A Note on the Relevance of Semilattice Relevance Logic

Australasian Journal of Logic 16 (6):177-185 (2019)
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Abstract

A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more intuitive arithmetical structures to establish the variable sharing property for the systems discussed.

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Yale Weiss
CUNY Graduate Center

Citations of this work

What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
Semantics for Pure Theories of Connexive Implication.Yale Weiss - 2022 - Review of Symbolic Logic 15 (3):591-606.
The relevance logic of Boolean groups.Yale Weiss - 2023 - Logic Journal of the IGPL 31 (1):96-114.

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