Optimality Theory adopts an explicitly declarative formalism of constraints in the formulation of structural regularities. Nevertheless, its vocabulary of input, output, and optimization carries an implicit procedural metaphor. The metaphor is actualized in EVAL, an algorithm that assigns violation marks to each output candidate and selects the best candidate through a pair-wise comparison of the violation marks on them. In this conception, constraints become variants of output filters that eliminate non-optimal outputs in a production algorithm. In other words, while the formulation of structural regularities is declarative, it is embedded in a procedural model of language structure.

Can the model itself be construed within a declarative conception and formalism? To answer this question, it would be useful to explore what we can learn by recasting OT in the language of formal logic rather than that of computational algorithms. In this talk, we will attempt such a translation, suggesting the following equivalents between OT and formal logic:

CONSTRAINTS	conditional premises (general propositions on linguistic forms)
INPUTS	premises on particular linguistic expressions
MARKEDNESS and FAITHFULNESS	defeasible conditional premises
GEN	non-defeasible conditional premises
OUTPUT CANDIDATES	propositions deducable from the input and GEN
RANKING	a formalism for the implementation of defeasible conditionals in a non-monotonic logic
OPTIMAL CANDIDATES	propositions deducible from the input, GEN, markedness, faithfulness, and ranking
OPTIMIZATION	selection of the final conclusion in a non-monotonic logic
TABLEAU	a visual form of proof, analogous to the use of truth tables

The aim of the talk is not to offer empirical defense for particular formal or substantive theoretical proposals, but rather to clarify the conceptual and formal underpinnings of OT as viewed from the perspective of formal logic. Such an exercise, we believe, would serve as the basis for a clearer understanding of some of the problems we currently face in OT (e.g. local conjunction, ineffability, and opacity), productive search for solutions and alternatives, and integration of various proposals available within (and outside) OT without inconsistency and redundancy.

For instance, once we recognize that markedness and faithfulness constraints are defeasible conditionals, it becomes easy to see that the formalism of inherent strength assignment can derive the effects of the formalism of relative ranking, including those of stochastic ranking. Inherent strength can also deduce the ranking of conjoined constraints (ganging up), ineffability (arising either from dead-lock resulting in both constraints losing, or from inputs for which non-defeasible constraints yield no outputs) and free variation (where both candidates win). It stands to reason that we should investigate the empirical grounds for using inherent strength either as an alternative to relative ranking, or as the gradient basis to derive the non-gradient relative ranking, whether or not we view it as part of a competence model. The exploration of the logical foundations also allows us to consider the possibility of replacing the EVAL algorithm with a simpler way to calculate deductions within defeasible logic (whether with ranking or inherent strength).