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Pure denumerable Łukasiewiczian implication

Published online by Cambridge University Press:  12 March 2014

R. K. Meyer
R. K. Meyer*
Affiliation:
West Virginia University
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Extract

In [1], McCall and I offered an axiomatization of the implicational fragment of the 3-valued Łukasiewiczian system defined in [2]. The following axiom schemata sufficed, together with the rule of modus ponens.1

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 4 , December 1966 , pp. 575 - 580
Copyright
Copyright © Association for Symbolic Logic 1997

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References

[1]McCall, S. and Meyer, R. K., Pure three-valued Łukasiewiczian implication, to appear in this Journal, vol. 31 (1966), no. 2.Google Scholar
[2]Łukasiewicz, J. and Tarski, A., Untersuchungen über den Aussagenkalkul, Comptes Rendus des séances de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 23, 1930, pp. 1–21; English translation in A. Tarski, Logic, semantics, metamathematics, translated by J. H. Woodger, Oxford (Clarendon), 1956.Google Scholar
[3]Meredith, C. A., The dependence of an axiom of Łukasiewicz, Transactions of the American Mathematical Society 87 (1958), p. 54.Google Scholar
[4]Rose, Alan and Rosser, J. B., Fragments of many-valued statement calculi, Transactions of the American Mathematical Society, 87 (1958), pp. 1–53.CrossRefGoogle Scholar
[5]Chang, C. C., Proof of an axiom of Łukasiewicz, Transactions of the American Mathematical Society, 87 (1958), p. 55f.Google Scholar
[6]Turquette, Atwell R., Independent axioms for infinite-valued logic, this Journal, vol. 28 (1963), pp. 217–221.Google Scholar