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Original Paper
Algebraization of logics defined by literal-paraconsistent or literal-paracomplete matrices
Article first published online: 7 MAR 2008
DOI: 10.1002/malq.200710021
Copyright © 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-3870/asset/cover.gif?v=1&s=3df32dbed8d9153ac6eafe1eaa786854b9b48345 "Mathematical Logic Quarterly")
Additional Information
How to Cite
Hirsh, E. and Lewin, R. A. (2008), Algebraization of logics defined by literal-paraconsistent or literal-paracomplete matrices. Mathematical Logic Quarterly, 54: 153–166. doi: 10.1002/malq.200710021
Publication History
- Issue published online: 7 MAR 2008
- Article first published online: 7 MAR 2008
- Manuscript Accepted: 4 MAY 2007
- Manuscript Revised: 26 APR 2007
- Manuscript Received: 29 JAN 2007
Funded by
- FONDECYT. Grant Number: 1060726
- Abstract
- References
- Cited By
Keywords:
- Algebraizable logic;
- matrix semantics;
- paraconsistency;
- paracompleteness
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 generator. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)