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An extension of computational logic

Published online by Cambridge University Press:  12 March 2014

Alan Rose
Alan Rose*
Affiliation:
College of Technology, Manchester, England
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Extract

There has recently been developed a system of computational logic to which was given an interpretation in terms of the 2-valued propositional calculus. The object of the present paper is to give the corresponding theory for 3-valued logic. We use the same notation as Levin, except that instead of using the numeral “2” as a constant, we use “3”.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 17 , Issue 1 , March 1952 , pp. 32 - 34
Copyright
Copyright © Association for Symbolic Logic 1952

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References

1 Levin, Nathan P., Computational logic, this Journal, vol. 14 (1949), pp. 167–172Google Scholar.

2 This theory was developed by Łukasiewicz and later generalised by him in conjunction with Tarski to m-valued systems. The m-valued systems were discovered independently by Post. The original papers include:

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

Łukasiewicz, Jan, 0 logice trójwartościowej, Ruch filozoficzny, vol. 5 (1920), pp. 169–171Google Scholar.

Łukasiewicz, Jan and Tarski, Alfred, Untersuchungen über den Aussagenkalkül, Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 23 (1930), pp. 30–50Google Scholar.

Rosser, J. B. and Turquette, A. R., Axiom schemes for m-valued propositional calculi, this Journal, vol. 10 (1945), pp. 61–82Google Scholar.

3 Wajsberg, M., Aksjomatyzacja trójewartościowego rachunku zdań, Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Classe III, vol. 24 (1931), pp. 126–148Google Scholar; or J. B. Rosser and A. R. Turquette, op. cit., pp. 73–74.