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Reinforced Logics

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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The device of representing a predicate by a universal sentence gives rise to logics of higher order. To represent an object constructed by a series of certain steps, we usually use terms. To represent a predicate constructed by a series of certain steps, we now use sentences in general. We can now substitute special predicates represented by sentences for predicate variables of a sentence just as we have been able to substitute special objects represented by terms for object variables. It is remarkable that we can always distinguish predicates from objects, proceeding in this way.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 28 , October 1966 , pp. 15 - 25
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Ono, K. [1] A formalism for primitive logic and mechanical proof-checking, Nagoya Math. J., vol. 26 (1966), 195–203.CrossRefGoogle Scholar
[2] Ono, K. [2] On universal character of the primitive logic, Nagoya Math. J., vol. 27–1 (1966), 331–353.Google Scholar
[3] Ono, K. [3] A certain kind of formal theories, Nagoya Math. J., vol. 25 (1965), 59–86.Google Scholar
[4] Takeuti, G. [1] On a generalized logic calculus, Jap. J. Math., vol. 23 (1953), 39–96 .Google Scholar
[5] Whitehead, A. N. and Russell, B. [1] Principia mathematica I-III, 2nd ed. Cambridge (1925–1927).Google Scholar