Fuzzy topology and łukasiewicz logics from the viewpoint of duality theory

Studia Logica 94 (2):245 - 269 (2010)
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.
Keywords fuzzy topology  Stone duality  Jónsson-Tarski duality  algebraic logic  many-valued logic  modal logic  Kripke semantics  compactness theorem
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References found in this work BETA
Lofti A. Zadeh (1965). Fuzzy Sets. Information and Control 8 (1):338--53.
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