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The sentential calculus using rule of inference Re

Published online by Cambridge University Press:  12 March 2014

R. B. Angell Jr.
R. B. Angell Jr.*
Affiliation:
Ohio Wesleyan University
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Extract

Axiomatizations of the sentential calculus which use Rmp (modus ponens), have been shown equivalent to axiomatizations similar in all respects except that Rmp is replaced by the less restricted rule Re (rule of excision)1:

Re. If S and (…(S⊃S') …), then (… S' …).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 25 , Issue 2 , June 1960 , pp. 143
Copyright
Copyright © Association for Symbolic Logic 1960

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References

1 Angell, R. B., On a less restricted type of rule of inference, Mind, n.s. vol. LXIX (1960).CrossRefGoogle Scholar

2 >Łukasiewicz, J. and Tarski, A., Untersuchungen über den Aussagenkalkül, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 23 (1930), pp. 30–50.Google Scholar