A Study of the Logic of Common Beliefs and Common Knowledge

The research on the philosophical logic of common belief and common knowledge has always been carried out together. There has been a lot of research on the logic of common knowledge. In addition to the simplest cognitive logic, there are also dynamic studies on the logic of common knowledge, the logic of common knowledge with weight, and the logic of common declaration of common knowledge. But the study of the philosophical logic of common beliefs has always been relatively marginalized. This paper tries to employ literature methods to present the language, models, and semantics of simple common belief logic according to the system of cognitive logic form about common knowledge by elaborating on the history of logical development and the standard research methods of modal logic.