Notre Dame Journal of Formal Logic 35 (3):369-397 (1994)
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Abstract |
In this paper two deductive systems associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first one turns out to be an axiomatic extension of WR. Moreover we provide WR with a natural Gentzen calculus. It is proved that both deductive systems have the same associated class of algebras but different classes of models on these algebras. The notion of model used here is an abstract logic, that is, a closure operator on an abstract algebra; the abstract logics obtained in the case of WR are also the models, in a natural sense, of the given Gentzen calculus.
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DOI | 10.1305/ndjfl/1040511344 |
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References found in this work BETA
Note on Algebraic Models for Relevance Logic.Josep M. Font & Gonzalo Rodríguez - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (6):535-540.
Reduced Models for Relevant Logics Without ${\rm WI}$.John K. Slaney - 1987 - Notre Dame Journal of Formal Logic 28 (3):395-407.
Algebraic Logic for Classical Conjunction and Disjunction.J. M. Font & V. Verdú - 1993 - Studia Logica 52 (1):181.
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Citations of this work BETA
Fregean Logics.J. Czelakowski & D. Pigozzi - 2004 - Annals of Pure and Applied Logic 127 (1-3):17-76.
On the Closure Properties of the Class of Full G-Models of a Deductive System.Josep Maria Font, Ramon Jansana & Don Pigozzi - 2006 - Studia Logica 83 (1-3):215-278.
View all 13 citations / Add more citations
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