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Relevant Closure: A New Form of Defeasible Reasoning for Description Logics


  • Authors:
    Giovanni Casini , Tommie Meyer , Kody Moodley , Riku Nortjé

    Publication date:

    CSIR Meraka Institute

    Output type:
    Conference proceedings

    Springer - LNAI vol.8761


    Among the various proposals for defeasible reasoning for description
    logics, Rational Closure, a procedure originally defined for propositional logic,
    turns out to have a number of desirable properties. Not only it is computationally
    feasible, but it can also be implemented using existing classical reasoners. One
    of its drawbacks is that it can be seen as too weak from the inferential point of
    view. To overcome this limitation we introduce in this paper two extensions of
    Rational Closure: Basic Relevant Closure and Minimal Relevant Closure. As the
    names suggest, both rely on defining a version of relevance. Our formalisation
    of relevance in this context is based on the notion of a justification (a minimal
    subset of sentences implying a given sentence). This is, to our knowledge, the
    first proposal for defining defeasibility in terms of justifications—a notion that
    is well-established in the area of ontology debugging. Both Basic and Minimal
    Relevant Closure increase the inferential power of Rational Closure, giving back
    intuitive conclusions that cannot be obtained from Rational Closure. We analyse
    the properties and present algorithms for both Basic and Minimal Relevant
    Closure, and provide experimental results for both Basic Relevant Closure and
    Minimal Relevant Closure, comparing it with Rational Closure.

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