Variable-Sharing as Relevance

In Andrew Tedder, Shawn Standefer & Igor Sedlar, New Directions in Relevant Logic. Cham: Springer. pp. 97-117 (2025)
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Abstract

A challenge for relevant logicians is to delimit their area of study. I propose and explore the definition of a relevant logic as a logic satisfying a variable-sharing property and closed under detachment and adjunction. This definition is, I argue, a good definition that captures many familiar logics and raises interesting new questions concerning relevant logics.

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Shawn Standefer
Tohoku University

Citations of this work

Ignorance and the Possibility of Error in Relevant Epistemic Logic.Shawn Standefer - 2026 - In Katsuhiko Sano, Ryo Hatano & Hiroakira Ono, Exploring Negation, Modality and Proof. Singapore: Springer. pp. 41-66.
On strong and weak logics for paraconsistent computability.Fernando Cano-Jorge & Zach Weber - 2025 - Journal of Applied Logics - IfCoLoG Journal of Logics and Their Applications 12 (5):1349-1381.
Symmetry and Completeness in Relevant Epistemic Logic.Shawn Standefer & Edwin Mares - 2025 - Journal of Philosophical Logic 54 (2):429-450.

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References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
The Connectives.Lloyd Humberstone - 2011 - MIT Press. Edited by Lloyd Humberstone.
An essay in classical modal logic.Krister Segerberg - 1971 - Uppsala,: Filosofiska föreningen och Filosofiska institutionen vid Uppsala universitet.
Entailment: The Logic of Relevance and Necessity. - 1975 - Studia Logica 54 (2):261-266.

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