Studia Logica 38 (2):187 - 200 (1979)

Authors
Nuel Belnap
University of Pittsburgh
Michael A. McRobbie
Indiana University, Bloomington
Abstract
Tableau formulations are given for the relevance logics E (Entailment), R (Relevant implication) and RM (Mingle). Proofs of equivalence to modus-ponens-based formulations are vialeft-handed Gentzen sequenzen-kalküle. The tableau formulations depend on a detailed analysis of the structure of tableau rules, leading to certain global requirements. Relevance is caught by the requirement that each node must be used; modality is caught by the requirement that only certain rules can cross a barrier. Open problems are discussed.
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DOI 10.1007/BF00370441
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References found in this work BETA

First-Order Logic.Raymond Merrill Smullyan - 1968 - Berlin, Germany: New York [Etc.]Springer-Verlag.
A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
The Collected Papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam: North-Holland Pub. Co..
Foundations of Mathematical Logic.Haskell Brooks Curry - 1963 - New York, NY, USA: Dover Publications.

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Citations of this work BETA

Heterogeneous Logic.I. L. Humberstone - 1988 - Erkenntnis 29 (3):395 - 435.
Multisets and Relevant Implication I.Robert K. Meyer & Michael A. McRobbie - 1982 - Australasian Journal of Philosophy 60 (2):107 – 139.
Relational Proof System for Relevant Logics.Ewa Orlowska - 1992 - Journal of Symbolic Logic 57 (4):1425-1440.
Relevance Via Decomposition.David Makinson - 2017 - Australasian Journal of Logic 14 (3).
A Note on the Admissibility of Cut in Relevant Tableau Systems.Michael A. McRobbie & Robert K. Meyer - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (32):511-512.

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