Studia Logica 41 (2-3):95 - 108 (1982)

The standard deduction theorem or introduction rule for implication, for classical logic is also valid for intuitionistic logic, but just as with predicate logic, other rules of inference have to be restricted if the theorem is to hold for weaker implicational logics.In this paper we look in detail at special cases of the Gentzen rule for and show that various subsets of these in effect constitute deduction theorems determining all the theorems of many well known as well as not well known implicational logics. In particular systems of rules are given which are equivalent to the relevance logics E,R, T, P-W and P-W-I.
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DOI 10.1007/BF00370338
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References found in this work BETA

Entailment. Vol. 1.Alan Ross Anderson & Nuel D. Belnap - 1977 - Canadian Journal of Philosophy 7 (2):405-411.
The System LD.Haskell B. Curry - 1952 - Journal of Symbolic Logic 17 (1):35-42.
Positive Logic and Λ-Constants.David Meredith - 1978 - Studia Logica 37 (3):269 - 285.

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Idealist Origins: 1920s and Before.Martin Davies & Stein Helgeby - 2014 - In Graham Oppy & Nick Trakakis (eds.), History of Philosophy in Australia and New Zealand. Dordrecht, Netherlands: Springer. pp. 15-54.

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