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A Characterization of the Intuitionistic Propositional Logic

Published online by Cambridge University Press:  22 January 2016

Nobol Muti
Nobol Muti*
Affiliation:
Mathematical Institute, Nagoya University
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In this short note, is shown a necessary and sufficient condition for a logic to be an intermediate propositional logic in Umezawa’s sense (see the reference), under such an assumption that any logic in consideration (as a subclass of LK-provable propositions) contains at least the axioms of the positive propositional logic LPS (Curry’s LA) as its axioms and is closed with respect to the rules of detachment and substitution.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 37 , March 1970 , pp. 131 - 136
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

References

Umezawa, Toshio: Über die Zwischensysteme der Aussagenlogik, Nagoya Math. J., 9 (1955), 181–189.Google Scholar