The Classical Constraint on Relevance

Logica Universalis 8 (1):1-15 (2014)
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Abstract

We show that as long as the propositional constants t and f are not included in the language, any language-preserving extension of any important fragment of the relevance logics R and RMI can have only classical tautologies as theorems . This property is not preserved, though, if either t or f is added to the language, or if the contraction axiom is deleted

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10.1007/s11787-013-0092-y

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Arnon Avron
Tel Aviv University

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References found in this work

Relevance Logic.Michael Dunn & Greg Restall - 1983 - In Dov M. Gabbay & Franz Guenthner (eds.), Handbook of Philosophical Logic. Dordrecht, Netherland: Kluwer Academic Publishers.
What is relevance logic?Arnon Avron - 2014 - Annals of Pure and Applied Logic 165 (1):26-48.
Whither relevance logic?Arnon Avron - 1992 - Journal of Philosophical Logic 21 (3):243 - 281.
Relevant entailment--semantics and formal systems.Arnon Avron - 1984 - Journal of Symbolic Logic 49 (2):334-342.
Relevance and paraconsistency—a new approach.Arnon Avron - 1990 - Journal of Symbolic Logic 55 (2):707-732.

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