Remarks on a Carnapian Extension of S5

Abstract

This paper surveys several results on a Carnapian modal propositional logic C that extends S5. We formally define C and attribute it to Carnap. We give a bibliographic review on C and related systems. We highlight the relationship between S5 and C, review different axiomatizations and derive a simple Kripke-style model theory for C. We discuss possible consequence operators for C and relate C to nonmonotonic and epistemic logics. Finally, we report on recent complexity results for checking validity in C. Note: An extended version of this article of interest to computer scientists has appeared as Review of a Carnapian Extension of S5 in Logic at Work, Ewa Orlowska editor, Physica Verlag (Studies in Fuzziness and Soft Computing, Vol. 24) ISBN 3-7908-1164-5, 1999.