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The Craig-Lyndon interpolation theorem in 3-valued logic

Published online by Cambridge University Press:  12 March 2014

R. R. Rockingham Gill
R. R. Rockingham Gill*
Affiliation:
University of St. Andrews
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Extract

The purpose of this paper is to provide a formal system which is (a) adequate (functionally complete), (b) consistent, and (c) complete, relative to 3-valued logic with one designated value, and for which, furthermore, (d) a simple normal form theorem, and (e) the Craig-Lyndon Interpolation Theorem [1], [2] holds.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 35 , Issue 2 , June 1970 , pp. 230 - 238
Copyright
Copyright © Association for Symbolic Logic 1970

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References

[1]Craig, W., Linear reasoning. A new form of the Herbrand-Gentzen theorem, this Journal, vol. 22 (1957), pp. 250–268.Google Scholar
[2]Lyndon, R., An interpolation theorem in the predicate calculus, Pacific journal of mathematics, vol. 9 (1959), pp. 129–142.CrossRefGoogle Scholar
[3]Rosser, J. B. and Turquette, A. R., Many-valued logics, North-Holland, Amsterdam, 1952.Google Scholar
[4]Jobe, W., Functional completeness and canonical forms in many-valued logic, this Journal, vol. 27 (1962), pp. 409–422.Google Scholar
[5]Robinson, A., A result on consistency and its application to the theory of definability, Indagationes Mathematicae, vol. 18 (1956), pp. 47–58.CrossRefGoogle Scholar
[6]Henkin, L., An extension of the Craig-Lyndon Interpolation Theorem, this Journal, vol. 28 (1963), pp. 201–216.Google Scholar
[7]Oberschelp, A., On the Craig-Lyndon Interpolation Theorem, this Journal, vol. 33 (1968), pp. 271–274.Google Scholar
[8]Nagashima, T., An extension of the Craig-Schütte Interpolation Theorem, Annals of the Japan Association for Philosophy of Science, vol. 3, no. 1 (1966), pp. 12–18.CrossRefGoogle Scholar