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By γ, we mean the rule, “From ├ A and ├ Ā V B, infer ├ B”.1 This rule has played an important and a controversial role in a set of relevant logics free of certain well-known paradoxes of implication, like AĀ-→B and A-→(B-→B). Among these logics we count the pioneering systems of strenge Implikation presented by Ackermann in [1],2 as well as the Anderson-Belnap systems E of entail-ment and R of relevant implication.3

I The basic formal ideas of this interpretation were in a certain sense anticipated by E. W. Beth with his "reduced logic" in [3]. We are grateful to Professor Bas C. van Fraassen for bringing this to our attention. The idea has also been employed by P. T. Geach in his "Quantification theory and the problem of identifying objects of reference" in Acta Philosophica Fennica, 1963, and by Henry S. Leonard in his "Essences, attributes, and predicates" in the Proceedings of the American Philisophical Association, 1963-64. Further, H. Leblanc has studied the interpretation in a pair of forthcoming papers, "A simplified strong completeness proof for QC=," and "A simplified account of validity and implication for quantification logic."