David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 83 (1-3):215 - 278 (2006)
In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACSs A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples.
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|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
J. M. Font, R. Jansana & D. Pigozzi (2009). Update to “a Survey of Abstract Algebraic Logic”. Studia Logica 91 (1):125 - 130.
Josep Maria Font (2013). The Simplest Protoalgebraic Logic. Mathematical Logic Quarterly 59 (6):435-451.
Similar books and articles
Andrzej W. Jankowski (1984). A Conjunction in Closure Spaces. Studia Logica 43 (4):341 - 351.
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.
George Voutsadakis (2003). Categorical Abstract Algebraic Logic Metalogical Properties. Studia Logica 74 (3):369 - 398.
David Miller (1991). An Open Problem in Tarski's Calculus of Deductive Systems. Bulletin of the Section of Logic 20 (2):36-43.
W. J. Blok & Don Pigozzi (1986). Protoalgebraic Logics. Studia Logica 45 (4):337 - 369.
Josep M. Font & Ventura Verdú (1993). The Lattice of Distributive Closure Operators Over an Algebra. Studia Logica 52 (1):1 - 13.
Josep Maria Font & Ramon Jansana (2011). Leibniz-Linked Pairs of Deductive Systems. Studia Logica 99 (1-3):171-202.
W. J. Blok & J. Rebagliato (2003). Algebraic Semantics for Deductive Systems. Studia Logica 74 (1-2):153 - 180.
Added to index2009-01-28
Total downloads6 ( #230,031 of 1,410,018 )
Recent downloads (6 months)1 ( #177,059 of 1,410,018 )
How can I increase my downloads?