Dualities for Algebras of Fitting's Many-Valued Modal Logics

• Autorzy: Maruyama Y.
• Języki publikacji: EN

Abstrakty

EN

Stone-type duality connects logic, algebra, and topology in both conceptual and technical senses. This paper is intended to be a demonstration of this slogan. In this paper we focus on some versions of Fitting’s L-valued logic and L-valued modal logic for a finite distributive lattice L. Building upon the theory of natural dualities, which is a universal algebraic theory of categorical dualities, we establish a Jonsson-Tarski-style duality for algebras of L-valued modal logic, which encompasses J´onsson-Tarski duality for modal algebras as the case L = 2. We also discuss how the dualities change when the algebras are enriched by truth constants. Topological perspectives following from the dualities provide compactness theorems for the logics and the effective classification of categories of algebras involved, which tells us that Stone-type duality makes it possible to use topology for logic and algebra in significant ways.

Słowa kluczowe

EN

stone-type duality; theory of natural dualities; algebraic logic; fitting's many-valued modal logic; compactness theorem; classification of categories

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2011
• Tom: Vol. 106, nr 2-4
• Strony: 273--294
• Opis fizyczny: Bibliogr. 35 poz.

Twórcy

autor

Maruyama Y.

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

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