A Duality for Algebras of Lattice-Valued Modal Logic

  • Yoshihiro Maruyama
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Yoshihiro Maruyama
    • 1
  1. 1.Department of Humanistic Informatics, Graduate School of LettersKyoto UniversityJapan

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