Implicational f-structures and implicational relevance logics

Journal of Symbolic Logic 65 (2):788-802 (2000)
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 logic is that the classical implication can faithfully be translated into them
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DOI 10.2307/2586570
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References found in this work BETA
Multiplicative Conjunction as an Extensional Conjunction.Arnon Avron - 1997 - Logic Journal of the IGPL 5 (2):181-208.
A Structurally Complete Fragment of Relevant Logic.John K. Slaney & Robert K. Meyer - 1992 - Notre Dame Journal of Formal Logic 33 (4):561-566.
Independent Axioms for the Implicational Fragment of Sobociński's Three-Valued Logic.Robert K. Meyer & Zane Parks - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (19-20):291-295.

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Fragments of R-Mingle.W. J. Blok & J. G. Raftery - 2004 - Studia Logica 78 (1-2):59-106.

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