Optimality Theory

Optimality Theory ("OT," Prince and Smolensky 1991, 1993) is a theory of LINGUISTIC UNIVERSALS AND UNIVERSAL GRAMMAR. According to OT, the grammars of all human languages share a set of constraints, denoted Con. These constraints are sufficiently simple and general that they conflict in many contexts: they cannot all be satisfied simultaneously. The grammar of an individual language resolves these conflicts: it ranks the universal constraints of Con into a constraint hierarchy, conflicts being resolved in favor of higher-ranked constraints, with each constraint having absolute priority over all lower-ranked constraints. Grammars may differ only in how they rank the universal constraints; the TYPOLOGY of all possible human languages may be computed as the result of all possible rankings of these constraints. An OT analysis explains why some grammatical patterns are possible while others are not. (That a particular language happens to have a particular constraint ranking is not considered a fact to be explained within grammatical theory proper.)

Consider, for example, the difference between the simple English sentence it rains and its Italian counterpart piove -- literally, "rains." What do these sentences reveal about the commonalities and differences between the two grammars? According to the OT analysis of Grimshaw and Samek-Lodovici (1995, 1998), at issue here is a conflict between two constraints -- SUBJECT : "Every sentence has a subject," and FULL-INTERPRETATION : "Every element of a linguistic expression contributes to its interpretation." In English, the conflict is resolved in favor of SUBJECT : to provide a subject, it must appear, even though it has no referent and contributes nothing to the interpretation of the sentence, violating FULL-INT . In Italian, the conflict is resolved the other way: no meaningless subject may appear, and FULL-INT prevails over SUBJECT .

In many other contexts, SUBJECT and FULL-INT do not conflict, and both constraints must be satisfied in both languages. Both constraints are parts of the grammars of both languages, but they do not have equal status: in English, SUBJECT has priority, or dominates; we write: SUBJECT >> FULL-INT . In Italian, the reverse constraint ranking holds. The lower-ranked constraint in each language must be obeyed, except in contexts in which doing so would violate the higher-ranked constraint; in this sense, constraints in OT are minimally violable. OT thus differs from earlier grammatical theories employing inviolable constraints, where any violation of a constraint renders a structure ungrammatical (e.g., RELATIONAL GRAMMAR, LEXICAL FUNCTIONAL GRAMMAR, HEAD-DRIVEN PHRASE STRUCTURE GRAMMAR).

To sketch the broad outline of the OT picture of cross-linguistic variation, we fix attention on a universal constraint (e.g., FULL-INT). In some languages, is very highly ranked (e.g., Italian); the effect is that those linguistic structures (e.g., meaningless it) that violate the constraint -- those that are marked by it -- are altogether banned from the language. In other languages, is somewhat lower ranked, so that the structures it marks (e.g., it) now appear -- but only in those highly restricted contexts in which the marked element is needed to satisfy one of the few constraints more highly ranked than (e.g., SUBJECT in English). Looking across still other languages, is ranked lower and lower, so that the structures it marks appear in more and more contexts, as more and more other constraints force violations of because they outrank it. The OT literature documents many specific cases of this general cross-linguistic pattern, which can be captured entirely by the simple statement: Con. Once this has been stated, the rest of the pattern follows from the formal structure of OT: languages differ in how they rank , and depending on this ranking, those structures marked by will be either banned altogether (highest ranking), allowed but only in a highly restricted set of contexts, or allowed in a wide range of contexts (lowest ranking).

Each universal constraint defines a class of dispreferred or marked structures: those that violate it. Through the single mechanism of constraint ranking, such marked elements are banned in some languages, and restricted in their distribution in all languages. OT thus builds on the notion of markedness developed in the 1930s by N. S. Trubetzkoy, Roman JAKOBSON, and others of the Prague Linguistics Circle; OT provides a formal, general markedness-based calculus within the tradition of GENERATIVE GRAMMAR. OT's formalization of markedness computation brings into sharp focus a number of issues otherwise obscure.

Competition To say that a linguistic structure S is grammatical in a language L because it optimally satisfies L's constraint hierarchy is to exploit a comparative property: even though S might not satisfy all the universal constraints, every alternative incurs more serious violations of L's hierarchy than does S. Specifying an OT grammar includes specifying the candidate sets of linguistic structures that compete for optimality. This must be universal, for in OT, only constraint ranking varies across grammars.

Aggregation of Multiple Dimensions of Markedness

What defines optimality when the constraints defining different dimensions of markedness disagree on which candidate is preferred? OT's answer is constraint ranking. S is optimal if and only if it is more harmonic than all other members S" of its candidate set, written S > S": this means that, of the constraints differentiating the markedness of S and S", S is favored by the highest ranked. It is perhaps surprising that within such a simple mechanism, reranking can succeed in accounting for such a diversity of observed grammatical patterns.

Faithfulness to Targets Why is it rains optimal, when its violation of FULL-INT could be avoided by selecting another candidate with an interpreted subject, say, John smiles? Implicit thus far in the competition for optimality is the target proposition, <rain(), tense = present>, to which it rains, but not John smiles, is faithful. In OT, each candidate is evaluated relative to a target, faithfulness to which is demanded by constraints in Con collectively called FAITHFULNESS . John smiles is indeed optimal, but for a different target, <smile(x), x = John, tense = present>. The multiplicity of grammatical -- optimal -- structures in a single language arises from the multiplicity of possible targets. In PHONOLOGY, the target is a sequence of phones, an underlying form such as /bat + d/ for the past tense of to bat. Optimal for this target is [bat d] "batted"; this includes a vowel ( [ ] ) not present in the target, so it violates a FAITHFULNESS constraint, . This minimally unfaithful candidate is optimal because of a universal constraint against certain word-final consonant clusters, including td; this constraint is higher ranked than in the phonological component of the English grammar. That a morpheme (like past-tense /d/) receives different (but closely related) pronunciations, depending on its context, follows in OT from a fixed underlying form for the morpheme, FAITHFULNESS to which is (minimally) violated in many optimal forms, forced by higher-ranked well-formedness constraints governing phones in various contexts. Violability of FAITHFULNESS plays a less obvious role in SYNTAX; Legendre, Smolensky, and Wilson (1998) use it to explain why some syntactic targets have no grammatical expression in a particular language: for such an ineffable target, every faithful candidate violates sufficiently high-ranking constraints that an unfaithful candidate, with a different interpretation, is optimal.

The candidates competing for a target I form a set written Gen(I); I is often called the input, and sometimes the index, of this candidate set. The set of targets and the candidate-generating function Gen are universal.

Implications A framework employing a novel type of grammatical computation, optimization, OT has cognitive implications for the classic questions of generative grammar that concern the nature of knowledge of language, its use, its acquisition, and its neural realization.

Violable constraints profoundly alter the analytic options in syntactic theory. When a grammatical sentence S appears to violate a putative simple, general, universal constraint , it becomes possible to simply say that it actually does; with inviolable constraints, it is typically necessary to posit invisible structures that allow S to covertly satisfy , or to complicate , often via language-particular parameters, so that it is no longer violated by S. Topics of OT syntactic analyses include grammatical voice alternations (GRAMMATICAL RELATIONS and THEMATIC ROLES), case, ANAPHORA, HEAD MOVEMENT, subject distribution, wh-questions (WH-MOVEMENT), scrambling, and clitic inventories and placement.

In phonological theory, the shift from serial, process-oriented frameworks (PHONOLOGICAL RULES AND PROCESSES) to OT's parallel, violable constraint optimization has enabled explanation of typological variation in a number of areas: segmental inventories, syllable structure, STRESS, TONE, vowel harmony, reduplicative and templatic MORPHOLOGY, phonology-morphology relations, the phonology- PHONETICS interface, and many others. (For an extensive bibliography and on-line database of OT papers and software, see the Rutgers Optimality Archive ROA at http://ruccs.rutgers.edu/roa.html.)

A unified grammatical framework for syntax and phonology, OT also provides results that span both these modules, including the relation of general to more specific constraints, the compatibility among related grammatical processes, and the computation and learnability of grammars. Formal results on the latter topics address algorithms for learning constraint rankings from positive examples, algorithms for computing optimal forms, and the complexity of formal languages specified by OT grammars. Empirical findings on the course of acquisition of PHONOLOGY in children, and on real-time SENTENCE PROCESSING, have been analyzed within OT. While detailed OT proposals for the neural basis of language and the neural basis of phonology do not currently exist, theoretical connections between optimization in OT and in NEURAL NETWORK models have proved fruitful for the continuing development of both OT and the theory of complex symbol processing in neural networks (Prince and Smolensky 1997).

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-- Paul Smolensky

References

Grimshaw, J., and V. Samek-Lodovici. (1995). Optimal subjects. In J. Beckman, L. Walsh-Dickey, and S. Urbanczyk, Eds., University of Massachusetts Occasional Papers in Linguistics 18: Papers in Optimality Theory. Amherst, MA: GLSA, University of Massachusetts, pp. 589-605.

Grimshaw, J., and V. Samek-Lodovici. (1998). Optimal subjects and subject universals. In P. Barbosa, D. Fox, P. Hagstrom, M. McGinnis, and D. Pesetsky, Eds., Is the Best Good Enough? Papers from the Workshop on Optimality in Syntax. Cambridge, MA: MIT Press and MIT Working Papers in Linguistics.

Legendre, G., P. Smolensky, and C. Wilson. (1998). When is less more? Faithfulness and minimal links in wh-chains. In P. Barbosa, D. Fox, P. Hagstrom, M. McGinnis, and D. Pesetsky, Eds., Is the Best Good Enough? Papers from the Workshop on Optimality in Syntax. Cambridge, MA: MIT Press and MIT Working Papers in Linguistics.

Prince, A., and P. Smolensky. (1991). Notes on Connectionism and Harmony Theory in Linguistics. Technical Report CU-CS-533-91. Boulder, CO: Department of Computer Science, University of Colorado.

Prince, A., and P. Smolensky. (1993). Optimality Theory: Constraint Interaction in Generative Grammar. RuCCS Technical Report 2. Piscataway, NJ: Rutgers Center for Cognitive Science, Rutgers University, and Boulder, CO: Department of Computer Science, University of Colorado.

Prince, A., and Smolensky, P. (1997). Optimality: From neural networks to universal grammar. Science 275:1604-1610.

Optimality Theory

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