Duality and Canonical Extensions of Bounded Distributive Lattices with Operators,and Applications to the Semantics of Non-Classical Logics I |
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Authors: | Sofronie-Stokkermans Viorica |
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Affiliation: | (1) Programming Logics Group, Max-Planck-Institut für Informatik, D-66123, Im Stadtwald, Saarbrücken, Germany |
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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. This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | Priestley duality distributive lattices canonical embedding algebras Kripke models non-classical logic |
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