A Duality for the Algebras of a Łukasiewicz n + 1-valued Modal System

Teheux, Bruno

doi:10.1007/s11225-007-9074-5

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Introduction1

Dyadic Numbers and Mv-terms1

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2009

2020

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Cited by 11 publications

(2 citation statements)

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“…There have been some studies on dualities for algebras of many-valued logics (see, e.g., [2,7,8,18,23,24,29]). However, they are based on the ordinary topology and therefore do not reveal relationships between manyvalued logic and fuzzy topology.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory

Maruyama

2010

Stud Logica

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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.

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Section: Introductionmentioning

confidence: 99%

Fuzzy Topology and Łukasiewicz Logics from the Viewpoint of Duality Theory

Maruyama

2010

Stud Logica

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“…The contents of this part summarizes the basic results about some folklore results of some MV-terms from [22] and [18]. The techniques described here have been used already in [4] and later, e.g., in [10], [12], [15] and [21].…”

Section: Dyadic Numbers and Mv-termsmentioning

confidence: 99%