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Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory

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Abstract

This paper explores relationships between many-valued logic and fuzzy topology from the viewpoint of duality theory. We first show a fuzzy topological duality for the algebras of Łukasiewicz n-valued logic with truth constants, which generalizes Stone duality for Boolean algebras to the n-valued case via fuzzy topology. Then, based on this duality, we show a fuzzy topological duality for the algebras of modal Łukasiewicz n-valued logic with truth constants, which generalizes Jónsson-Tarski duality for modal algebras to the n-valued case via fuzzy topology. We emphasize that fuzzy topological spaces naturally arise as spectrums of algebras of many-valued logics.

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Authors and Affiliations

  1. Department of Humanistic Informatics, Graduate School of Letters, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto, 606-8501, Japan

    Yoshihiro Maruyama

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  1. Yoshihiro Maruyama
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Maruyama, Y. Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory. Stud Logica 94, 245–269 (2010). https://doi.org/10.1007/s11225-010-9234-x

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