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Extensions of some theorems of Anderson and Belnap

Published online by Cambridge University Press:  12 March 2014

Alan Rose
Alan Rose*
Affiliation:
The University, Nottingham, England
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Extract

The object of this note is to extend to Post's m-valued propositional calculus1 the axiomatization by Anderson and Belnap2 of the 2-valued propositional calculus.

Notation and definitions. We shall use the symbols ∼ and v for the primitives of Post and shall otherwise, except as stated below, use the same notation and definitions as in the previous paper.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 27 , Issue 4 , December 1962 , pp. 423 - 425
Copyright
Copyright © Association for Symbolic Logic 1962

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References

1 Post, Emil L., Introduction to a general theory of elementary propositions, American journal of mathematics, Vol. 43 (1921), pp. 163–185.CrossRefGoogle Scholar

2 Anderson, Alan Ross and Belnap, Nuel D. Jr., A simple treatment of truthfunctions, this Journal , Vol. 24 (1959), pp. 301–302.Google Scholar

3 (Dated July 19, 1961.) The remarks of Anderson and Belnap (op. cit., p. 302) concerning derived rules are, in general, applicable to the present paper. However, they do not apply to every case in which the conclusion of a rule is shorter than one of the premises since φ(∼Av ∼B) is a premise of rule 2 and φ(∼(A v B)) is the conclusion.

4 Rosser, J. B. and Turquette, A. R., Many-valued logics, Amsterdam, 1952, pp. 25–26.Google Scholar