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Varieties of monadic Heyting algebras part II: Duality theory
Studia Logica 62 (1):21-48 (1999)
Abstract
In this paper we continue the investigation of monadic Heyting algebras which we started in [2]. Here we present the representation theorem for monadic Heyting algebras and develop the duality theory for them. As a result we obtain an adequate topological semantics for intuitionistic modal logics over MIPC along with a Kripke-type semantics for them. It is also shown the importance and the effectiveness of the duality theory for further investigation of monadic Heyting algebras and logics over MIPC.Reprint years
2004
DOI
10.1023/a:1005173628262
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Citations of this work
Varieties of monadic Heyting algebras. Part I.Guram Bezhanishvili - 1998 - Studia Logica 61 (3):367-402.
Algebraic semantics and model completeness for Intuitionistic Public Announcement Logic.Minghui Ma, Alessandra Palmigiano & Mehrnoosh Sadrzadeh - 2014 - Annals of Pure and Applied Logic 165 (4):963-995.
Monadic Intuitionistic and Modal Logics Admitting Provability Interpretations.Guram Bezhanishvili, Kristina Brantley & Julia Ilin - 2023 - Journal of Symbolic Logic 88 (1):427-467.
Temporal Interpretation of Monadic Intuitionistic Quantifiers.Guram Bezhanishvili & Luca Carai - 2023 - Review of Symbolic Logic 16 (1):164-187.
The universal modality, the center of a Heyting algebra, and the Blok–Esakia theorem.Guram Bezhanishvili - 2010 - Annals of Pure and Applied Logic 161 (3):253-267.
References found in this work
The Algebra of Topology.J. C. C. Mckinsey & Alfred Tarski - 1944 - Annals of Mathematics, Second Series 45:141-191.
Topoi: The Categorial Analysis of Logic.R. I. Goldblatt - 1982 - British Journal for the Philosophy of Science 33 (1):95-97.
On Closed Elements in Closure Algebras.J. C. C. Mckinsey & Alfred Tarski - 1946 - Annals of Mathematics, Ser. 2 47:122-162.
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