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Preferential Reasoning for Modal Logic

2011

  • Authors:
    Britz, K. , Tommie Meyer , Ivan Varzinczak

    Publication date:
    2011

    Institution:

    Output type:
    Journal paper

    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 we fill this gap by providing a natural and intuitive semantics for preferential and rational modal consequence. We do so by placing a preference order on possible worlds indexed by Kripke models they belong to. We also prove representation results for both preferential and rational consequence, which paves the way for effective decision procedures for modal preferential reasoning. We then illustrate applications of our constructions to modal logics widely used in AI, notably in the contexts of reasoning about actions, knowledge and beliefs. We argue that our semantics constitutes the foundation on which to explore preferential reasoning in modal logics in general.