Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T17:26:32.505Z Has data issue: false hasContentIssue false
  • English
  • Français

On η-valued functionally complete truth functions

Published online by Cambridge University Press:  12 March 2014

R. L. Graham
R. L. Graham*
Affiliation:
Bell Telephone Laboratories, Murray Hill, New Jersey
Get access Rights & Permissions [Opens in a new window]

Extract

It is well known that the familiar Sheffer stroke function of the 2-valued propositional calculus is functionally complete (i.e., for any m, all 22m truth functions of m variables can be defined1 in terms of the stroke function). Indeed, it is not difficult to show that of the 16 2-valued functions of two variables, exactly two of them are functionally complete.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 2 , August 1967 , pp. 190 - 195
Copyright
Copyright © Association for Symbolic Logic 1967

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]Foxley, E., The determination of all Sheffer functions in 3-valued logic, using a logical computer, Notre Dame journal of formal logic, vol. 3 (1962), pp. 41–50.CrossRefGoogle Scholar
[2]Martin, Norman M., The Sheffer functions of 3-valued logic, this Journal, vol. 1954), pp. 45–51.Google Scholar
[3]Martin, Norman M., Some analogues of the Sheffer stroke function in n-valued logic, Indagationes Mathematicae, vol. 12 (1950), pp. 393–400.Google Scholar
[4]Post, Emil L., Introduction to a general theory of elementary propositions, American Journal of mathematics, vol. 34 (1921), pp. 163–185.CrossRefGoogle Scholar
[5]Riordan, J., An introduction to combinatorial analysis, Wiley, New York, 1958, p. 128.Google Scholar
[6]Rosser, J. B. and Turquette, A. R., Many-valued logics, North-Holland, Amsterdam, 1952.Google Scholar
[7]Salomaa, A., On the composition of functions of several variables ranging over a finite set, Annales Universitates Turkuensis Ser AI, vol. 41 (1960).Google Scholar
[8]Salomaa, A., Some completeness criteria for sets of functions over a finite domain. I, II, Annales Vniversitates Turkuensis, vol. 53 (1962) and vol. 63 (1963).Google Scholar
[9]Webb, Donald L., Definition of Post's generalized negative and maximum in terms of one binary operation, American journal of mathematics, vol. 58 (1936), pp. 193–194.CrossRefGoogle Scholar
[10]Wheeler, R. F., Complete propositional connectives, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 7 (1961), pp. 185–198.CrossRefGoogle Scholar
[11]Wheeler, R. F., An asymptotic formula for the number of complete propositional connectives, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 8 (1962), pp. 1–4.CrossRefGoogle Scholar
[12]Wheeler, R. F., Complete connectives for the 3-valued propositional calculus, Proceedings of the London Mathematical Society, vol. 16 (1966), pp. 167–191.CrossRefGoogle Scholar