Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-02-02T04:17:28.779Z Has data issue: false hasContentIssue false
  • English
  • Français

New axiomatizations of S3 and S4

Published online by Cambridge University Press:  12 March 2014

Leo Simons
Leo Simons*
Affiliation:
Stanford University
Get access Rights & Permissions [Opens in a new window]

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
Information
The Journal of Symbolic Logic , Volume 18 , Issue 4 , December 1953 , pp. 309 - 316
Copyright
Copyright © Association for Symbolic Logic 1953

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

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. 1–15.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. 78–80.CrossRefGoogle Scholar
[7]Wajsberg, M., Ein erweiterter Klassenkalkül, Monatshefte für Mathematik und Physik, vol. 40 (1933) pp. 113–126.CrossRefGoogle Scholar