Algebraization of logics defined by literal-paraconsistent or literal-paracomplete matrices
✍ Scribed by Eduardo Hirsh; Renato A. Lewin
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 165 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
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 ℳ︁^3^~2,2~, ℳ︁^3^~2,1~, ℳ︁^3^~1,1~, ℳ︁^3^~1,3~, and ℳ︁^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)