Optimality Theory (OT, cf. [Prince and Smolensky(1993), Grimshaw(1995)]) assumes that a grammar consists of ranked, violable constraints. In OT, the linguistic structure of an utterance is computed as the optimal structure of a set of possible candidates, where ``optimal'' is defined as satisfying most of the most highly ranked constraints. Like traditional linguistic theories, OT is based on a binary notion of grammaticality: the optimal candidate is grammatical; no assumptions are made about the relative grammaticality of suboptimal candidates.

To account for graded data, we propose to extend OT such that degrees of grammaticality are assigned to competing candidates according to the number and ranks of the constraints they violate. More precisely, we postulate that the optimality theoretic harmony of a candidate corresponds to its relative grammaticality in the candidate set. Under this assumption, evidence for constraint rankings can be obtained from judgments for suboptimal candidates. While a standard OT grammar makes predictions of the form: a structure is grammatical, but is ungrammatical, graded OT predicts that a structure more or less grammatical than , a claim that can be tested against graded experimental data.

Thu Feb 13 14:35:39 GMT 1997