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Super-Łukasiewicz implicational logics

Published online by Cambridge University Press:  22 January 2016

Yuichi Komori
Yuichi Komori*
Affiliation:
Department of Mathematics, Faculty of Science, Shizuoka University
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In the traditional study of Łukasiewicz propositional logic, the finite-valued or infinite-valued linearly ordered model exists at the start, and then the axiomatization of the set of all formulas valid in its model are studied. On the other hand, we are in a point of view such that the set of provable formulas is important and models are no more than means to characterize the set.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 72 , December 1978 , pp. 127 - 133
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Komori, Y., The separation theorem of the ℵ0-valued Lukasiewicz propositional logic, Rep. Fac. Sci., Shizuoka Univ., 12 (1978), 1’5.Google Scholar
[2] Rose, A., Formalisation du calcul propositionnel implicatif a ℵ0 valeurs de Lukasiewicz, CR. Acad. Sc. Paris, 243 (1956), 1183’1185.Google Scholar
[3] Rose, A. and Rosser, J. B., Fragments of many-valued statement calculi, Trans. Amer. Math. Soc., 87 (1957), 1’53.Google Scholar