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

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Book cover Logics in Artificial Intelligence (JELIA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8761))

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Abstract

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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Authors and Affiliations

  1. Centre for Artificial Intelligence Research (CSIR Meraka and UKZN), South Africa

    Giovanni Casini, Thomas Meyer, Kodylan Moodley & Riku Nortjé

Authors
  1. Giovanni Casini
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  2. Thomas Meyer
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  3. Kodylan Moodley
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  4. Riku Nortjé
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Editor information

Editors and Affiliations

  1. University of Madeira, Funchal, Madeira, Portugal

    Eduardo Fermé

  2. CENTRIA, Universidade Nova de Lisboa, Caparica, Portugal

    João Leite

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Casini, G., Meyer, T., Moodley, K., Nortjé, R. (2014). Relevant Closure: A New Form of Defeasible Reasoning for Description Logics. In: Fermé, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_7

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  • DOI: https://doi.org/10.1007/978-3-319-11558-0_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11557-3

  • Online ISBN: 978-3-319-11558-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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