A logical reconstruction of constraint relaxation hierarchies in logic programming

Abstract

We propose an extension to Definite Horn Clauses by placing partial orders on the bodies of clauses. Such clauses are called relaxable clauses. These partial orders are interpreted as a specification of relaxation criteria in the proof of the consequent of a relaxable clause, i.e., the order in which to relax the conditions of truthhood of the consequent if all the goals in the body cannot be satisfied. We present a modal logic of preference that enables us to characterize these preference orders, both syntactically and semantically. The richer structure of the modal preference models reflects these preference orders; something that is absent in the essentially flat structure of traditional Herbrand models. A variant of SLD-resolution that generates solutions in the preferred order is presented. The notion of control as preference is introduced as a first step towards specifying control information in a logically coherent fashion. Relaxable Horn clauses can be used to succinctly specify constraint problems in formal design. It is worth noting that the development of preference logic was driven by the desire to characterize declaratively, problems in document layout. In [4] we give a completely declarative account of the stable models of a general logic program. The reader is referred to [3],[5]and [14] for a detailed account of nonmonotonicity as preferential reasoning,the soundness and completeness proofs for the logics and applicationsto Artificial Intelligence, such as deontic reasoning.