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Ordered Interpretations and Entailment for Defeasible Description Logics


  • Authors:
    Giovanni Casini , Tommie Meyer , Ivan Varzinczak , Kody Moodley , Britz, K

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    We enrich description logics with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption relation in the spirit of KLM-style defeasible consequence. In particular we provide a natural and intuitive semantics for defeasible subsump- tion in terms of DL interpretations enriched with a preference relation. We propose syntactic characterizations for both preferential and rational subsumption relations (in terms of Gentzen-style rules or postulates) and prove representation results for the description logic ALC. We then move to non-monotonicity in DLs at the level of entailment. We investigate versions of entailment in the context of both preferential and rational subsumption, relate them to preferential and rational closure, and show that computing them can be reduced to classical ALC entailment, pro- viding further evidence that our semantic constructions are appropriate in a non-monotonic DL setting.