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On Equivalent Truth-Tables of Many-Valued Logics

Published online by Cambridge University Press:  20 January 2009

J. Kalicki
J. Kalicki
Affiliation:
The University, Leeds.
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Many-valued or non-Aristotelian calculi of propositions (logics) were originally introduced by generalisation of the truth-table method. It was known by the end of the nineteenth century that ordinary “binary” formulae of the calculus of propositions, such as

could be verified directly by means of the truth-table:

although the terminology and symbolism used were different.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 10 , Issue 2 , December 1954 , pp. 56 - 61
Copyright
Copyright © Edinburgh Mathematical Society 1954

References

REFERENCES

1.Heyting, A., “Die formalen Regeln der intuitionistischen Logik,” Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse, 1930.Google Scholar
2.Kalieki, J., “On Tarski's Matrix Method,” Comptes Bendus des Seances de la Societe des Sciences et des Lettres de Varsovie, XLI (1948), Classe III, 130–142.Google Scholar
3.Kalieki, J., “Note on Truth-Tables,” Journal of Symbolic Logic, 15 (1950), 174–181.CrossRefGoogle Scholar
4.Kalieki, J., “A Test for the Existence of Tautologies according to Many-Valued Truth-Tables,” Journal of Symbolic Logic, 15 (1950), 182–184.CrossRefGoogle Scholar
5.Łukasiewicz, J., A Review, Ruch Filozoficzny, vol. 5, No. 9 (1920).Google Scholar
6.Łukasiewicz, J., “Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls,” Comptes Rendus des Séances de la Société des Sciences et des Ltttres de Varsovie, XXIII (1930).Google Scholar
7.Łukasiewicz, J. and Tarski, A., “Untersuchungen über den Aussagenkalkül,” Comptes Rendus des Seances de la Société des Sciences et des Lettres de Varsovie, XXIII (1930).Google Scholar
8.Peirce, C. S., “On the Algebra of Logic; A Contribution to tbe Philosophy of Notation,” American J. of Math., VII (1885).Google Scholar
9.Post, E. L., “Introduction to a general theory of elementary propositions,” American J. of Math., XLIII (1921).Google Scholar
10.Rosser, J. B. and Turquette, A. R., “Axiom schemes for m-valued propositional calculi,” Journal of Symbolic Logic, X (1945).CrossRefGoogle Scholar