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On a Method of Describing Formal Deductions Convenient for Theoretical Purposes

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute Nagoya University
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In my paper [2], I have proposed a method of describing formal deductions which seems to be convenient for practical purposes. In my paper [3], I have employed an index-system to exactly express tree-form configurations of proofs in Gentzen’s formalism for sequents. In the present paper, I would like to propose a method of describing formal deductions which seems to be convenient for theoretical purposes. The device employed for this purpose relies mostly on an index-system. Just as in [2] as well as in [3], I propose here also to denote every proposition and every denomination of a variable, or every sequent in Gentzen’s formalism, by an index-word.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 36 , November 1969 , pp. 83 - 97
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

References

[1] Gentzen, G., Untersuchungen über das logische Schliessen. Math. Z. 39 (1935), 176–210, 405–431.Google Scholar
[2] Ono, K., On a practical way of describing formal deductions. Nagoya Math. J., 21 (1962), 115–121.Google Scholar
[3] Ono, K., Reduction of logics to the primitive logic. J. Math. Soc. Japan, 19–3 (1967), 384–398.Google Scholar