Only Knowing Meets Common Knowledge

Only knowing captures the intuitive notion that the beliefs of an agent are precisely those that follow from its knowledge base. While only knowing has a simple possible-world semantics in a single agent setting, the many agent case has turned out to be much more challenging. In a recent paper, we proposed an account which arguably extends only knowing to multiple agents in a natural way. However, the approach was limited in that the semantics cannot deal with infinitary notions such as common knowledge. In this work, we lift that serious limitation to obtain a first-order language with only knowing and common knowledge, allowing us to study the interaction between these notions for the very first time. By adding a simple form of public announcement, we then demonstrate how the muddy children puzzle can be cast in terms of logical implications given what is only known initially.