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A theorem concerning the composition of functions of several variables ranging over a finite set

Published online by Cambridge University Press:  12 March 2014

Arto Salomaa
Arto Salomaa*
Affiliation:
University of Turku, Finland
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Extract

Consider functions whose variables, finite in number, range over a fixed finite set N and whose values are elements of N. The elements of N are denoted simply by the natural numbers 1,2, …, n. There are nnm distinct m-place functions. If N is chosen to be the set of n truth-values then the functions considered are obviously truth-functions in n-valued logic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 25 , Issue 3 , September 1960 , pp. 203 - 208
Copyright
Copyright © Association for Symbolic Logic 1960

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References

[1]Piccard, Sophie, Sur les fondions définies dans les ensembles finis quelconques, Fundamenta mathematicae, vol. 24 (1935), pp. 298–301.CrossRefGoogle Scholar
[2]Post, Emil L., Introduction to a general theory of elementary propositions, American journal of mathematics, vol. 43 (1921), pp. 163–185.CrossRefGoogle Scholar
[3]Słupecki, Jerzy, Kryterium pelności wielowartościowych systemów logiki zdań, Comptes rendus des séances de la Société des Sciences et des Lettres de Varsovie, Classe III, 32 Année (1939), pp. 102–109.Google Scholar