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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]
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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

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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