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

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons45516

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 I. Studia Logica, 64(1), 93-132.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-3427-D
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.