Abstract
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.
Highlights
Universität Tübingen abstractMany Optimality-Theoretic tableaux contain exactly the same information, and equivalence-preserving operations on them have been an object of study for some two decades
As a concrete example of how OT works, consider the pattern of final obstruent devoicing in Dutch.3 Underlyingly, Dutch morphemes may have both voiced and voiceless obstruents: the morpheme for ‘bed’ is /bɛd/, surfacing faithfully in [bɛd-ən] ‘beds’, while the morpheme for ‘dab’ is /bɛt/, surfacing faithfully in [bɛt-ən] ‘(we) dab’
Another pair [bɛt]∼[pɛd] does not add any useful information: without any Ls in the row, [pɛd] is going to lose to [bɛt] on any possible ranking of our three constraints In what follows, I will be largely talking in terms of comparative rows and tableaux, but it is easy to translate this into talk about ERCs and ERC sets
Summary
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. Any equivalence-preserving operation on comparative tableaux (ERC sets) is computable, and normal form tableaux may represent their equivalence classes without loss of generality. The present paper fills this gap: I show that any (finite) comparative tableau may be (computably, and quite efficiently) transformed into a normal form, which is unique for the whole equivalence class This transformation is possible by applying a sequence of a set of five elementary operations and their inverses. I prove that the equivalence-preserving operations introduced in the earlier literature are already enough to handle equivalence classes of comparative tableaux/ERC sets, once we add the necessary proofs. (3) Row swaps: swapping any two rows preserves OT equivalence
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