Common Knowledge and the Knowledge Account of Assertion

Abstract

In this chapter, I present the assertion account of common knowledge in the framework of a multi-agent system for the epistemic logic of knowledge and assertion: the propositional content of a formula \(\upvarphi \) is common knowledge to a group of agents G iff everyone in G knows that \(\upvarphi \) is true and that \(\upvarphi \) is asserted. Three current accounts of common knowledge, including the iterated account, the fixed-point account, and shared environment approach, will be examined. I argue that common knowledge arises from communication which results from overtly observable interactions among agents in a group. I then propose that assertion plays a substantial role in communication, and a fortiori, in the acquisition of common knowledge, given the knowledge account of assertion—one must assert \(\upvarphi \) only if one knows \(\upvarphi \). I point out some semantic implications of the knowledge account of assertion in multi-agent systems, specifically, the transmission of individual knowledge to others, the transition of individual knowledge to common knowledge, and the luminosity of common knowledge. The assertion account of common knowledge is then proposed and justified by a class of Kripke models (referred to as TWC-models) appropriate for a multi-agent system of epistemic logic of common knowledge and assertion. The construction of TWC-models will be specified, and the related semantic rules will be given.