Public announcements, private actions and common knowledge in S5 structures

Abstract

In this paper we take the S5 definition of knowledge, and have a new look at logics combining modalities for public announcements, action models, common knowledge and relativized common knowledge. In particular, we prove two expressivity results which previously have only been shown for the case where knowledge is represented using arbitrary Kripke models but have remained open for the case of S5 models: public announcement logic with relativized common knowledge is strictly more expressive than public announcement logic with common knowledge, and action model logic with common knowledge is strictly more expressive than public announcement logic with common knowledge. We also propose and study a definition of relativized common knowledge for action model logic. © 2013 Springer-Verlag.