Abstract
A system of natural deduction is presented whose set of theses is identical with that of the systemE of entailment. For that system a decision procedure is described proving the decidability ofE.
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References
Nuel D. Belnap, Jr.,Entailment and relevance,The Journal of Symbolic Logic 25 (1960), pp. 144–146.
Alan R. Anderson,Completeness theorems for the systems E of entailment and EQ of entailment with quantification,Zeitschrift für mathematische Logik und Grundlagen der Mathematik 6 (1960), pp. 201–216.
E. K. Vojshvillo,Natural variants of some systems of relevant logic (in Russian), inLogičecki Wyvod. Nauka, Moscow 1979.
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The decision problem for the systemR (of relevant implication) is solved as a consequence of solving the decision problem ofE. The proposed solution was reported by the author at the XV International Philosophical Congress (Varna, 1973) and at the Conference on problems of propositional logic (Wrocław, 1975). The publication of a detailed presentation was hindered by the absence of suitable proof for the adequacy of the proposed procedure. The current presentation involves some modifications and simplifications in the formulation of the procedure (in connection with the proof of its adequacy). In particular, a more convenient language with implication is used instead of strict disjunction in the initial variant.
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Vojshvillo, E.K. A decision procedure for the systemE (of entailment). I.. Stud Logica 42, 139–164 (1983). https://doi.org/10.1007/BF01063835
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DOI: https://doi.org/10.1007/BF01063835