Algebraic Study of Two Deductive Systems of Relevance Logic

Notre Dame Journal of Formal Logic 35 (3):369-397 (1994)
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.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1305/ndjfl/1040511344
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 31,856
External links

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.

Add more references

Citations of this work BETA
Fregean Logics.J. Czelakowski & D. Pigozzi - 2004 - Annals of Pure and Applied Logic 127 (1-3):17-76.
Selfextensional Logics with a Conjunction.Ramon Jansana - 2006 - Studia Logica 84 (1):63-104.
Taking Degrees of Truth Seriously.Josep Maria Font - 2009 - Studia Logica 91 (3):383-406.

View all 7 citations / Add more citations

Similar books and articles
Added to PP index

Total downloads
22 ( #259,435 of 2,231,724 )

Recent downloads (6 months)
11 ( #41,972 of 2,231,724 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature