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Algebraization of logics defined by literal‐paraconsistent or literal‐paracomplete matrices
Author(s) -
Hirsh Eduardo,
Lewin Renato A.
Publication year - 2008
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710021
Subject(s) - literal (mathematical logic) , mathematics , algebraic number , algebra over a field , algebraic semantics , generator (circuit theory) , pure mathematics , algorithm , mathematical analysis , power (physics) , physics , quantum mechanics
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 ℳ 3 2,2 , ℳ 3 2,1 , ℳ 3 1,1 , ℳ 3 1,3 , and ℳ 4 appearing in [11] proving that they are not varieties and finding the free algebra over one generator. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)