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Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I

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Abstract

The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics that are sound and complete with respect to varieties of distributive lattices with operators in the above-mentioned classes.

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Authors and Affiliations

  1. Programming Logics Group, Max-Planck-Institut für Informatik, D-66123, Im Stadtwald, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

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  1. Viorica Sofronie-Stokkermans
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Sofronie-Stokkermans, V. Duality and Canonical Extensions of Bounded Distributive Lattices with Operators, and Applications to the Semantics of Non-Classical Logics I. Studia Logica 64, 93–132 (2000). https://doi.org/10.1023/A:1005298632302

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