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A Duality for Algebras of Lattice-Valued Modal Logic

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Logic, Language, Information and Computation (WoLLIC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5514))

Abstract

In this paper, we consider some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Using the theory of natural dualities, we first obtain a natural duality for algebras of L-valued logic (i.e., L -VL-algebras), which extends Stone duality for Boolean algebras to the L-valued case. Then, based on this duality, we develop a Jónsson-Tarski-style duality for algebras of L-valued modal logic (i.e., L -ML-algebras), which extends Jónsson-Tarski duality for modal algebras to the L-valued case. By applying these dualities, we obtain compactness theorems for L-valued logic and for L-valued modal logic, and the classification of equivalence classes of categories of L -VL-algebras for finite distributive lattices L.

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Authors and Affiliations

  1. Department of Humanistic Informatics, Graduate School of Letters, Kyoto University, Japan

    Yoshihiro Maruyama

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  1. Yoshihiro Maruyama
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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, 923-1292, Ishikawa, Japan

    Hiroakira Ono

  2. National Institute of Informatics, 2–1–2 Hitotsubashi, Chiyoda-ku, 101–8430, Tokyo, Japan

    Makoto Kanazawa

  3. Centro de Informática, Universidade Federal de Pernambuco, Recife, PE, Brazil

    Ruy de Queiroz

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Maruyama, Y. (2009). A Duality for Algebras of Lattice-Valued Modal Logic. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2009. Lecture Notes in Computer Science(), vol 5514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02261-6_23

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  • DOI: https://doi.org/10.1007/978-3-642-02261-6_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02260-9

  • Online ISBN: 978-3-642-02261-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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