Rules in relevant logic — II: Formula representation

Studia Logica 52 (4):565 - 585 (1993)
Abstract
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 B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A 1&A 2& ...A n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C.
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DOI 10.1007/BF01053260
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References found in this work BETA
The Undecidability of Entailment and Relevant Implication.Alasdair Urquhart - 1984 - Journal of Symbolic Logic 49 (4):1059-1073.
Completeness of Relevant Quantification Theories.Robert K. Meyer, J. Michael Dunn & Hugues Leblanc - 1974 - Notre Dame Journal of Formal Logic 15 (1):97-121.
The Gentzenization and Decidability of RW.Ross T. Brady - 1990 - Journal of Philosophical Logic 19 (1):35 - 73.

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Citations of this work BETA
Four Basic Logical Issues.Ross Brady & Penelope Rush - 2009 - Review of Symbolic Logic 2 (3):488-508.

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