Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-02-06T06:53:14.424Z Has data issue: false hasContentIssue false
  • English
  • Français

A constructive proof of McNaughton's theorem in infinite-valued logic

Published online by Cambridge University Press:  12 March 2014

Daniele Mundici
Daniele Mundici*
Affiliation:
Department of Computer Science, University of Milan, via Comelico 39-41, 20135 Milan, Italy, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of Lukasiewicz. For the proof we only use Minkowski's convex body theorem and the rudiments of piecewise linear topology.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 596 - 602
Copyright
Copyright © Association for Symbolic Logic 1994

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

REFERENCES

[1] Anderson, M. and Feil, T., Lattice-ordered groups, An introduction, D. Reidel, Kluwer, Dordrecht, 1988.CrossRefGoogle Scholar
[2] Cassels, J. W. S., An introduction to the geometry of numbers, Grundlagen der Mathematischen Wissenschaften, vol. 99 (1959).Google Scholar
[3] Hudson, J. F. P., Piecewise linear topology, W. Benjamin, New York, 1968.Google Scholar
[4] McNaughton, R., A theorem about infinite-valued sentential logic, this Journal, vol. 16 (1951), pp. 1–13.Google Scholar
[5] Rose, A. and Rosser, J. B., Fragments of many-valued statement calculi, Transactions of the American Mathematical Society, vol. 87 (1958), pp. 1–53.Google Scholar
[6] Rourke, C. P. and Sanderson, B. J., Introduction to piecewise-linear topology, Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, Berlin, 1972.Google Scholar
[7] Tarski, A. and Lukasiewicz, J., Investigations into the sentential calculi, Logic, semantics, metamathematics, Oxford University Press, London and New York, 1956, pp. 38–59. Reprinted by Hackett Publishing Company. Indianapolis, 1983.Google Scholar