New axiomatizations of S3 and S4

1 December 1953

journal article
Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic

Vol. 18 (4) , 309-316
https://doi.org/10.2307/2266554

Abstract

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.

Keywords

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