David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 52 (1):181 (1993)
In this paper we study the relations between the fragment L of classical logic having just conjunction and disjunction and the variety D of distributive lattices, within the context of Algebraic Logic. We prove that these relations cannot be fully expressed either with the tools of Blok and Pigozzi's theory of algebraizable logics or with the use of reduced matrices for L. However, these relations can be naturally formulated when we introduce a new notion of model of a sequent calculus. When applied to a certain natural calculus for L, the resulting models are equivalent to a class of abstract logics (in the sense of Brown and Suszko) which we call distributive. Among other results, we prove that D is exactly the class of the algebraic reducts of the reduced models of L, that there is an embedding of the theories of L into the theories of the equational consequence (in the sense of Blok and Pigozzi) relative to D, and that for any algebra A of type (2,2) there is an isomorphism between the D-congruences of A and the models of L over A. In the second part of this paper (which will be published separately) we will also apply some results to give proofs with a logical flavour for several new or well-known lattice-theoretical properties
|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
Josep Maria Font, Àngel J. Gil, Antoni Torrens & Ventura Verdú (2006). On the Infinite-Valued Łukasiewicz Logic That Preserves Degrees of Truth. Archive for Mathematical Logic 45 (7):839-868.
Similar books and articles
W. J. Blok & J. Rebagliato (2003). Algebraic Semantics for Deductive Systems. Studia Logica 74 (1-2):153 - 180.
Andrea Sorbi (1990). Some Remarks on the Algebraic Structure of the Medvedev Lattice. Journal of Symbolic Logic 55 (2):831-853.
W. J. Blok (1980). The Lattice of Modal Logics: An Algebraic Investigation. Journal of Symbolic Logic 45 (2):221-236.
Josep Maria Font, Ramon Jansana & Don Pigozzi (2006). On the Closure Properties of the Class of Full G-Models of a Deductive System. Studia Logica 83 (1-3):215 - 278.
Ramon Jansana (2006). Selfextensional Logics with a Conjunction. Studia Logica 84 (1):63 - 104.
Josep Maria Font & Miquel Rius (2000). An Abstract Algebraic Logic Approach to Tetravalent Modal Logics. Journal of Symbolic Logic 65 (2):481-518.
W. J. Blok & Don Pigozzi (1986). Protoalgebraic Logics. Studia Logica 45 (4):337 - 369.
Alexej P. Pynko (1995). Algebraic Study of Sette's Maximal Paraconsistent Logic. Studia Logica 54 (1):89 - 128.
Josep M. Font & Ventura Verdú (1993). The Lattice of Distributive Closure Operators Over an Algebra. Studia Logica 52 (1):1 - 13.
Josep M. Font & Ventura Verdú (1991). Algebraic Logic for Classical Conjunction and Disjunction. Studia Logica 50 (3-4):391 - 419.
Added to index2009-01-28
Total downloads6 ( #203,094 of 1,100,472 )
Recent downloads (6 months)1 ( #289,155 of 1,100,472 )
How can I increase my downloads?