Depth Relevance and Hyperformalism

Journal of Philosophical Logic 51 (4):721-737 (2022)
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Abstract

Formal symptoms of relevance usually concern the propositional variables shared between the antecedent and the consequent of provable conditionals. Among the most famous results about such symptoms are Belnap’s early results showing that for sublogics of the strong relevant logic R, provable conditionals share a signed variable between antecedent and consequent. For logics weaker than R stronger variable sharing results are available. In 1984, Ross Brady gave one well-known example of such a result. As a corollary to the main result of the paper, we give a very simple proof of a related but strictly stronger result.

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Shay Logan
Kansas State University

Citations of this work

Varieties of Relevant S5.Shawn Standefer - 2023 - Logic and Logical Philosophy 32 (1):53–80.
Variable-Sharing as Relevance.Shawn Standefer - forthcoming - In Andrew Tedder, Shawn Standefer & Igor Sedlar (eds.), New Directions in Relevant Logic. Springer.
What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.

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References found in this work

What Does It Mean to Say That Logic is Formal?John MacFarlane - 2000 - Dissertation, University of Pittsburgh
Strong Depth Relevance.Shay Allen Logan - 2021 - Australasian Journal of Logic 18 (6):645-656.
Universal Logic.Ross Brady - 2006 - Bulletin of Symbolic Logic 13 (4):544-547.
Universal Logic.Ross Brady - 2007 - Studia Logica 87 (2-3):359-362.
Entailment and relevance.Nuel D. Belnap - 1960 - Journal of Symbolic Logic 25 (2):144-146.

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