Preference Logic Programming: Optimization as Inference

Preference Logic Programming (PLP) is an extension of Constraint Logic Programming (CLP) for declaratively specifying optimization problems. In the PLP framework, the deenite clauses of a CLP program are augmented by two new kinds of clauses: optimization clauses and arbiter clauses. Optimization clauses specify which predicates are to be optimized and arbiter clauses specify the criteria to be used for optimization. Together, these three kinds of clauses form a preferential theory, for which a possible worlds semantics was rst given by Mantha et al. This paper shows how modal concepts can be used to capture the notion of optimization: Essentially, each world in the possible-worlds semantics for a preference logic program is a model of the program, and an ordering over these worlds is enforced by the arbiter clauses in the program. We introduce the notion of preferential consequence as truth in the optimal worlds. We propose an operational semantics that is an extension of SLD derivation and prove its soundness. Finally, we provide a variety of examples to illustrate our paradigm: minimum and maximum predicates, partial-order programming, syntactic ambiguity resolution and its application in document formatting, and general optimization problems.