An abstract algebraic logic approach to tetravalent modal logics

Journal of Symbolic Logic 65 (2):481-518 (2000)
Abstract
This paper contains a joint study of two sentential logics that combine a many-valued character, namely tetravalence, with a modal character; one of them is normal and the other one quasinormal. The method is to study their algebraic counterparts and their abstract models with the tools of Abstract Algebraic Logic, and particularly with those of Brown and Suszko's theory of abstract logics as recently developed by Font and Jansana in their "A General Algebraic Semantics for Sentential Logics". The logics studied here arise from the algebraic and lattice-theoretical properties we review of Tetravalent Modal Algebras, a class of algebras studied mainly by Loureiro, and also by Figallo, Landini and Ziliani, at the suggestion of the late Antonio Monteiro
Keywords Abstract Logic   Generalized Matrix   Tetravalent Modal Algebra   Four-Valued Modal Algebra   De Morgan Algebra   Three-Valued Lukasiewicz Algebra   Four-Valued Logic   Modal Logic   Algebraizable Logic   Full Model   Strongly Adequate Gentzen Calculus
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