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 via“left-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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McRobbie, M.A., Belnap, N.D. Relevant analytic tableaux. Stud Logica 38, 187–200 (1979). https://doi.org/10.1007/BF00370441
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DOI: https://doi.org/10.1007/BF00370441