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Repairing Non-monotonic Knowledge Bases

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Logics in Artificial Intelligence (JELIA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11468))

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Abstract

Minimal inconsistent subsets of knowledge bases in monotonic logics play an important role when investigating the reasons for conflicts and trying to handle them. In the context of non-monotonic reasoning this notion is not as meaningful due to the possibility of resolving conflicts by adding information. In this paper we investigate inconsistency in non-monotonic logics while taking this issue into account. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics even if we allow adding novel information to a given knowledge base. We illustrate the versatility of the main theorems by covering more sophisticated situations and demonstrate how to utilize our results to analyze inconsistency in abstract argumentation.

This work was funded by Deutsche Forschungsgemeinschaft DFG (Research Training Group 1763; project BR 1817/7-2).

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Notes

  1. 1.

    S is upward closed if \(B \in S\), \(B \subseteq B'\) implies \(B' \in S\).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Leipzig University, Leipzig, Germany

    Markus Ulbricht

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  1. Markus Ulbricht
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Correspondence to Markus Ulbricht .

Editor information

Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Francesco Calimeri

  2. University of Calabria, Rende, Italy

    Nicola Leone

  3. Mathematics and Computer Science, University of Calabria, Rende, Italy

    Marco Manna

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Ulbricht, M. (2019). Repairing Non-monotonic Knowledge Bases. In: Calimeri, F., Leone, N., Manna, M. (eds) Logics in Artificial Intelligence. JELIA 2019. Lecture Notes in Computer Science(), vol 11468. Springer, Cham. https://doi.org/10.1007/978-3-030-19570-0_10

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  • DOI: https://doi.org/10.1007/978-3-030-19570-0_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-19569-4

  • Online ISBN: 978-3-030-19570-0

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