Algebraization of logics defined by literal-paraconsistent or literal-paracomplete matrices
Mathematical Logic Quarterly 54 (2):153-166 (2008)
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 [3] 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 ℳ32,2, ℳ32,1, ℳ31,1, ℳ31,3, and ℳ4 appearing in [11] proving that they are not varieties and finding the free algebra over one generatorDOI
10.1002/malq.200710021
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Citations of this work
First order theory for literal‐paraconsistent and literal‐paracomplete matrices.Renato A. Lewin & Irene F. Mikenberg - 2010 - Mathematical Logic Quarterly 56 (4):425-433.
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On the algebraizability of annotated logics.Renato A. Lewin, Irene F. Mikenberg & María G. Schwarze - 1997 - Studia Logica 59 (3):359-386.
Algebraizability and Beth's Theorem for equivalential logics.Burghard Herrmann - 1993 - Bulletin of the Section of Logic 22:85-88.
