What is relevance logic?

Annals of Pure and Applied Logic 165 (1):26-48 (2014)
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Abstract

We suggest two precise abstract definitions of the notion of ‘relevance logic’ which are both independent of any proof system or semantics. We show that according to the simpler one, R → source is the minimal relevance logic, but R itself is not. In contrast, R and many other logics are relevance logics according to the second definition, while all fragments of linear logic are not

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10.1016/j.apal.2013.07.004

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Arnon Avron
Tel Aviv University

Citations of this work

What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
Variable-Sharing as Relevance.Shawn Standefer - 2025 - In Andrew Tedder, Shawn Standefer & Igor Sedlar, New Directions in Relevant Logic. Springer.
Relevance logic.Edwin Mares - 2008 - Stanford Encyclopedia of Philosophy.
An Analysis of Poly-connexivity.Luis Estrada-González - 2022 - Studia Logica 110 (4):925-947.
The Relevance of Premises to Conclusions of Core Proofs.Neil Tennant - 2015 - Review of Symbolic Logic 8 (4):743-784.

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References found in this work

Relevance Logic.Michael Dunn & Greg Restall - 1983 - In Dov M. Gabbay & Franz Guenthner, Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers.
The Semantics and Proof Theory of Linear Logic.Arnon Avron - 1988 - Theoretical Computer Science 57 (2):161-184.
The undecidability of entailment and relevant implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.
Many-valued logic.Alasdair Urquhart - 1986 - In D. Gabbay & F. Guenther, Handbook of Philosophical Logic, Vol. Iii. D. Reidel Publishing Co..

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