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New axiomatizations of S3 and S4

Published online by Cambridge University Press:  12 March 2014

Leo Simons
Leo Simons*
Affiliation:
Stanford University
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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

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References

BIBLIOGRAPHY

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