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Non-Normal Modal Description Logics

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

Modal logics are widely used in multi-agent systems to reason about actions, abilities, norms, or epistemic states. Combined with description logic languages, they are also a powerful tool to formalise modal aspects of ontology-based reasoning over an object domain. However, the standard relational semantics for modalities is known to validate principles deemed problematic in agency, deontic, or epistemic applications. To overcome these difficulties, weaker systems of so-called non-normal modal logics, equipped with neighbourhood semantics that generalise the relational one, have been investigated both at the propositional and at the description logic level. We present here a family of non-normal modal description logics, obtained by extending \(\smash {\mathcal {ALC}} \)-based languages with non-normal modal operators. For formulas interpreted on neighbourhood models over varying domains, we provide a modular framework of terminating, correct, and complete tableau-based satisfiability checking algorithms in \(\textsc {NExpTime}\). For a subset of these systems, we also consider a reduction to satisfiability on constant domain relational models. Moreover, we investigate the satisfiability problem in fragments obtained by disallowing the application of modal operators to description logic concepts, providing tight \(\textsc {ExpTime}\) complexity results.

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Notes

  1. 1.

    Other approaches (out of the scope of this paper) to avoid such consequences would involve rejecting the principle of excluded middle, as done e.g. in intuitionistic description logics [9, 30, 33].

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Acknowledgements

This research has been partially supported by the Province of Bolzano and DFG through the project D2G2 (DFG grant n. 500249124). Andrea Mazzullo acknowledges the support of the MUR PNRR project FAIR - Future AI Research (PE00000013) funded by the NextGenerationEU. Ana Ozaki is supported by the Research Council of Norway, project number 316022.

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Authors and Affiliations

  1. Free University of Bozen-Bolzano, Bolzano, Italy

    Tiziano Dalmonte & Nicolas Troquard

  2. University of Trento, Trento, Italy

    Andrea Mazzullo

  3. University of Oslo, Oslo, Norway

    Ana Ozaki

  4. University of Bergen, Bergen, Norway

    Ana Ozaki

Authors
  1. Tiziano Dalmonte
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  2. Andrea Mazzullo
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  3. Ana Ozaki
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  4. Nicolas Troquard
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Correspondence to Andrea Mazzullo .

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Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Dalmonte, T., Mazzullo, A., Ozaki, A., Troquard, N. (2023). Non-Normal Modal Description Logics. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_22

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  • DOI: https://doi.org/10.1007/978-3-031-43619-2_22

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