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New axiomatizations of S3 and S4

Published online by Cambridge University Press:  12 March 2014

Leo Simons*
Affiliation:
Stanford University

Extract

Axiomatizations of two systems of modal logic are presented in this paper. The first consists of six axiom schemata and one rule of inference; this axiomatization is proved equivalent to Lewis' S3. The addition of a seventh schema, the analogue of C10. 1, yields an axiomatization equivalent to S4. Our axiom schemata for S3 are proved mutually independent, as are our schemata for S4.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1953

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References

BIBLIOGRAPHY

[1]Diamond, A. H. and McKinsey, J. C. C., Algebras and their subalgebras, Bulletin of the American Mathematical Society, vol. 53 (1947), No. 10, pp. 959–62.CrossRefGoogle Scholar
[2]Hilbert, H. and Ackermann, W., Principles of mathematical logic, New York, 1950.Google Scholar
[3]Lewis, C. I. and Langford, C. H., Symbolic logic, New York, 1932.Google Scholar
[4]McKinsey, J. C. C. and Tarski, A., Some theorems about the Lewis and Heyting calculi, this Journal, vol. 13 (1948), pp. 115.Google Scholar
[5]Parry, W. T., Modalities in the survey system of strict implication, this Journal, vol. 4 (1939), pp. 137–54.Google Scholar
[6]Parry, W. T., Postulates for strict implication, Mind, n.s., vol. 43 (1934), pp. 7880.CrossRefGoogle Scholar
[7]Wajsberg, M., Ein erweiterter Klassenkalkül, Monatshefte für Mathematik und Physik, vol. 40 (1933) pp. 113126.CrossRefGoogle Scholar