Duality and canonical extensions of bounded distributive lattices with operators, and applications to the semantics of non-classical logics I
Studia Logica 64 (1):93-132 (2000)
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.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
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Citations of this work BETA
Duality for Double Quasioperator Algebras Via Their Canonical Extensions.M. Gehrke & H. A. Priestley - 2007 - Studia Logica 86 (1):31-68.
Truth-Values as Labels: A General Recipe for Labelled Deduction.Cristina Sernadas, Luca Viganò, João Rasga & Amílcar Sernadas - 2003 - Journal of Applied Non-Classical Logics 13 (3-4):277-315.
Boolean Algebras Arising From Information Systems.Ivo Düntsch & Ewa Orłowska - 2004 - Annals of Pure and Applied Logic 127 (1-3):77-98.
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