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A Study on Formal Deductions in the Primitive Logic

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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Main purpose of the present paper is to study formal deductions described along the line of my former work [1]. In the present paper, I restrict myself to the primitive logic. To extend this method to other logics such as the lower classical predicate logic or the intuitionistic predicaste logic, my way of practical discription has to undergo a certain extent of modification.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 1 - 14
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

Gentzen, G. [1] Untersuchungen über das logische Schliessen, Math. Z. 39 (1934), 176–210, 405–431.CrossRefGoogle Scholar
Ono, K. [1] On a practical way of describing formal deductions, Nagoya Math. J., 21 (1962), 115–121.Google Scholar
Ono, K. [2] A certain kind of formal theories, Nagoya Math. J., 25 (1965), 59–86.Google Scholar
Ono, K. [3] On universal character of the primitive logic, Nagoya Math. J., 27-1, (1966), 331–353.Google Scholar
Ono, K. [4] Reduction of logics to the primitive logic, J. Math. Soc. Jap., Vol. 19, No. 3 (1967), 384–398.Google Scholar