Title Fuzzy Topology and Łukasiewicz Logics from the
نویسنده
چکیده
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 Lukasiewicz 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 Lukasiewicz 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.
منابع مشابه
Compactness of fuzzy logics
This contribution is concerned with the compactness of fuzzy logics, where we concentrate on the three standard fuzzy logics—Łukasiewicz logic, Gödel logic, and product logic.
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