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A Rational Entailment for Expressive Description Logics via Description Logic Programs

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Artificial Intelligence Research (SACAIR 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1551))

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Abstract

Lehmann and Magidor’s rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment for expressive DLs, such as \(\mathcal {SROIQ}\), providing a novel reasoning procedure that compiles a non-monotone DL knowledge base into a description logic program (dl-program).

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Notes

  1. 1.

    http://www.dlvsystem.com.

  2. 2.

    The definition given here is again simpler than the original one, as we consider only the form strictly required for our proposal.

  3. 3.

    Of course, \(\mathtt {Exceptional}(\cdot )\) and, thus, \(\mathtt {ComputeRanking}(\cdot )\), can be applied to a DL \(\mathcal {SROIQ}\) knowledge base L as the classical entailment relation for \(\mathcal {SROIQ}\) is decidable.

  4. 4.

    We assume to simplify double negation: that is, for a concept name F, \(\lnot \lnot F\) is F, and similarly, for a logic program predicate f, \(\lnot \lnot f\) is f. See also Example 4 later on.

  5. 5.

    For ease of comprehension, we write concept assertions as D(b) in place of the equivalent inclusion axiom \(\{b\} \sqsubseteq D\) in expressions like \(L\cup \{D(b)\}\).

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Acknowledgments

This research was supported by TAILOR, a project funded by EU Horizon 2020 research and innovation programme under GA No. 952215.

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Authors and Affiliations

  1. ISTI - CNR, Pisa, Italy

    Giovanni Casini & Umberto Straccia

  2. CAIR - University of Cape Town, Cape Town, South Africa

    Giovanni Casini

Authors
  1. Giovanni Casini
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  2. Umberto Straccia
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Correspondence to Giovanni Casini .

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Editors and Affiliations

  1. University of KwaZulu-Natal, Durban, South Africa

    Edgar Jembere

  2. University of Pretoria, Pretoria, South Africa

    Aurona J. Gerber

  3. University of KwaZulu-Natal, Durban, South Africa

    Serestina Viriri

  4. University of KwaZulu-Natal, Durban, South Africa

    Anban Pillay

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Casini, G., Straccia, U. (2022). A Rational Entailment for Expressive Description Logics via Description Logic Programs. In: Jembere, E., Gerber, A.J., Viriri, S., Pillay, A. (eds) Artificial Intelligence Research. SACAIR 2021. Communications in Computer and Information Science, vol 1551. Springer, Cham. https://doi.org/10.1007/978-3-030-95070-5_12

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  • DOI: https://doi.org/10.1007/978-3-030-95070-5_12

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