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European Conference on Symbolic and Quantitative Approaches with Uncertainty

ECSQARU 2019: Symbolic and Quantitative Approaches to Reasoning with Uncertainty pp 212–225Cite as

Reasoning About Exceptions in Ontologies: An Approximation of the Multipreference Semantics

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11726))

Abstract

Starting from the observation that rational closure has the undesirable property of being an “all or nothing” mechanism, we here consider a multipreferential semantics, which enriches the preferential semantics underlying rational closure in order to separately deal with the inheritance of different properties in an ontology with exceptions. We show that the MP-closure of an \(\mathcal {ALC}\) knowledge base is a construction which is sound with respect to minimal entailment in the multipreference semantics for \(\mathcal {ALC}\).

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Notes

  1. 1.

    Indeed, it is easy to see that, for a satisfiable \(K_i\), in the minimal ranked models \(\mathcal {M}_i\) of \(K_i\), which are the models of the rational closure of \(K_i\), two elements \(x,y \in \varDelta \) either have rank 0, and satisfy all the conditionals \(\mathbf{T}(C) \sqsubseteq A_i\) in \( K_i\), or have rank 1, and falsify at least some conditional \(\mathbf{T}(C) \sqsubseteq A_i\) in \( K_i\).

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Acknowledgement

This research is partially supported by INDAM-GNCS Project 2018 “Metodi di prova orientati al ragionamento automatico per logiche non-classiche”.

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Authors and Affiliations

  1. DISIT - Università del Piemonte Orientale, Alessandria, Italy

    Laura Giordano

  2. Dipartimento di Informatica, Università di Torino, Turin, Italy

    Valentina Gliozzi

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  1. Laura Giordano
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  2. Valentina Gliozzi
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Correspondence to Laura Giordano .

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Editors and Affiliations

  1. Technische Universität Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

  2. Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Zoran Ognjanović

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Giordano, L., Gliozzi, V. (2019). Reasoning About Exceptions in Ontologies: An Approximation of the Multipreference Semantics. In: Kern-Isberner, G., Ognjanović, Z. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science(), vol 11726. Springer, Cham. https://doi.org/10.1007/978-3-030-29765-7_18

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  • DOI: https://doi.org/10.1007/978-3-030-29765-7_18

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