Duality and Canonical Extensions of Bounded Distributive Lattices with 
Operators and Applications to the Semantics of Non-Classical Logics. Part II

Sofronie-Stokkermans, Viorica

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Duality and Canonical Extensions of Bounded Distributive Lattices with Operators and Applications to the Semantics of Non-Classical Logics. Part II

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Sofronie-Stokkermans, Viorica
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

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Sofronie-Stokkermans, V. (2000). Duality and Canonical Extensions of Bounded Distributive Lattices with Operators and Applications to the Semantics of Non-Classical Logics. Part II. Studia Logica, 64(2), 151-172.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-342B-5

Abstract

In this paper we explain the link between the algebraic models and the Kripke-style models for certain classes of propositional non-classical logics. We consider logics that are sound and complete with respect to varieties of distributive lattices with certain classes of well-behaved operators for which a Priestley-style duality holds, and present a way of constructing topological and non-topological Kripke-style models for these types of logics. Moreover, we show that, under certain additional assumptions on the variety of the algebraic models of the given logics, soundness and completeness with respect to these classes of Kripke-style models follows by using entirely algebraical arguments from the soundness and completeness of the logic with respect to its algebraic models.