Algebraization of logics defined by literal-paraconsistent or literal-paracomplete matrices

Abstract

We study the algebraizability of the logics constructed using literal-paraconsistent and literal-paracomplete matrices described by Lewin and Mikenberg in [11], proving that they are all algebraizable in the sense of Blok and Pigozzi in [31 but not finitely algebraizable. A characterization of the finitely algebraizable logics defined by LPP-matrices is given.

We also make an algebraic study of the equivalent algebraic semantics of the logics associated to the matrices M-2,2(3), M-2,1(3), M-1,1(3), M-1,(3)(3) and M-4 appearing in [11] proving that they are not varieties and finding the free algebra over one generator. 1 Introduction and preliminaries (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.