An Abstract Algebraic Logic approach to Tetravalent Modal Logics
by Josep Maria Font and Miquel Rius
The Journal of Symbolic Logic 65 (2000) 481--518
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 quasi-normal.
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 Zilliani, at the suggestion of the late Antonio Monteiro.