Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-20T10:27:31.108Z Has data issue: false hasContentIssue false
  • English
  • Français

On ternary logic

Published online by Cambridge University Press:  12 March 2014

Paul Dienes
Paul Dienes*
Affiliation:
Birkbeck College, University of London
Get access Rights & Permissions [Opens in a new window]

1. the problem

In this paper we give the complete list of the functions of one variable with some of their properties, and lists of functions corresponding to various properties of sum, product, implication, and equivalence. The range of the variables as well as that of functional values will be о (false), ½, 1 (true). As an application we consider Frege's, Russell's and Heyting's systems in ternary logic. The proofs are mostly omitted as obvious if sometimes laborious.

Functions will be denned by matrices: e.g. F(p, q)

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 14 , Issue 2 , 23 June 1949 , pp. 85 - 94
Copyright
Copyright © Association for Symbolic Logic 1949

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 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. 30–50.Google Scholar

2 Reichenbach, Hans, Philosophic foundations of quantum mechanics, Berkeley and Loe Angeles 1944, see pp. 144–168.Google Scholar (Seen after the completion of the paper.)

3 Hilbert, D. and Ackermann, W., Grundzüge der theoretischen Logik, 2nd edition, Berlin 1938, see p. 23.CrossRefGoogle Scholar

4 See pp. 23–25.

5 Arend, Heyting, Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, Ergebnisse der Mathematik, vol. 3 no. 4, Berlin1934.Google Scholar

6 Stanisław, Jaśkowski, Recherches sur le système de la logique intuitioniste, Actes du Congrès International de Philosophie Scientifique, VI Philosophie des mathématiques, Paris 1936, pp. 58–61.Google Scholar