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International Conference on Automated Reasoning with Analytic Tableaux and Related Methods

TABLEAUX 2021: Automated Reasoning with Analytic Tableaux and Related Methods pp 38–55Cite as

Analytic Tableaux for Non-deterministic Semantics

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12842))

Abstract

Analytic tableau systems for the family of non-deterministic semantics are introduced. These are based on tableaux for many-valued logics using sets-as-signs DNF representations. Karnaugh maps illustrate the construction of tableau rules. In contrast to classical many-valued tableaux, we add a rule called sign intersection. Soundness and completeness are shown. As an example demonstrates, some tableau systems would be incomplete without sign intersection. There is a correspondence to well-studied canonical calculi based on sequent systems: Tableau systems can be translated into canonical calculi, but not vice-versa (structural rules are missing on the tableau side).

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Notes

  1. 1.

    Also note that a tableau system for a particular non-deterministic semantics is already listed in [19, p. 211]. Unfortunately, we could not find out more about it; an approach to contact the author was unsuccessful.

  2. 2.

    A usage of this nmatrix in a meaningful logic would be nice but is not intended.

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Acknowledgements

I am indebted to Peter Steinacker for the supervision of my master’s thesis and to Andreas Maletti, second reviewer, for spotting the mistake in my thesis which initiated the work on the present paper. I would like to thank Daniel Skurt, Hitoshi Omori, Reiner Hähnle, Richard Bubel, Elio La Rosa, Pawel Pawlowski for useful suggestions.

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Authors and Affiliations

  1. Technische Universität Darmstadt, Darmstadt, Germany

    Lukas Grätz

  2. Universität Leipzig, Leipzig, Germany

    Lukas Grätz

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  1. Lukas Grätz
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Correspondence to Lukas Grätz .

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Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Anupam Das

  2. University of Genoa, Genoa, Italy

    Sara Negri

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Grätz, L. (2021). Analytic Tableaux for Non-deterministic Semantics. In: Das, A., Negri, S. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2021. Lecture Notes in Computer Science(), vol 12842. Springer, Cham. https://doi.org/10.1007/978-3-030-86059-2_3

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  • DOI: https://doi.org/10.1007/978-3-030-86059-2_3

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