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A Tableaux Calculus for Default Intuitionistic Logic

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Book cover Automated Deduction – CADE 27 (CADE 2019)

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Abstract

We build a Default Logic variant on Intuitionistic Propositional Logic and develop a sound, complete, and terminating, tableaux calculus for it. We also present an implementation of the calculus. We motivate and illustrate the technical elements of our work with examples.

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Notes

  1. 1.

    This notion is referred to as local consequence in the literature on Modal Logic.

  2. 2.

    This notion is referred to as sceptical consequence in the literature on Default Logics.

  3. 3.

    The ‘@’ notation is borrowed from Hybrid Logic [3].

  4. 4.

    The signs \(+\) and − are necessary since in \(\mathsf {IPL}\) we cannot use the symbol \(\lnot \) of negation for expressing that a formula does not hold in a world.

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Ackowledgements

This work was partially supported by ANPCyT-PICTs-2017-1130 and 2016-0215, MinCyT Córdoba, SeCyT-UNC, the Laboratoire International Associé INFINIS and the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 690974 for the project MIREL: MIning and REasoning with Legal texts.

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Authors and Affiliations

  1. CONICET and Universidad Nacional de Córdoba, Córdoba, Argentina

    Valentin Cassano, Raul Fervari, Guillaume Hoffmann & Carlos Areces

  2. CONICET and Universidad Nacional de Río Cuarto, Río Cuarto, Argentina

    Pablo F. Castro

Authors
  1. Valentin Cassano
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  2. Raul Fervari
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  3. Guillaume Hoffmann
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  4. Carlos Areces
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  5. Pablo F. Castro
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Corresponding author

Correspondence to Carlos Areces .

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Editors and Affiliations

  1. University of Lorraine, Villers-lès-Nancy, France

    Pascal Fontaine

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Cassano, V., Fervari, R., Hoffmann, G., Areces, C., Castro, P.F. (2019). A Tableaux Calculus for Default Intuitionistic Logic. In: Fontaine, P. (eds) Automated Deduction – CADE 27. CADE 2019. Lecture Notes in Computer Science(), vol 11716. Springer, Cham. https://doi.org/10.1007/978-3-030-29436-6_10

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  • DOI: https://doi.org/10.1007/978-3-030-29436-6_10

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