Relevance and conformity
type: Item
instance of: scholarly article
title: Relevance and conformity
zbMATH Open document ID: 0596.03011
author: Harry Deutsch
published in: Notre Dame Journal of Formal Logic
publication date: 1985-01-01T00:00:00Z
review text: This is a discussion of some of the features of the author's systems of relevant logic, which he calls ''conforming'' relevant logics. They obey the principle of conformity to Boolean ordering: theorems are entailed by their negations. An example of a conforming relevant logic already in the literature is J. M. Dunn's R-Mingle. The author gives semantics for first-degree conforming implication that diverge somewhat from Dunn's for first-degree entailment. For example, the non-entailment \(A\vee B\to B\vee \sim B\) is validated. The author's semantics for his full systems in effect uses semilattices for possible worlds but no inconsistent worlds. This semantics is easily generalized to quantification, unlike the semantics of R. Sylvan, R. K. Meyer, and K. Fine for the nonconforming relevant logic R. It also extends nicely the Kantian content containment claimed by Anderson and Belnap for their variable- sharing property. In conforming relevant logic, contraposition is invalid and transitivity holds only in the weak imported from (A\(\to B)\&(B\to C)\to (A\to C)\).
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 3959373
zbMATH Keywords: entailment
zbMATH Keywords: paraconsistency
zbMATH Keywords: relevant implication
zbMATH Keywords: relevant logic
zbMATH Keywords: semantics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093870937
OpenAlex ID: W2025262844
DOI: 10.1305/NDJFL/1093870937
description: scientific article; zbMATH DE number 3959373