On duality for the modal
نویسنده
چکیده
We consider the modal-calculus due to Kozen, which is a nitary modal logic with least and greatest xed points of monotone operators. We extend the existing duality between the category of modal algebras with homomorphisms and the category of descriptive modal frames with contractions to the case of having xed point operators. As a corollary, we obtain a completeness result for Kozen's original system with respect to a certain class of modal frames.
منابع مشابه
Modal De Vries Algebras
We introduce modal de Vries algebras and develop a duality between the category of modal de Vries algebras and the category of coalgebras for the Vietoris functor on compact Hausdorff spaces. This duality serves as a common generalization of de Vries duality between de Vries algebras and compact Hausdorff spaces, and the duality between modal algebras and modal spaces.
متن کاملDualities for modal N4-lattices
We introduce a new Priestley-style topological duality for N4-lattices, which are the algebraic counterpart of paraconsistent Nelson logic. Our duality differs from the existing one, due to S. Odintsov, in that we only rely on Esakia duality for Heyting algebras and not on the duality for De Morgan algebras of Cornish and Fowler. A major advantage of our approach is that we obtain a simple desc...
متن کاملTitle Fuzzy Topology and Łukasiewicz Logics from the
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 al...
متن کاملA Duality for the Algebras of a Lukasiewicz n + 1-valued Modal System
In this paper, we develop a duality for the varieties of a Lukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory. . . ) are the derived and we propose some ideas for future research.
متن کاملDualities for Algebras of Fitting's Many-Valued Modal Logics
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. Using the theory of natural dualities, we first obtain a duality for algebras of L-valued logic. Based on th...
متن کاملPriestley duality for (modal) N4-lattices
N4-lattices are the algebraic semantics of paraconsistent Nelson logic, which was introduced in [1] as an inconsistency-tolerant counterpart of the better-known logic of Nelson [7, 13]. Paraconsistent Nelson logic combines interesting features of intuitionistic, classical and many-valued logics (e.g., Belnap-Dunn four-valued logic); recent work has shown that it can also be seen as one member o...
متن کامل