Typology in Optimality Theory Matthew Gordon Department of Linguistics University of California, Santa Barbara [email protected] 1 Abstract 2 The mechanism of constraint re-ranking basis makes Optimality Theory a typologically oriented 3 theory of phonology. By permuting the prioritization of constraints on a language specific basis a 4 factorial typology of phonological patterns is generated. The factorial typology may be 5 constrained by the incorporation of phonetically-driven constraint hierarchies that capture 6 implicational distributions. Patterns generated by an Optimality-theoretic account can be 7 compared to the set of attested patterns found in languages of the world to determine how well 8 the analysis fits the observed typology. A particular challenge is presented by overgeneration, 9 which may be pathologic, may reflect accidental gaps due to the paucity of a given phenomenon, 10 or may be grounded in diachronic biases in speech perception. 11 11 1. Introduction 12 The primary responsibility of any phonological theory is to capture the range of variation 13 observed in sound systems of the world’s languages. While all theories take this goal seriously, 14 the formalism of Optimality Theory (Prince and Smolensky 2004) is particularly well suited to 15 making explicit typological predictions that can be rigorously tested by permuting the 16 prioritization of a series of phonological constraints. The fundamental assumption of Optimality 17 Theory that constraint ranking varies from language to language has provided fertile ground for 18 typological research in phonology. 19 2. The formalism of Optimality Theory 20 Unlike earlier rule-based generative treatments of phonology, Optimality Theory (Prince and 21 Smolensky 2004), abbreviated OT, in its original conception assumes a one step mapping 22 between underlying and surface forms. The crucial element in this mapping operation is a set of 23 hierarchically ranked constraints that evaluate a series of potential surface forms, or candidate 24 forms, corresponding to the underlying form. These constraints are of two basic types. Some 25 constraints are sensitive to the well-formedness of candidate forms, banning dispreferred or 26 marked structures or requiring felicitous or unmarked properties. Other constraints are sensitive 27 to the mapping, or correspondence, between underlying forms and candidate forms. Ideally all 28 constraints find principled motivation in independent properties of speech production, 29 perception, and processing. By imposing this grounding requirement on constraints, OT avoids a 30 proliferation of unprincipled constraints and the unattested patterns they would generate (see 31 section 7 for further discussion of generation in OT). The actual surface form is determined by 32 evaluating how well the candidates satisfy the constraints, which, in many cases, impose 33 competing demands. Crucially, the ranking of constraints varies from language to language, 34 thereby accounting for cross-linguistic variation in surface forms. 35 To take an example of constraint evaluation and language specific constraint ranking, 36 consider the case of syllable structure. Many languages, e.g. Hawai’ian, Cayuvava, only allow 37 open syllables, whereas other languages also permit syllables closed by a consonant. The 38 dispreference for closed syllables is attributed to a constraint against coda consonants, *CODA, 39 where the asterisk indicates that a given structure is prohibited. A competing constraint, FAITHC, 40 requires surface faithfulness to underlying consonants, i.e. requires that underlying consonants 41 survive to the surface. Given an underlying string consisting of a consonant-final root followed 42 by a consonant-initial prefix, i.e. CVC-CV, there are at least two possible candidates in 43 competition to surface. One of the two intervocalic consonants could be deleted, a strategy that 44 would satisfy the ban on coda consonants but that would run afoul of FAITHC due to its missing 45 consonant. Alternatively, both members of the consonant cluster could be preserved, thereby 46 honoring faithfulness but not the ban on coda consonants. The ranking of *CODA and FAITHC 47 relative to each other in a given language determines that language’s response to the potential 48 consonant cluster. If *CODA outranks FAITHC, one of the consonants does not survive to the 49 surface, whereas if FAITHC is ranked above *CODA, both intervocalic consonants emerge 50 unscathed. These two outcomes are depicted in (1) by means of a tableau, the standard way of 51 formalizing OT. First, in (1a), the ranking of *CODA above FAITHC is depicted, while in (1b), the 52 ranking of the two constraints is reversed. 53 (1) Two rankings of CODA and FAITHC 54 (a) Coda deletion: *CODA >> FAITHC /CVC-CV/ *CODA FAITHC ☞ CVCV * CVCCV *! 55 56 (b) Coda preservation: FAITHC >> *CODA /CVC-CV/ FAITHC *CODA CVCV *! ☞ CVCCV * 57 58 In tableaux, the underlying (or “input”) form customarily appears in the top left corner followed 59 in the same column by competing candidate forms corresponding to that underlying form. After 60 the first column, each constraint is given its own column where constraints to the left outrank 61 those to their right. Each cell under a constraint name depicts the number of times the candidate 62 in the corresponding row violates that constraint, where each violation is indicated by an asterisk. 63 A candidate that commits one or more violations of a constraint is eliminated from contention, 64 indicated by an asterisk after the fatal violation, if there is at least one other surviving candidate 65 that commits fewer violations of that constraint. Candidates are gradually eliminated as 66 constraint evaluation proceeds from higher to lower ranked constraints until there is only one 67 candidate remaining. This winning candidate is the surface form, traditionally indicated by a 68 pointing finger ☞. Crucially, once a candidate is weeded out due to a violation of a high ranked 69 constraint, it cannot be redeemed no matter how well it satisfies lower ranked constraints. Cells 70 that occur to the right of a fatal violation as well as cells occurring to the right of the constraint 71 that has enabled determination of a unique winner are shaded to indicate their irrelevance to the 72 process of selecting a winning candidate. 73 In (1a), the second candidate, the one containing both consonants in the cluster, is 74 eliminated from contention due to its violation of the anti-coda constraint. This leaves the first 75 candidate, the one in which a consonant has been deleted, as the winner even though it commits 76 a violation of lowly ranked faithfulness. If the constraints are reversed, the faithful candidate 77 with both intervocalic consonants emerges victorious, as shown in (1b). 78 Of course, other constraints come into play in the evaluation of additional candidate 79 forms corresponding to the input. For example, in languages in which *CODA is ranked above 80 FAITHC, another constraint must determine which of the intervocalic consonants is deleted in 81 order to satisfy *CODA. 82 3. Reranking and typology in OT 83 Cross-linguistic variation in rankings is one of the cornerstones of Optimality Theory and makes 84 the theory inherently well suited to tackle typological issues in phonology. An OT analysis of a 85 given phenomenon can be evaluated on the basis of how closely the patterns predicted through 86 constraint re-ranking, as in our syllabification example in 2, fit patterns attested in languages of 87 the world. Ideally, the patterns generated through permutation of the constraint rankings exactly 88 match the set of patterns found cross-linguistically. In reality, this ideal fit is seldom achieved. 89 Rather, analyses typically overgenerate by predicting patterns that either do not occur cross- 90 linguistically or at least have not been identified yet. Overgeneration is often difficult to assess 91 critically, since unattested patterns predicted to occur by an analysis potentially reflect accidental 92 gaps due to insufficient cross-linguistic data as opposed to pathologic patterns that could not 93 reasonably be expected to occur. More seriously, analyses may undergenerate by failing to 94 capture patterns that have been found in one or more languages. The issue of overgeneration and 95 undergeneration in OT is discussed in section 7. 96 4. Conspiracies in OT 97 One of the virtues of Optimality Theory in the typological domain is its prediction of 98 “conspiracies”: instances where different languages employ diverse strategies that conspire to 99 avoid the same ill-formed configuration. OT explicitly predicts the existence of such 100 conspiracies due to its formal separation of constraints banning a particular structure from 101 constraints sensitive to potential ways of eliminating that prohibited structure. For example, the 102 constraint against coda consonants merely penalizes candidates that have a coda consonant 103 without determining the path a language will take to avoid codas. There are several routes a 104 language could take to avoid coda consonants ranging from deletion of the first consonant 105 (CVC1C2V → CVC2V), to deletion of the second consonant (CVC1C2V → CVC1V), to insertion 106 of an epenthetic vowel (CVC1C2V → CVC1VC2V), to changing a consonant into a vowel 107 (CVC1C2V → CVVC2V). The choice among these options is governed by the relative ranking of 108 other constraints, e.g. an anti-epenthesis constraint banning vowels that are not present 109 underlyingly, an anti-deletion constraint requiring that underlying consonants surface, a 110 constraint banning the conversion of an underlying consonant to a vowel on the surface. A key 111 feature of the OT analysis is its unification of these processes as strategies all serving the same 112 goal driven by the same constraint against codas. This differs from traditional rule-based 113 approaches that collapse the ill-formed configuration and the process eliminating the ill-formed 114 structure into a single rule. The result is a series of formally distinct rules, each one capturing a 115 different strategy for avoiding codas.