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Decidability for \(\mathsf S4\) Gödel Modal Logics

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Computational Intelligence and Mathematics for Tackling Complex Problems 4

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1040))

Abstract

We introduce semantics for crisp and fuzzy Gödel \(\mathsf S4\) based on bi-relational frames. We then show that each version of the logic is sound and complete for its respective class of frames and enjoys the finite model property. From this we conclude that both the crisp and fuzzy versions of Gödel \(\mathsf S4\) are decidable.

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Acknowledgements

Martín Diéguez has been partially supported by the projects EL4HC and étoiles montantes CTASP at Région Pays de la Loire, France. David Fernández-Duque was supported by RVO 67985807 and by the Czech Science Foundation project GA22-01137S and the SNSF-FWO Lead Agency Grant 200021L_96176 (SNSF)/G0E2121N (FWO).

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Authors and Affiliations

  1. UFR des Sciences, Université d’Angers, 2 Bd de Lavoisier, 49000, Angers, France

    Martín Diéguez

  2. Department of Mathematics WE16, Ghent University, Ghent, Belgium

    David Fernández-Duque

  3. Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic

    David Fernández-Duque

Authors
  1. Martín Diéguez
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  2. David Fernández-Duque
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Corresponding author

Correspondence to David Fernández-Duque .

Editor information

Editors and Affiliations

  1. Faculty of Engineering, Department of Mathematics, University of Cádiz, Puerto Real, Spain

    María Eugenia Cornejo

  2. Department of Mathematics and Computational Sciences, Széchenyi István University, Győr, Hungary

    István Á. Harmati

  3. Faculty of Engineering Sciences, Széchenyi István University, Győr, Hungary

    László T. Kóczy

  4. Science Faculty, Department of Mathematics, University of Cádiz, Cádiz, Spain

    Jesús Medina-Moreno

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Diéguez, M., Fernández-Duque, D. (2023). Decidability for \(\mathsf S4\) Gödel Modal Logics. In: Cornejo, M.E., Harmati, I.Á., Kóczy, L.T., Medina-Moreno, J. (eds) Computational Intelligence and Mathematics for Tackling Complex Problems 4. Studies in Computational Intelligence, vol 1040. Springer, Cham. https://doi.org/10.1007/978-3-031-07707-4_1

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