Journal of Symbolic Logic

Implicational F-Structures and Implicational Relevance Logics

A. Avron

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We describe a method for obtaining classical logic from intuitionistic logic which does not depend on any proof system, and show that by applying it to the most important implicational relevance logics we get relevance logics with nice semantical and proof-theoretical properties. Semantically all these logics are sound and strongly complete relative to classes of structures in which all elements except one are designated. Proof-theoretically they correspond to cut-free hypersequential Gentzen-type calculi. Another major property of all these logics is that the classical implication can faithfully be translated into them.

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J. Symbolic Logic, Volume 65, Issue 2 (2000), 788-802.

First available in Project Euclid: 6 July 2007

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Avron, A. Implicational F-Structures and Implicational Relevance Logics. J. Symbolic Logic 65 (2000), no. 2, 788--802.

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