Summary: Multi-modal versions of the propositional logics S5 or S4 – commonly accepted as logics of knowledge – are capable of describing static states of knowledge but they do not reflect how the knowledge changes after communications among agents. In the present paper (part of broader research on logics of knowledge and communications) we define extensions of the logic S5 which can deal with public communications. The logics have natural semantics. We prove some completeness, decidability and interpretability results and formulate a general method that solves a certain kind of problems involving public communications – among them the well-known puzzles of Muddy Children and Mr. Sum & Mr. Product. As the paper gives a formal logical treatment of the operation of restriction of the universe of a Kripke model, it contributes also to investigations of semantics for modal logics.
This paper was originally published in: M. L. Emrich et al. (eds.), Proceedings of the fourth international symposium on methodologies for intelligent systems. Poster session program. Oak Ridge National Laboratory. 201–216 (1989).