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Rational Defeasible Reasoning for Expressive Description Logics


  • Authors:
    Arina Britz , Casini, G. , Tommie Meyer , Kody Moodley , Sattler, U. , Varzinczak, I.

    Publication date:

    CSIR Meraka Institute, UKZN, Stellenbosch University, UCT

    Output type:


    In this paper, we enrich description logics (DLs) with non-monotonic reasoning features in a number of ways. We start by investigating a notion of defeasible conditional in the spirit of KLM-style defeasible consequence. In particular, we consider a natural and intuitive semantics for defeasible subsumption in terms of DL interpretations enriched with a preference relation. We propose and investigate syntactic properties (à la Gentzen) for both preferential and rational conditionals and prove representation results for the description logic ALC. This representation result paves the way for more effective decision procedures for defeasible reasoning in DLs. 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. This provides further evidence that our semantic constructions are appropriate in a non-monotonic DL setting. One of the barriers to evaluating performance scalability of rational closure is the abscence of naturally occurring DL-based ontologies with defeasible features. We overcome this barrier by devising an approach to introduce defeasible subsumption into classical real world ontologies. This culminates in a set of semi-natural defeasible ontologies that is used, together with a purely artificial set, to test our rational closure algorithms. We found that performance is scalable on the whole with no major bottlenecks.

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