Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-25T00:40:58.708Z Has data issue: false hasContentIssue false
  • English
  • Français

On logics intermediate between intuitionistic and classical predicate logic

Published online by Cambridge University Press:  12 March 2014

Toshio Umezawa
Toshio Umezawa*
Affiliation:
Nagoya University, Nagoya, Japan
Get access Rights & Permissions [Opens in a new window]

Extract

In [1] and [2] I investigated logics intermediate between intuitionistic and classical propositional logic. In the present paper I shall study inclusion and non-inclusion between certain intermediate predicate logics. All the logics considered result from intuitionistic predicate logic by addition of classically valid axiom schemes.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 24 , Issue 2 , June 1959 , pp. 141 - 153
Copyright
Copyright © Association for Symbolic Logic 1959

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Umezawa, T., Über die Zwischensysteme der Aussagenlogik, Nagoya mathematical journal, vol. 9 (1955), pp. 181–189.CrossRefGoogle Scholar
[2]Umezawa, T., On intermediate propositional logics, this Journal, vol. 24 (1959) pp. 20–36.Google Scholar
[3]Gentzen, G., Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, vol. 39 (1934–1935), pp. 176–210, 405–431.CrossRefGoogle Scholar
[4]Kleene, S. C., Introduction to metamathematics, Amsterdam-Groningen-New York, 1952.Google Scholar
[5]Maehara, S., Eine Darstellung der intuitionistischen Logik in der klassischen, Nagoya mathematical journal, vol. 7 (1954), pp. 46–64.CrossRefGoogle Scholar
[6]Mostowski, A., Proofs on non-deducibility in intuitionistic functional calculus, this Journal, vol. 13 (1948), pp. 204–207.Google Scholar
[7]Glivenko, V., Sur quelques points de la logique de M. Brouwer, Académie Royale de Belgique, Bulletins de la classe des sciences, ser. 5, 15 (1929), pp. 183–188.Google Scholar