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A Characterization of the Intuitionistic Propositional Logic
Published online by Cambridge University Press: 22 January 2016
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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.
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- 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