pair of consonants 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, collapsed over place of articulation, are shown in Table 1. It should be noted that they omitted pairs with identical consonants, which behave differently; we have also omitted the pharyngeals, since these are irrelevant to a comparison with Muna, the language we discuss in section 3.
Labial Dorsal Coronal Sonorant Coronal Fricative Coronal Plosive b f m k g q l r n θ s z s z t d t d Labial 0.00 Dorsal 1.15 0.02
Coronal 1.18 1.48 0.06 Sonorant Coronal 1.31 1.16 1.21 0.04 Fricative Coronal 1.37 0.80 1.23 0.52 0.14 Plosive 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 highly underrepresented. Sonorants co-occur with plosives and fricatives at a rate slightly higher than expected. Fricative-plosive pairs co-occur at an intermediate rate.
McCarthy (1988) accounts for the split between sonorants and obstruents by specifying that the constraint against homorganic segments, the OCP for consonantal place, applies only within the subclasses 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 specific constraints that are violated only by segments that are identical in particular ways (see especially Padgett 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, the consonants in question are assumed to be adjacent at a derivational level in which intervening vowels are absent.
(1) OCP-LAB Adjacent labials are prohibited OCP-DOR Adjacent dorsals are prohibited OCP-PHAR Adjacent pharyngeals are prohibited OCP-COR[αSON] Adjacent coronals agreeing in [+/-sonorant] are prohibited
These constraints are categorical: the grammar bans pairs of consonants that fall under their scope, 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 of sonorants are banned.
The difficulty is in creating a grammar compatible with the intermediate degree of representation of the fricative/stop pairs; given the constraints in (1), they should be ruled out. If the OCP-COR for 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. Neither of 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, but not in their standard interpretation. In (2), a further elaborated set of OCP-COR constraints is presented. We continue to use the term ‘adjacent’, but under the standard OT assumption that markedness constraints apply at the surface, adjacency must be defined so as to ignore intervening vowels (see Suzuki 1998, Rose 2000):
(2) OCP-COR No adjacent coronals OCP-COR[+SON] No adjacent coronal sonorants OCP-COR[-SON] No adjacent coronal obstruents OCP-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 highly underrepresented, with O/E values approaching 0. Pairs of segments that fall outside the scope of those constraints, but that do meet the definition of the constraint in the middle stratum have an O/E value of 0.52. Pairs of segments that meet only the definition of the lowest ranked constraint have an O/E value of above 1.
1 McCarthy (1988) also divides the dorsals by sonority, classifying /w, j/ as the dorsal sonorants, though he 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 handle variation, allow the ranking in (3) to express an Arabic speaker’s knowledge of the observed lexical gradience. For a markedness constraint to be violated, a conflicting constraint must outrank it. Because we are not dealing with alternations, we will use the undifferentiated faithfulness 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 be ranked beneath the topmost stratum, so that sonorant pairs as well as obstruent pairs agreeing in continuancy will be altered to fit the demands of the markedness constraints (we temporarily abstract 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 perfectly well-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-fricative pair will vary between a faithful output, and one that is altered (for example by deleting, or changing the place, of one of the segments). But lexical items in Arabic that have stop-fricative pairs are not reported to show variation. Hammond’s (2004) approach to lexically gradient acceptability does not distinguish between variation and exceptionality, and without further modification 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 this account only covers cases involving alternation.
In a theory with lexically specific constraints, we can resolve this dilemma by having a specific version 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 relative grammaticality of forms from the ranking in (5). So far, one might simply say that a speaker knows that forms with stop-fricative pairs must be lexically marked as exceptions, and that this gives them an intermediate status between forms that are ruled out completely (for which the relevant markedness constraints dominate FAITH-L), and those that are perfectly acceptable (for which the relevant markedness constraints are dominated by FAITH).
However, this would not be sufficient to deal with further degrees of gradience. In Arabic, forms that violate OCP-COR[-SON][αCONT] and OCP-COR[+SON] are very rare, but are attested. This means 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 been installed to allow for the exceptional forms with pairs of coronal fricatives, coronal stops, and coronal sonorants. Pairs of labials, on the other hand, are completely absent from the lexicon of Arabic 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), marginally acceptable (e.g. pairs of coronal obstruent stops), moderately acceptable (pairs of coronal obstruents disagreeing in continuancy) and acceptable (pairs of coronals disagreeing in sonorancy). Ungrammaticality is expressed by the fact that a word with a pair of labials will never surface intact, no matter which faithfulness constraint it is indexed to. Perfect acceptability is expressed by the fact that a word with an obstruent-sonorant pair of coronals will always surface faithfully.
One way to distinguish intermediate grades is by submitting a word to the grammar with each lexical indexation. The more often it surfaces faithfully, the more acceptable it is (cf. Anttila’s 1997 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, or leaving it unindexed, will force it to be altered to satisfy OCP-COR[-SON][αCONT]. That is, in 1/3 of the possible indexations, a pair of coronal obstruent stops will surface faithfully (8b). On the other hand, a pair of coronal obstruents disagreeing in continuancy will surface faithfully with 2/3 of the indexations: it will be altered only if it is left unindexed (8c). A pair of labials will never surface faithfully (8a), while a pair of coronals disagreeing in sonorancy will survive intact regardless of indexation (8d). The ordering that thus emerges is shown in (8e).2
(8) a. *p-m *p-mL1 *p-mL2 0/3 b. *t-d *t-dL1 ✓t-dL2 1/3 c. *t-s ✓t-sL1 ✓t-sL2 2/3
d. ✓t-n ✓t-n L1 ✓t-n L2 3/3 e. t-n > t-s > t-d > p-m
The indexations shown in (8) are those that are considered when evaluating the well-formedness of a word, nonce or real. Under the learnability proposal discussed in section 4.2, an actual word will 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 lexical frequency, but does not directly mirror lexical frequency. For example, a language with only one word with a coda and a language with more exceptional coda-bearing words (say, three) could have the same grammars, and the same ratings for well-formedness of codas. Whether they do or not would depend on other patterns of exceptionality. If these languages both had two words with a cluster, then the grammar for the one coda language would be MAX-L1 >> NOCODA >> MAX-L2 >> *COMPLEX >> MAX, whereas the three coda language would have MAX-L1 >> *COMPLEX >> MAX-L2 >> NOCODA >> MAX. Thanks to 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-fricative pair will be indexed only to FAITH-L3.
Another possibility is to compute relative well-formedness by comparing tableaux for different forms (as suggested in Everett and Berent 1998; see Coetzee 2004 for a formally explicit proposal). 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’s rank-ordering model of OT, the grammar can use this information to place forms into a harmonic ordering. Both of these approaches make use of the ranked and violable constraints of standard OT to generate gradient well-formedness. They extend the theory in different ways, but neither is inconsistent with its use for categorical patterns. For concreteness, we use the “possible indexation” approach in our discussion of Muna.
3. Gradient phonotactics in Muna 3.1 The data
Muna is a Western Austronesian language spoken on an island off Southern Sulawesi (van den Berg 1989). It has place co-occurrence restrictions that in interesting ways resemble, and differ from, those in Arabic. In this section, we provide a description of these restrictions; section 2.2 provides an analysis in terms of the approach just introduced in the discussion of Arabic, and section 2.3 discusses the relevance of these data to Frisch et al.’s similarity metric account of Arabic.
Muna’s consonantal inventory is presented in (9).3
(9) labial coronal velar uvular glottal voiceless p t k voiced b d implosive nasal m n -vce, prenas mp nt k ns +vce, prenas mb nd -vce, fric f s h +vce, fric trill r lateral l glide w
3 Muna also has a set of palatals recently borrowed from Indonesian, which are omitted from the inventory in (3), and from all other discussion in this paper. Van den Berg (1989: 16) states: “The palatal consonants /c/, /j/, and /y/ are marginal loan phonemes. The number of words containing these recent loan phonemes 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 of 1100 CVCV roots. He found restrictions against multiple prenasalized obstruents (as in Timugon Murut; Prentice 1971, and Gurindji; McConvell 1988 and Evans 1995), and against pairs of unlike liquids (as in Sundanese; Cohn 1992). Van den Berg also noted that homorganic stops that differ in voicing do not co-occur, nor do nasals and homorganic obstruents. These last two gaps are 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)CVCV and (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-occurrence found between consonants in what Frisch et al. (2004) call “adjacent” positions – that is, ones separated only by a vowel. The total number of such pairs of consonants is 7892; it is greater than the total number of roots, since (V)CVCVCV roots have two adjacent pairs. The following tables present O/E values for consonants grouped according to place of articulation. The uvular fricative is classified as a dorsal since it behaves as such, and the glottal fricative is omitted, as it appears to co-occur freely with all segments. Table 2 presents these figures for non-identical consonants, with pairs of prenasalized segments omitted, since they are subject to an independent, absolute co-occurrence restriction. As expected, co-occurrence of homorganic segments is below expected rates, especially that of labial and dorsals. The table also presents examples of Muna words of each shape.
Labial Dorsal Coronal Obs Exp O/E Obs Exp O/E Obs Exp O/E Labial 156 477.8 0.33 bafu, mopi, mafaka Dorsal 875 770.9 1.14 63 210.6 0.30 meko, bage, bugi kangia, kagala, kagundi Coronal 2741 2179.0 1.26 1766 1522.5 1.16 1400 1751.5 0.80 bida, 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 Coronal Obs Exp O/E Obs Exp O/E Obs Exp O/E Labial 103 59.8 1.72 bebe, kapopo, fefuna Dorsal 84 65.0 1.29 kakolo, gogoso, hakeka Coronal 274 268.2 1.02 kariri, 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 section 2.2. One peculiarity is that the exemption also seems to apply between consonants that are identical 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 Coronal Obs Exp O/E Obs Exp O/E Obs Exp O/E Labial 132 441.9 0.30 Dorsal 875 770.9 1.14 29 163.6 0.18 Coronal 2741 2179.0 1.26 1766 1522.5 1.16 1338 1686.0 0.79 Table 4 O/E for “adjacent” non-identical consonants in Muna roots, revised
To facilitate a more detailed examination of the restrictions on homorganic consonants, the following three tables present the O/E figures for consonant pairs within each place of articulation.
k k k 0.82 0.07 4.40 k 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 1.73 Table 5: Observed/Expected frequencies of dorsal co-occurence
p b mp mb f w m p 1.46 b 0.10 2.79 mp 0.79 0.20 0.00 mb 0.31 0.52 0.00 0.00 0.11 0.28 0.34 0.69 1.70 f 0.22 0.58 0.29 0.09 0.20 2.50 w 0.16 0.00 0.29 0.74 0.40 0.65 2.04 m 0.39 0.07 0.43 0.23 0.00 1.04 0.09 1.24 Table 6: Observed/Expected frequencies of labial co-occurrence Gradient phonotactics in Muna and OT p.10
t d nt nd s ns l r n t 1.02 d 0.60 2.54 0.37 0.18 2.94 nt 0.74 0.92 0.10 0.00 nd 1.22 1.31 0.45 0.00 0.00 s 0.37 0.55 0.51 0.63 1.01 1.21 ns 0.05 1.68 0.00 0.00 0.00 1.12 0.00 l 0.78 0.79 0.99 1.07 1.45 1.13 1.37 0.89 r 0.88 0.84 1.37 1.15 1.28 1.08 1.67 0.19 0.45 n 0.70 0.25 0.39 1.28 0.57 1.17 1.51 0.32 0.56 2.94 Table 7 Observed/Expected frequencies of coronal co-occurrence
It is clear that there are many exceptions to a restriction against non-identical homorganic consonants in Muna. However, it is also clear that as in Arabic, there are phonological generalizations about the patterning of these exceptions.
One obvious factor in co-occurrence in Muna is the place of articulation: coronals co-occur more freely than labials or dorsals. This can be confirmed by comparing similar pairs across places of articulation; 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 of articulation (voiced and voiceless stops, nasals, and prenasalized stops),4 omitting identical pairs and 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 Coronal Obs Exp O/E Obs Exp O/E Obs Exp O/E 31 143.9 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 are more 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 in other 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 particularly underrepresented with the nasal because of its voicing, rather than its place. The inventory of approximants 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 across place of articulation.
Nasals- Nasals- Voiced stops- voiced stops voiceless stops voiceless stops Obs Exp O/E Obs Exp O/E Obs Exp O/E 6 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 freely with the voiceless stops than with the voiced ones, while the voiced uvular fricative never occurs with 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 the Wilcoxon 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 identical pairs and pairs of prenasalized segments, as well as pairs that are identical except for prenasalization.
(10) “Agree” “Disagree” m-b m-p p-f b-f l-d l-t ns-t ns-d
For the 21 such pairs of pairs, the Wilcoxon test indicated that the effect of voicing agreement is highly statistically significant (signed rank sum S+ = 148, p < .005).
The primacy of voicing in determining the strength of a restriction on non-adjacent homorganic consonants is unique to Muna. While place co-occurrence restrictions are best known in Semitic languages (Greenberg 1950), there is a growing list of languages outside of that family that show these 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 less frequently 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 voiceless ones; only the coronal oral stops buck this trend. The implosive labial co-occurs with /f/ at about the same rate as /p/ (with both more frequent than /b-f/), but the coronal implosive co-occurs with /s/ at about the same rate as /d/ (with both more frequent than /t-s/). In sum, the implosives seem to be neutral with respect 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 determined by whether the segments agree in sonorancy, as in Arabic. Frisch et al. (2004) report effects of voicing similarity for Arabic, but they are much weaker (see also Kawahara et al. to appear for similar findings in Yamato Japanese). Within the class of coronal obstruents, pairs of segments that 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 with voiceless obstruents than with voiced ones (O/E of 1.31 vs. 1.15); this difference does not reach statistical significance on the Wilcoxon test. The Muna pattern is not entirely unprecedented however: voicing agreement seems to play a strong role in disfavoring sequences of homorganic consonants 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 place restriction in Muna. The sonorants /l/ and /r/ are more restricted with /n/ (O/E = 0.43) than they are with the obstruent /d/ (O/E = 0.81). However, the labial sonorant /w/ is about equally underrepresented with /b/ (0.00) as it is with /m/ (0.07). When /w/ is paired with the segments that are not [+voice] (/p/, // and /f/), its representation is somewhat higher (0.16, 0.40 and 0.65 respectively). 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 in sonorancy, most strongly influences the restriction against homorganic segments in Muna. However, the shared voicing of the liquids with /d/ is not sufficient to force much underrepresentation, presumably because agreement in continuancy is also required amongst the coronals.
Other manner effects can be seen as well, and they are all subjugated to voicing. When a prenasalized segment is paired with a segment that is not identical to its oral portion, a difference in 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 and prenasalized stops (O/E {p-mb, b-mp, k-, -k, d-nt, t-nd} = 0.49). This is also evident in a comparison between s-d (0.55) and ns-d (1.68). However, when the oral portions agree in voicing, 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 place restriction: /p-b/ more restricted than /f-b/ (0.10 vs. 0.58), but this is again overridden by voicing similarity: /p-f/ is not well represented (0.22). Within the coronal obstruents, there is no noticeable effect for continuancy (though see section 2.2.2 on effects across the sonorancy divide). When segments differ for sonorancy and continuancy, as well as voicing, they co-occur freely: /n-s/, /m-f/, and /n-ns/ all have O/E values above 1. However, voicing similarity overrides even this large manner difference; the voiced uvular fricative never occurs with //.
2.2 Muna and the relativized OCP 2.2.1 Core analysis
In this section, we use ranked relativized OCP constraints to provide an analysis of one part of the 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 2.2.3 discuss 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 within each of the three places of articulation, along with examples of words of each type. Again, pairs of identical segments are omitted.
Coronal Labial Dorsal d t 0.60 (3) b p 0.10 (1) k 0.07 (1) Voiced Stop + Voiceless Stop datu pabu kagala n d 0.25 (2) m b 0.07 (1) 0.00 (0) Nasal + Voiced Stop da:no bomu t n 0.70 (3) m p 0.39 (3) 0.10 (1) Nasal + Voiceless Stop k tunani mopi kagia n s 1.17 (4) m f 1.04 (4) 0.00 (0) Nasal + Fricative nasi mafaka s d 0.55 (3) f b 0.58 (3) 0.00 (0) Fricative + Voiced Stop sida febuni s t 0.37 (3) f p 0.07 (1) k 0.40 (3) Fricative + Voiceless Stop tisore fopanto kaa Table 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 not clear what distinctions the analysis must encode. In absence of such data, we adopt the following working hypothesis about the mapping between O/E values and acceptability, where ‘0’ = unacceptable and ‘4’ = fully acceptable:
(12) Hypothesized acceptability values 0 → ‘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/E values 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-formedness the basic structure of the Muna grammar will be as in (13), where “M-stratum” stands for a set of Markedness 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 faithfulness constraint. 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 of those constraints, regardless of which lexically specific faithfulness constraint they are indexed to. If word types that get an acceptability score of ‘0’ violate a constraint in M-stratum0, they are correctly 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 are indexed to. Word types that get an acceptability score of ‘4’ must therefore violate no markedness constraint in an M-stratum higher than M-stratum4. The intermediate acceptability values are similarly generated by ensuring that the relevant word-types violate at least one markedness constraint in the appropriate stratum, and no markedness constraint in any higher stratum. For instance, a word type ranked as ‘1’ must violate a constraint in M-stratum1, and none in M-stratum0.
In order to facilitate discussion, Table 11 groups the consonant pairs at each place of articulation from Table 10 according to the acceptability scores that each would be assigned.
Acceptability score Coronal Labial Dorsal 0 N-g, Â-g, N-Â 1 b-p, f-p, m-b g-k, N-k 2 n-d 3 t-n, s-d, d-t, s-t m-p, f-b Â-k 4 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 acceptability group. The pairs [N-g], [Â-g] and [N-Â] are completely unacceptable. These three pairs are separated from the others by the fact that they consist entirely of [+VOICE] segments. Thus, an OCP-DOR constraint relativized to shared voicing, OCP-DOR[αVOICE], will correctly pick them out. Since there is only one voiceless dorsal, [k], this constraint can apply to dorsals that share voicing, rather than just [+VOICE] dorsals.
The pairs [g-k] and [N-k] receive an acceptability score of 1, and they should therefore violate a markedness constraint ranked in the M-stratum1 in (13). These two pairs share the feature of being non-continuants, and they therefore violate the constraint OCP-DOR[αCONT]. Since there is 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 constraint from M-stratum3. Since we have already accounted for all other pairs of dorsal consonants, we can use the general OCP-constraint for dorsals, OCP-DOR. The grammar necessary to account for 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] shares the feature [+voice] and the pair [f-p] shares the feature [-voice]. These two pairs will therefore both violate OCP-LAB[αVOICE]. Inspection of the labial pairs that receive acceptability ratings other 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] or OCP-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 a markedness 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 therefore safely use OCP-LAB[αCONTINUANT] to account for the score that [m-p] receives. The [f-b] pair shares only the feature [-sonorant]. Again, since [m-f] does not share this feature, we can use OCP-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 will violate only the general OCP-LAB, which should be ranked right at the bottom to account for the perfect acceptability of words that have this pair of labials. The grammar necessary to explain the co-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 pair should therefore violate a markedness constraint ranked in M-stratum2. This pair shares the features [+voice] and [-continuant]. There are other coronal pairs that also have the same specification for [voice] ([s-t]) or for continuancy ([t, n], [d, t]). We can therefore use neither OCP-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 the pair [n-d]. Ranking this constraint between FAITH-L2 and FAITH-L1 will account for the acceptability 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 therefore violate 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 the pair [d-t] also violates this constraint, this one constraint also takes care of this pair. This leaves the 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 only violate markedness constraints that rank below all faithfulness constraints in M-stratum4. Aside from place [n-s] share no other features. The only OCP-constraint that this pair violates, is then the general OCP-COR constraint. In (16) we give the grammar necessary to account for the relative 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 the acceptability 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 “>>” is omitted.
(17) Muna consonantal co-occurrence grammar OCP-DOR OCP-LAB OCP-COR OCP-COR OCP-COR
[αVOI] -L3 [αVOI] -L2 [αVOI][βCNT] -L1 [αCNT] AITH
OCP-LAB OCP-COR F OCP-LAB AITH AITH AITH
F [αCNT][βSON] F F [αSON] OCP-DOR OCP-LAB [αCNT] [αCNT] OCP-LAB [αSON] OCP-DOR
Accept: 0 Accept: 1 Accept: 2 Accept: 3 Accept: 4
Most of the markedness constraints we have used have precedents in the analysis of other languages. As discussed in section 2, OCP-PLACE constraints relativized to continuancy and sonorancy have been used to analyze the Arabic root constraints; see also Padgett (1995) on Russian and Javanese (as well as Mester 1986 and Yip 1989 on the latter). The novelty here is the use of [voice] to further subdivide the sets of consonants that the OCP applies to, though as mentioned above, [voice]-specific OCP constraints have been posited for consonants that are strictly 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-specific version 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 (see section 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 full set of coronals. Table 12 presents the Observed/Expected values and hypothetical acceptability rankings 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 is between 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-nasal segments, and may thus be relativized to [-nasal]. The role of nasality in mitigating OCP-LAB effects 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 an expansion 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 is some evidence that /w/ may not be a true sonorant. René van den Berg (p.c.) notes that though it is described as an approximant in van den Berg (1989), it is sometimes realized as a voiced bilabial fricative. With a classification of /w/ as an voiced obstruent continuant, nasality would not 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 identical consonants. In Muna, identical consonants are permitted in all positions, as the following tables show. Gradient phonotactics in Muna and OT p.18
Labial Dorsal Coronal Obs Exp O/E Obs Exp O/E Obs Exp O/E Non-Identical 76 249.2 0.30 32 108.1 0.30 652 822.9 0.79 Homorganic Identical 54 32.2 1.68 39 27.7 1.41 105 113.7 0.92 Table 13 Biconsonantal roots
Labial Dorsal Coronal Obs Exp O/E Obs Exp O/E Obs Exp O/E Non-Identical 57 156.3 0.36 25 60.7 0.41 235 335.4 0.70 Homorganic 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 Coronal Obs Exp O/E Obs Exp O/E Obs Exp O/E Non-Identical 23 82.0 0.28 6 38.3 0.16 513 600.0 0.86 Homorganic 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 Muna and these other languages can be seen in triconsonantal roots. In Arabic, identical segments are only permitted in the second two positions (e.g. [s-m-m], *[s-s-m]), while in Javanese they are only permitted in the first two (e.g. [s-s-m], *[s-m-m]; see also Gafos 1998 on Temiar). In
Muna, 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 genetic affiliation of Muna with Javanese than with the Semitic languages. However, except for the coronals, 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-Place in Optimality Theory (cf. MacEachern 1999 on identity in laryngeal cooccurence, and see Frisch et al. 2004: 189 for speculation on an OT-style account for Arabic). For Arabic, one might draw on 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 reason to propose such a structure for Muna, and one would have to further allow it to apply to either C1 and 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 when the oral portion of the prenasalized stop is identical to the segment with which it co-occurs. One cannot simply say that the nasal portion is ignored, since pairs of voiced and voiceless obstruents are 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 segments whose ‘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 also account for the Japanese data in Kawahara et al. (2004), in which voicing disagreement weakens OCP effects, yet is irrelevant for the identity exemption. The ban against identical segments, as seen in Semitic and Javanese, would be imposed by a separate constraint, which is ranked low in Muna.
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 of identical segments as completely ill-formed. For Arabic, this fits with the absence of identical segments from C1/C2 position. For C2/C3 position, they suggest that the similarity metric might be overridden by a separate constraint demanding identity (p. 189). Insofar as Muna does not allow for that option, it would seem that the OCP-PLACE is not a constraint on similarity tout court, but rather 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-occurrence of pairs of homorganic consonants using a similarity metric. Similarity is calculated for a segment pair by dividing the number of shared natural classes by the total number of natural classes 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 Muna place co-occurrence restrictions are clearly strengthened by similarity, and the effects of similarity go well beyond the division of consonants into major classes on the basis of sonorancy and continuancy. Because voicing plays such a central role, Muna shows more robust evidence of “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 the less 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 relativized OCP constraints. Neither cross-classification, nor redundant feature activity poses a problem. As we discussed in the introduction, one difference between these analyses is that the similarity metric is more predictive; there is no reason that a particular ranking of the relativized OCP constraints should hold. To see how the similarity metric fares in predicting the relative rates of co-occurrence for Muna, we calculated similarity values using the featural classifications in the Appendix. These were calculated as in Frisch et al. (2004): by dividing the number of natural classes that both segments belong to by the sum of the numbers that each belongs to. We checked 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 oral portion of a prenasalized segment is identical to the other segment. We also fitted a regression line to these data.
2
1.5
1 O/E
0.5
0 0 0.2 0.4 0.6 0.8 1 Similarity
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% of the 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 results for each place of articulation, with O/E values in parentheses. Gradient phonotactics in Muna and OT p.21
k k 0.44 (0.07) 0.42 0.21 k (0.65) (0.00) 0.25 0.44 0.42 (0.20) (2.25) (0.00) 0.29 0.47 0.14 0.27 (0.40) (0.00) (0.48) (0.00) 0.27 0.47 0.14 0.27 0.29 (0.10) (0.00) (0.00) (0.62) (0.00) Table 16: Similarity values for non-identical dorsals (with O/E)
p b mp mb w 0.50 b (0.10) m 0.28 0.28 p(0.79)(0.20) m 0.29 0.48 0.62 b(0.31)(0.52)(0.00) 0.65 0.59 0.39 0.35 (0.11)(0.28)(0.34)(0.69) 0.55 0.36 0.33 0.24 0.50 f (0.22)(0.58)(0.29)(0.09)(0.20) 0.17 0.35 0.10 0.20 0.19 0.26 w (0.16)(0.00)(0.29)(0.74)(0.40)(0.65) 0.29 0.48 0.20 0.30 0.35 0.24 0.26 m (0.39)(0.07)(0.43)(0.23)(0.00)(1.04)(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 0.43 d (0.60) 0.62 0.50 (0.37)(0.18) n 0.38 0.22 0.27 t (0.74)(0.92)(0.10) n 0.20 0.45 0.24 0.38 d(1.22)(1.31)(0.45)(0.00) 0.50 0.26 0.40 0.22 0.14 s (0.37)(0.55)(0.51)(0.63)(1.01) n 0.24 0.13 0.20 0.46 0.22 0.40 s (0.05)(1.68)(0.00)(0.00)(0.00)(1.12) 0.19 0.36 0.22 0.10 0.19 0.32 0.16 l (0.78)(0.79)(0.99)(1.07)(1.45)(1.13)(1.37) 0.19 0.36 0.22 0.10 0.19 0.32 0.16 0.86 r (0.88)(0.84)(1.37)(1.15)(1.28)(1.08)(1.67)(0.19) 0.11 0.32 0.13 0.06 0.18 0.11 0.06 0.31 0.31 n (0.70)(0.25)(0.39)(1.28)(0.57)(1.17)(1.51)(0.32)(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 the similarity metric does at predicting the weakening of the co-occurrence restrictions amongst coronals, as well as the more subtle difference between labials and dorsals. Looking at the voiced and voiceless stops in the top left corner of the tables, one would conclude that it does not do very well: the similarity values are roughly equivalent, yet the coronals have a much higher O/E value. The average similarity and O/E values for the pairs that can be compared across all three places of articulation (voiced and voiceless stops, nasals, and prenasalized stops), omitting those that may be subject to the identity effect or the ban on multiple prenasalized stops, are presented in Table 19. The raw observed and expected values were presented in Table 8 above.
Coronals Labials Dorsals O/E 0.78 0.22 0.09 Similarity 0.22 0.33 0.29 Table 19 O/E and average similarity values
The differences amongst the similarity values are relatively small; these would all be grouped together 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 large size of the Arabic coronal inventory, which increases the comparison space. As an inspection of the inventory in (9) shows, the coronal inventory size in Muna is only marginally larger than that of the labials. McCarthy (2003b) finds a similar problem in Rotuman: like Arabic, co-occurrence between coronals is much freer across sonorancy classes than within them, but unlike Arabic, the coronal 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 no account of the coronal effect is offered in our own analysis (cf. Alderete 1997), it cannot be considered an advantage of the similarity metric that it derives it from the size of the coronal inventory.
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 are more restricted in their co-occurrence. The raw observed and expected values for these sets of pairs are shown in Table 9.
Nasals+ Voiced Stops+ Voiced Stops Voiceless Stops O/E 0.15 0.32 Similarity 0.22 0.33 Table 20 O/E and average similarity values
Particularly dramatic instances of this difficulty are the pairs /-/ and /w-b/, which have little in common 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 they function in OCP effects, but the similarity metric has no featural weighting mechanism. Frisch et al. (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 other features, such as [voice]. In Muna, on the other hand, [voice] appears to be the feature in need of a boost. Thus not only do features need to be weighted, as Frisch et al. (2004) suggest, but the weighting must be allowed to vary between languages. However, adding language-specific featural weighting weakens the theory considerably, and does not provide an answer to why languages should vary in this way.
The similarity metric approach has different goals than the relativized OCP analysis presented here (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-based should be reconsidered. Since the similarity metric predicts neither the differences across place of articulation nor the effects of voicing seen in Muna, it is not at all obvious that it is superior to an analysis based on relativized OCP constraints (cf. Frisch et al. 2004: 219). Besides its predictive capabilities, the other argument in its favor is its built-in gradience. But as we have shown in the last two sections, when relativized OCP constraints are ranked, they can also express lexically gradient well-formedness. In this case, non-conflicting constraints are placed in a ranking to express their relative strength. Of course, the original motivation for constraint ranking is to negotiate the demands of conflicting constraints, which the similarity metric-based approach 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 of alternation. Place co-occurrence restrictions are seen not only within underived words, but they also play a role in phonologically conditioned alternations (see Suzuki 1998 and especially Fukuzawa 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) (van den 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 can be accounted for by ranking OCP-LABIAL above the relevant faithfulness constraints,6 thus using the same constraint to account for phonotactic well-formedness and alternation. The similarity metric uses natural classes in its computations, but the output is numeric, and does not distinguish between pairs at different places of articulation. Therefore, it is hard to see how it could be used to create a constraint that would pick the right pairs – just labials, just coronals, or just dorsals, as the case may be.
It should also be emphasized that the relativized OCP account does make predictions about the range of cross-linguistic patterns. Because of the very nature of the constraints, they cannot express a pattern in which consonants that differ along some dimension are less well-formed than ones that are similar; they can only express the reverse, actually observed, pattern (Padgett 1995). In addition, if as Alderete (1997) proposes, the OCP-CORONAL constraints are in a fixed ranking beneath OCP-LABIAL and OCP-DORSAL, then a language that imposed a restriction on coronals that is not enforced on the other places should be impossible. If a learner were presented with a lexicon that contained an impossible pattern, the lexicon would be learned, but the grammar would not encode the pattern.7 Patterns that are encoded in the grammar would be more robust over time, as they would affect processing more strongly than those that are not (Coetzee 2004), 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 a potential 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 and Tessier 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 by incorporating constraint rankings that are based on the degree to which the constraints are obeyed in the lexicon. In addition, we have used the Muna data to argue for some expansions to the set of relativized OCP-Place constraints. However, if phonology is responsible only for alternations, and/or for categorical lexical generalizations, then neither this lexicon-responsive ranking, nor some parts of this expanded set of OCP-Place constraints would be necessary.8 In this part of the paper, we argue that phonological theory should, and can be responsible for this type of data: ‘should’ because the arguments for the inclusion of phonotactics in general also apply to gradient phonotactics; ‘can’ because lexicon-responsive ranking is learnable with a minor 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, ones that do not induce alternations. Even though Muna does have alternations that seem to respond to an 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 to account for static phonotactics using the same system that deals with alternations. One reason is that 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 - the rule governing voicing of obstruent sequences in Russian, for example - and to avoid duplication of such rules in the grammar it is necessary to regard them not as redundancy rules but as phonological rules that also happen to apply internally to a lexical item (p. 382)
Subsequent research cast doubt on the viability of a purely rule-based approach to this duplication problem, and this became one of the early arguments for the introduction of constraints into phonological theory (see especially Kenstowicz and Kisseberth 1977, 1979). OT resolves the duplication problem by using the same ranking to produce alternations and filter out ill-formed structures from a rich base (see McCarthy 2002 and Hayes 2004 for discussion). Pater and Tessier (2003) provide experimental evidence that speakers do use their knowledge of static lexical 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 captured by a purely categorical grammar. If phonology is only held to distinguish between possible and impossible patterns, then one might claim that only the consonant pairs that are entirely absent from the lexicon need be ruled out. However, phonological theory does not typically restrict itself to exceptionless generalizations. 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 to ungrammaticality. Gradient phonotactics in Muna and OT p.26
The other argument for the incorporation of phonotactics in phonological grammars is that speakers 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, the same cannot be said about gradient phonotactics. Though it is certainly uncontroversial to make a 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 been incorporated 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 to native speaker judgments to justify the need for a grammar to rule out structures that are unattested in a language, then if these judgments reveal that different structures are ranked along a 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 Hayes 2003, Coetzee 2004, and Hammond 2004 on gradient well-formedness judgments, as well as Pierrehumbert 2001 and references therein).
Unfortunately, we do not have experimental data from native speakers of Muna, which could directly inform the analysis above. However, English has a consonantal co-occurrence restriction that has some of the same key features as Muna and Arabic. In particular, its strength varies by place of articulation, with coronals co-occurring more freely than dorsals, and dorsals more freely than labials. The English restriction applies to consonants in words of the shape sC1V(C)C2: C1 and C2 are underrepresented if they are homorganic (see e.g. Fudge 1969, Davis 1991, Lamontagne 1993). However, the degree of underrepresentation varies by place: pairs of labial oral stops are unattested, dorsals are somewhat more common, and coronals are so common that they are sometimes taken to co-occur freely (cf. Lamontagne 1993: 267). Examples appear in (21).
(21) sTVT e.g. stud, stood, stead, stat, state, staid, stilt, stunt, stand… sKVK e.g. skeg, skag, skunk, skank, skulk sPVP e.g. ?
Coetzee (2004) examined English native speakers’ judgments and lexical decision times on nonce words of the shape [sC1VC2], where C1 and C2 are identical stops, [p], [t], or [k]. The results show that the subjects ranked the words as in (22), where ‘>’ indicates higher grammaticality rating, and slower lexical decision time.
(22) stVt > skVk > spVp
In addition, Coetzee (to appear) shows that these restrictions also affect judgments of ambiguous stimuli: a segment ambiguous between [t] and [k] is more often judged as [t] in the coda position of 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 in comparisons involving non-coronals ([skVC] vs. [spVC]), Coetzee concludes that speakers are aware 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 of questions 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 on arbitrary distinctions between O/E values. Obviously, one question is whether these disctinctions correspond to those that a Muna speaker would make. This analysis is also based on an even more 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. The O/E measure is sensitive to the independent frequency of the segments involved. One occurrence of a pair of segments whose overall frequency is high will result in a lower O/E value than that of a pair of segments whose overall frequency is low. If these pairs of segments each violated a single constraint, and no other structures in the language violated those constraints, then the frequency of constraint violation would be equivalent. In accounts of gradient acceptability and variation in stochastic OT (e.g. Boersma 1998, Boersma and Hayes 2001), as well as in the learnability account for grammars encoding lexical gradience discussed in the next section, it is raw frequency of violation that determines constraint ranking. Whether O/E, or frequency of constraint 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 judgments and more standard phonological data like alternations is that while alternations do not seem to show evidence of cumulative ill-formedness (see below), studies of well-formedness judgments indicate that a form with two unattested, or low probability structures are judged as worse than a form with one (Ohala and Ohala 1986, Coleman and Pierrehumbert 1997, Hay, Pierrehumbert and Beckman 2001, Pierrehumbert 2001). A promising aspect of the OT based model of gradient well-formedness presented here is that it may resolve this apparent contradiction, as we will now show 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 few exceptional words containing instances of each. The grammar for this language would contain rankings like those shown in (23):
(23) C-MAX-L1 >> NOCODA >> C-MAX V-MAX-L2 >> ONSET >> V-MAX
The repair for NOCODA violations is assumed to be consonant deletion (e.g. /bat/ -> [ba]), and for ONSET vowel deletion (e.g. /uma/ -> [ma]). These violate MAX constraints relativized to consonants (C-MAX) and vowels respectively (V-MAX). The exceptional words with codas and onsetless 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 of possible indexations, the outcomes for a nonce word containing just a coda, just an onsetless syllable, or both a coda and an onset syllable are shown in (24).
(24) a. *bat ✓batL1 *batL2 ✓batL1,L2 2/4 b. *aba *abaL1 ✓abaL2 ✓batL1,L2 2/4 c. *abat *abatL1 *abatL2 ✓abatL1,L2 1/4 d. bat, aba > abat
A word with both a coda and an onsetless syllable (24c) will surface faithfully only if specified as both L1 and L2. It is thus rated as less well-formed than a word with just one of the marked structures (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, but cannot occur in alternations because of OT’s tenet of strict constraint domination. No ranking of ONSET, 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 such alternations cross-linguistically, despite the large number of languages that delete consonants from coda position, and vowels in hiatus.9 Unrestricted cumulative constraint activity can create even more bizarre results, such as vowel reduction in the presence of a complex onset anywhere in the word, or cluster reduction in all syllables when one has a voiced coda. One of the most striking results of the typological research that has been conducted in Optimality Theory is that there 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 objection to 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 the cumulative constraint activity observed in grammaticality judgments and other psycholinguistic tasks matches that found in both in lexical restrictions and in phonological alternations. The approach to gradient well-formedness judgments proposed here provides one way of explaining their 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 raise three learnability problems (see also Ota 2004):
9 Levelt and van de Vijver (2004) claim that a restriction against specifically VC syllables, and not CVC or V, holds in a stage of child language. However, this stage is derived from a statistical analysis of a group of children’s productions, and they do not provide evidence of a stable stage in one child’s productions in which only target VC syllables are altered. They also mention Central Sentani (Hartzler 1976) as a possible example of a language that has this same restriction, but again, no examples of the application of a process affecting only VC syllables are provided, and Elenbaas (1999) notes that codas are 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 to phonotactics? 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 that the 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 initially conservative, 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 and Smolensky (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. When this proposal is incorporated into Prince and Tesar’s (2004) Biased Constraint Demotion Algorithm, it automatically yields an answer to the second two problems. Here we offer just a simplified summary of the account so as to give some sense that the learnability problems are not insuperable; see Pater and Coetzee (2005) for more details.
In Error-driven learning, the grammar is used to parse the data presented to the learner. When this parse results in an output that does not match the target data (an error), the grammar is revised 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 would then be demoted beneath MAX, so that CVC is made correctly optimal. The amendment in Pater and Coetzee (2005) is that the faithfulness constraint is also indexed to the lexical item. The result is that instead of the grammar in (26a), presentation of CVC to a learner with NOCODA >> MAX produces in (26b).
(26) a. MAX >> NOCODA b. 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 is reached. 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 larger set will end up with (26a).
Intermediate grades of well-formedness are achieved as a by-product of the relative sizes of the sets of lexically specific constraints. For example, a language with two codas, and one complex onset, 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 and Tesar’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 lexical frequency. When applied to (27), the BCDA first installs MAX-L3, which allows *COMPLEX to be 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 ends up ranked higher than the more frequently violated NOCODA.
Because it is sensitive to frequency of constraint violation, Boersma’s (1998) Gradual Learning Algorithm (GLA) might also be adapted to acquire rankings consistent with gradient phonotactics. Though we leave the full exploration of this possibility for further research, each algorithm would appear to have its own advantage related to this domain. The Constraint Demotion Algorithm detects inconsistency, which seems crucial in learning some cases of exceptionality (Tesar et al. 2003, Tesar 2004, Pater 2005), as well as for learning underlying forms (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 understanding of the cross-linguistic range of place co-occurrence restrictions. We have analyzed the Muna data in terms of relativized OCP-Place constraints, including constraints relativized to [voice], which Muna uniquely motivates. By ranking these constraints with interspersed lexically specific faithfulness 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 the possibility of accounting for gradient phonotactics in OT, and also in view of the difficulties that their alternative analysis has in accounting for the place co-occurrence patterns in Muna.
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Appendix: Features for similarity calculations
k k sonorant - - - - - + continuant - - - - + - voice - + - + + + nasal - - - - - + prenasal - - + + - - dorsal + + + + + + consonantal + + + + + +
p b mp mb f w m sonorant ------+ + continuant - - - - - + + - voice - + - + - + + nasal ------+ prenasal - - + + - - - - sonorant ------+ + implosive + consonantal + +_ + + + + - +
t d nt nd s ns l r n sonorant ------+ + + continuant - - - - - + + + + - voice - + - + - - + + + nasal ------+ prenasal - - - + + - + - - - sonorant ------+ + + implosive + consonantal + + + + + + + + + + lateral + -