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  1. (2 other versions)Gentzen formulations of two positive relevance logics.Aleksandar Kron - 1980 - Studia Logica 39 (4):381 - 403.
    The author gentzenizes the positive fragmentsT + andR + of relevantT andR using formulas with, prefixes (subscripts). There are three main Gentzen formulations ofS +{T+,R +} calledW 1 S +,W 2 S + andG 2 S +. The first two have the rule of modus ponens. All of them have a weak rule DL for disjunction introduction on the left. DL is not admissible inS + but it is needed in the proof of a cut elimination theorem forG 2 S (...)
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  • Rules in relevant logic — II: Formula representation.Ross T. Brady - 1993 - Studia Logica 52 (4):565 - 585.
    This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A 1 .A 2 . ... .A n B, the conjunctive form,A 1&A 2 & ...A n (...)
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