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On some Alleged Decision Procedures for S4

Published online by Cambridge University Press:  12 March 2014

Hanson Willam H.
Hanson Willam H.*
Affiliation:
Univac Division of Sperry Rand Corporation, St Paul, Minnesota
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Extract

In [1] Anderson gave what he claimed was a decision procedure for Lewis's calculus S4. One of the proofs of [1] was faulty, however, and he sought to remedy the situation in [2] by modifying slightly one of the conditions of the decision procedure of [1]. Poliferno subsequently reported in [5] that, according to Anderson, the procedure of [2] was not adequate either, but tha t a correct decision procedure for S4 could be obtained by combining the procedures of [1] and [2]. The purpose of the present note is to show tha t none of the three procedures referred to above are correct decision procedures for S4.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 31 , Issue 4 , December 1966 , pp. 641 - 643
Copyright
Copyright © Association for Symbolic Logic 1997

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References

[0]Carnap, R., Modalities and Quantification, this Journal, v. 11 (1946), pp 33–64.Google Scholar
[1]Church, A., Introduction to Mathematical Logic, Vol. I. Princeton: Princeton U. Press, 1956.Google Scholar
[2]Feys, R., Modal Logics. Louvain: E. Nauwelaerts, 1965.Google Scholar
[3]Kripke, S., A Completeness Theorem in Modal Logic, this Journal, v. 24 (1959), pp. 1–14.Google Scholar
[4]Kripke, S., Semantical Considerations on Modal Logic, Acta Philosophica Fennica, Fasc. 16 (1963), pp. 83–94.Google Scholar
[5]Kripke, S., Semantical Analysis of Modal Logic I, Normal Modal Propositional Calculi, Zeit. für math. Logik und Grundlagen der Math., Bd. 9 (1963), pp. 76–96.Google Scholar
[6]Leonard, H., Two-Valued Truth Tables for Modal Functions in Henle, et al., eds., Structure, Method and Meaning. New York: Liberal Arts Press, 1951.Google Scholar
[7]Quine, W., Methods of Logic. New York: Holt, Rinehart & Winston, 1963.Google Scholar