Varieties of Monadic Heyting Algebras Part II: Duality Theory

Author: Bezhanishvili, G.

Source: Studia Logica, Volume 62, Number 1, January 1999 , pp. 21-48(28)

Publisher: Springer

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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.

Keywords: Kripke bundles; Ono frames; augmented Kripke frames; monadic Heyting algebras; topological augmented Kripke frames

Document Type: Regular Paper

Affiliations: Institute of Cibernetics Georgian Academy of Sciences S. Euli 5 Tbilisi 86, Georgia guram@cybern.acnet.ge

Publication date: January 1, 1999

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