Handling Equivalence Classes of Optimality-theoretic Comparative Tableaux

Many Optimality-Theoretic tableaux contain exactly the same information, and equivalence-preserving operations on them have been an object of study for some two decades. This paper shows that several of the operations proposed in the earlier literature together are actually enough to express any possible equivalence-preserving transformation. Moreover, every equivalence class of comparative tableaux (equivalently, of sets of Elementary Ranking Conditions, or ERC sets) has a unique and computable normal form that can be derived using those elementary operations in polynomial time. Any equivalence-preserving operation on comparative tableaux (ERC sets) is thus computable, and normal form tableaux may therefore represent their equivalence classes without loss of generality. Optimality Theory (OT) is a grammatical formalism based on constraint competition, formulated by defined by [Prince and Smolensky, 1993] (later published as [Prince and Smolensky, 2004]). OT is especially popular in phonology, and is used to some extent in other branches of linguistics. In OT, a set of competing output forms {Out1, Out2, ...} is generated by machine Gen for the underlying form Inp. Each pair 〈Inp,OutM〉 is then evaluated against a set of constraints Con. The grammar of a particular language is modeled as an ordering of the universal set of constraints Con which determines the winning input-output pair for each Inp: an input-output pair α = 〈Inp,OutM〉 wins over another pair β = 〈Inp,OutN〉 in case α incurs less violations than β in the most highly ranked constraint where α and β differ. The input-output pairs that do not lose to any other pair are declared grammatical. The OT formalism expresses two important intuitions regarding how languages might function. First, it easily captures conditions of the form “try A; if impossible, try B; if also impossible, resort to C”, which seem to frequently occur in natural language (though, of course, for many seeming “defeasibility phenomena” analyses have been proposed that do not invoke actual defeasibility of constraints or rules). Second, OT allows for elegant modeling of cross-linguistic variation and language change in terms of re-ranking of a universal set of constraints. The information that a given dataset contributes constrains the possible rankings of constraints. Such information may be represented in the form of a comparative tableau ([Prince, 2000]) or the corresponding set of Elementary Ranking Conditions, Date: August 14, 2013.