Preference logics: Towards a unified approach to nonmonotonicity in deductive reasoning

Abstract

The notion ofpreference is central to most forms of nonmonotonic reasoning. Shoham, in his dissertation, used this notion to give a single semantical point of view from which most nonmonotonic reasoning systems could be studied. In this paper, we study the notion of preference closely and devise a class of logics of preference that extract the logicalcore of the notion of preference. Earlier attempts have been largely unsuccessful, because of adoption as matters of logic of certain theory-specific preference principles such asasymmetry andtransitivity. Soundness, completeness and decidability proofs for the logics are given. We define the notion of a preferential theory and reframe nonmonotonicity as a symbolic optimization problem where defaults are coded aspreference criteria which place preference orders on the models of a first-order theory. We study the relationship between normal default theories and show the correspondence between models of extensions and optimal worlds. We give a preferential account of some forms of circumscription. Thelocal nature of preference logic is contrasted with the global notion of normality and preference that is used by conditional logics of normality and cumulative inference operations. In related papers, we give a completely declarative semantics for the stable models of normal logic programs, a deontic logic based on preferences that is free of the anomalies of standard deontic logic, and extend Horn clause logic programming to impose partial orders on the bodies of clauses as declarative specification of the relaxation criteria for the truth-hood of the heads.