Journal of Symbolic Logic

An Abstract Algebraic Logic Approach to Tetravalent Modal Logics

Josep Maria Font and Miquel Rius

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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.

Article information

J. Symbolic Logic, Volume 65, Issue 2 (2000), 481-518.

First available in Project Euclid: 6 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35]
Secondary: 03B50: Many-valued logic 03B45: Modal logic (including the logic of norms) {For knowledge and belief, see 03B42; for temporal logic, see 03B44; for provability logic, see also 03F45} 06D30: De Morgan algebras, Lukasiewicz algebras [See also 03G20]

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


Font, Josep Maria; Rius, Miquel. An Abstract Algebraic Logic Approach to Tetravalent Modal Logics. J. Symbolic Logic 65 (2000), no. 2, 481--518.

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