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An abstract algebraic logic approach to tetravalent modal logics

Published online by Cambridge University Press:  12 March 2014

Josep Maria Font  and
Miquel Rius
Josep Maria Font
Affiliation:
Faculty of Mathematics, University of Barcelona, Gran Via 585, E-08007 Barcelona, Spain, E-mail: [email protected]
Miquel Rius
Affiliation:
Faculty of Mathematics, University of Barcelona, Gran Via 585, E-08007 Barcelona, Spain, E-mail: [email protected]
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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 logicgeneralized matrixtetravalent modal algebrafour-valued modal algebraDe Morgan algebrathree-valued Łukasiewicz algebrafour-valued logicmodal logicalgebraizable logicfull modelstrongly adequate Gentzen calculus
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 481 - 518
Copyright
Copyright © Association for Symbolic Logic 2000

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