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A Tableau Calculus for a Multi-modal Logic of Dishonesty

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Book cover AI*IA 2018 – Advances in Artificial Intelligence (AI*IA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11298))

Abstract

In recent years, several approaches for formalising dishonest agents have been proposed in the artificial-intelligence literature. In particular, many of these approaches are based on a modal-logic setting. A prominent specimen of such a formalism is the multi-modal logic \(\mathsf {BIC}\), proposed by Sakama, Caminada, and Herzig, where the name “\(\mathsf {BIC}\)” stands for belief, intention, and communication. In their work, Sakama et al. introduce a Kripke semantics for \(\mathsf {BIC}\) and provide a corresponding Hilbert-style axiomatisation. In this paper, we complement this investigation by introducing a tableau calculus for \(\mathsf {BIC}\). Our approach is based on the single-step tableau method, an important proof method for automated deduction, originally proposed by Massacci for certain normal modal logics and subsequently elaborated by Goré. We provide soundness and completeness proofs, extending methods of Goré.

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Notes

  1. 1.

    Here, (\(4^{B_aB_a}\)) refers to the rule (\(4^{B_a}\)).

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Authors and Affiliations

  1. Institute of Logic and Computation, Knowledge-Based Systems Group E192-03, Technische Universität Wien, Favoritenstraße 9-11, 1040, Vienna, Austria

    Sanja Pavlović & Hans Tompits

Authors
  1. Sanja Pavlović
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  2. Hans Tompits
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Correspondence to Hans Tompits .

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Editors and Affiliations

  1. Fondazione Bruno Kessler, Povo (TN), Italy

    Chiara Ghidini

  2. Fondazione Bruno Kessler, Povo (TN), Italy

    Bernardo Magnini

  3. University of Trento, Povo (TN), Italy

    Andrea Passerini

  4. Fondazione Bruno Kessler, Povo (TN), Italy

    Paolo Traverso

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Pavlović, S., Tompits, H. (2018). A Tableau Calculus for a Multi-modal Logic of Dishonesty. In: Ghidini, C., Magnini, B., Passerini, A., Traverso, P. (eds) AI*IA 2018 – Advances in Artificial Intelligence. AI*IA 2018. Lecture Notes in Computer Science(), vol 11298. Springer, Cham. https://doi.org/10.1007/978-3-030-03840-3_18

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  • DOI: https://doi.org/10.1007/978-3-030-03840-3_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03839-7

  • Online ISBN: 978-3-030-03840-3

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