Relevant analytic tableaux

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

Nuel Belnap
University of Pittsburgh
Michael A. McRobbie
Indiana University, Bloomington

Citations of this work

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.
Idealist Origins: 1920s and Before.Martin Davies & Stein Helgeby - 2014 - In Graham Oppy & Nick Trakakis (eds.), History of Philosophy in Australia and New Zealand. Dordrecht, Netherlands: Springer. pp. 15-54.
Relevance via decomposition.David Makinson - 2017 - Australasian Journal of Logic 14 (3).

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References found in this work

First-order logic.Raymond Merrill Smullyan - 1968 - New York [etc.]: Springer Verlag.
Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan Ross Anderson & Nuel D. Belnap - 1975 - Princeton, N.J.: Princeton University Press. Edited by Nuel D. Belnap & J. Michael Dunn.
A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
The collected papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam,: North-Holland Pub. Co.. Edited by M. E. Szabo.
Foundations of mathematical logic.Haskell Brooks Curry - 1963 - New York: Dover Publications.

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