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A Remark on Peirce’s Rule in Many-Valued Logics

Published online by Cambridge University Press:  22 January 2016

Katuzi Ono
Katuzi Ono*
Affiliation:
Mathematical Institute, Nagoya University
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Recently, S. Nagata gave an interesting series of rules beginning with Peirce’s rule introduced in [3], each rule in the series being really stronger than its successor in the intuitionistic logics. (See [1] Nagata.) Namely, let p0, p1, … be any series of mutually distinct propositional variables.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 69 - 70
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Nagata, S., A series of successive modifications of Peirce’s rule, Proc. Japan Acad., 42 (1966), 859–861.Google Scholar
[2] ONO, K., On a class of truth-value evaluations of the primitive logic, Nagoya Math. J., 31 (1967), 71–80.CrossRefGoogle Scholar
[3] Peirce, C.S., On the algebra of logic: A contribution to the philosophy of notation, Amer. J. of Math., 7 (1885), 180–202.Google Scholar