Studia Logica

, Volume 94, Issue 2, pp 245–269 | Cite as

Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory

  • Yoshihiro Maruyama


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.


fuzzy topology Stone duality Jónsson-Tarski duality algebraic logic many-valued logic modal logic Kripke semantics compactness theorem 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Humanistic Informatics, Graduate School of LettersKyoto UniversitySakyo, KyotoJapan

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