Preferential reasoning for modal logics

Abstract

Modal logic is the foundation for a versatile and well-established class of knowledge representation formalisms in artificial intelligence. Enriching modal logics with non-monotonic reasoning capabilities such as preferential reasoning as developed by Lehmann and colleagues would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in modal logics. In this paper the authors fill this gap by providing a natural and intuitive semantics for preferential and rational modal consequence. They do so by placing a preference order on possible worlds indexed by Kripke models they belong to. They also prove representation results for both preferential and rational consequence, which paves the way for effective decision procedures for modal preferential reasoning. They then illustrate applications of their constructions to modal logics widely used in AI, notably in the contexts of reasoning about actions, knowledge and beliefs. They argue that their semantics constitute the foundation on which to explore preferential reasoning in modal logics in general.