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On a Formalism Which Makes any Sequence of Symbols Well-Formed

Published online by Cambridge University Press:  22 January 2016

Shigeo Ōhama
Shigeo Ōhama*
Affiliation:
Nagoya University
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Any finite sequence of primitive symbols is not always well-formed in the usual formalisms. But in a certain formal system, we can normalize any sequence of symbols uniquely so that it becomes well-formed. An example of this kind has been introduced by Ono [2]. While we were drawing up a practical programming along Ono’s line, we attained another system, a modification of his system. The purpose of the present paper is to introduce this modified system and its application. In 1, we will describe a method of normalizing sentences in LO having only two logical constants, implication and universal quantifier, so that any finite sequence of symbols becomes well-formed. In 2, we will show an application of 1 to proof. I wish to express my appreciation to Prof. K. Ono for his significant suggestions and advices.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 1 - 4
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Ono., K: A certain kind of formal theories, Nagoya Math. J., Vol. 25 (1965), pp. 59–86.Google Scholar
[2] Ono., K: A formalism for primitive logic and mechanical proof-checking, Nagoya Math. J., Vol. 26 (1966), pp. 195–203.Google Scholar