Fundamenta Informaticae - Special issue: logics for artificial intelligence
Fundamenta Informaticae - Special issue on modal logics in knowledge representation
Modal logic
A Paradigm for Program Semantics: Power Structures and Duality
A Paradigm for Program Semantics: Power Structures and Duality
Fundamenta Informaticae
Many-Valued Non-Monotonic Modal Logics
TVER '92 Proceedings of the Second International Symposium on Logical Foundations of Computer Science
Algebraic Study of Lattice-Valued Logic and Lattice-Valued Modal Logic
ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
Category Theory
Reasoning about fuzzy belief and common belief: with emphasis on incomparable beliefs
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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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 Jónsson-Tarski-style duality for algebras of L-valued modal logic, which encompasses Jónsson-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. The author is grateful to Professor Susumu Hayashi for his encouragement, to Shohei Izawa for his comments and discussions, and to Kentaro Sato for his suggesting a similar result to Theorem 2.5 for the category of algebras of Łukasiewicz n-valued logic.