Algebraic study of two deductive systems of relevance logic

17Citations
Citations of this article
10Readers
Mendeley users who have this article in their library.

Abstract

In this paper two deductive systems (i.e., two consequence relations) 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 Wojcicki 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 (of a classical kind). 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. © 1994, Duke University Press. All Rights Reserved.

Cite

CITATION STYLE

APA

Font, J. M., & Rodríguez, G. (1994). Algebraic study of two deductive systems of relevance logic. Notre Dame Journal of Formal Logic, 35(3), 369–397. https://doi.org/10.1305/ndjfl/1040511344

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free