David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 54 (1):89 - 128 (1995)
The aim of this paper is to study the paraconsistent deductive systemP 1 within the context of Algebraic Logic. It is well known due to Lewin, Mikenberg and Schwarse thatP 1 is algebraizable in the sense of Blok and Pigozzi, the quasivariety generated by Sette's three-element algebraS being the unique quasivariety semantics forP 1. In the present paper we prove that the mentioned quasivariety is not a variety by showing that the variety generated byS is not equivalent to any algebraizable deductive system. We also show thatP 1 has no algebraic semantics in the sense of Czelakowski. Among other results, we study the variety generated by the algebraS. This enables us to prove in a purely algebraic way that the only proper non-trivial axiomatic extension ofP 1 is the classical deductive systemPC. Throughout the paper we also study those abstract logics which are in a way similar toP 1, and are called hereabstract Sette logics. We obtain for them results similar to those obtained for distributive abstract logics by Font, Verdú and the author.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Fernando M. Ramos & Víctor L. Fernández (2009). Twist-Structures Semantics for the Logics of the Hierarchy InPk. Journal of Applied Non-Classical Logics 19 (2):183-209.
Similar books and articles
W. J. Blok & Eva Hoogland (2006). The Beth Property in Algebraic Logic. Studia Logica 83 (1-3):49 - 90.
J. M. Font & V. Verdú (1993). Algebraic Logic for Classical Conjunction and Disjunction. Studia Logica 52 (1):181.
Josep M. Font & Ventura Verdú (1991). Algebraic Logic for Classical Conjunction and Disjunction. Studia Logica 50 (3-4):391 - 419.
Josep Maria Font & Miquel Rius (2000). An Abstract Algebraic Logic Approach to Tetravalent Modal Logics. Journal of Symbolic Logic 65 (2):481-518.
Renato A. Lewin, Irene F. Mikenberg & Maria G. Schwarze (1994). P1 Algebras. Studia Logica 53 (1):21 - 28.
Antoni Torrens (2008). An Approach to Glivenko's Theorem in Algebraizable Logics. Studia Logica 88 (3):349-383.
Antoni Torrens Torrell (2008). An Approach to Glivenko's Theorem in Algebraizable Logics. Studia Logica 88 (3):349 - 383.
A. M. Sette & Walter A. Carnielli (1995). Maximal Weakly-Intuitionistic Logics. Studia Logica 55 (1):181 - 203.
Larisa Maksimova (2006). Definability and Interpolation in Non-Classical Logics. Studia Logica 82 (2):271 - 291.
W. J. Blok & J. Rebagliato (2003). Algebraic Semantics for Deductive Systems. Studia Logica 74 (1-2):153 - 180.
Added to index2009-01-28
Total downloads3 ( #293,241 of 1,101,088 )
Recent downloads (6 months)3 ( #116,335 of 1,101,088 )
How can I increase my downloads?