Reasoning about Epistemic Actions and Knowledge in Multi-Agent Systems Using Coq

In this paper, the authors outline a formal system for reasoning about agents＇ knowledge in knowledge games-a special type of multi-agent system. Knowledge games are card games where the agents＇ actions involve an exchange of information with other agents in the game. The authors＇ system is modeled using Coq-a formal proof management system. To the best of the authors＂ knowledge, there are no papers in which knowledge games are considered using a Coq proof assistant. The authors use the dynamic logic of common knowledge, where they particularly focus on the epistemic consequences of epistemic actions carried out by agents. The authors observe the changes in the system that result from such actions. Those changes that can occur in such a system that are of interest to the authors take the form of agents＇ knowledge about the state of the system, knowledge about other agents＇ knowledge, higher-order agents＇ knowledge and so on, up to common knowledge. Besides an axiomatic ofepistemic logic, the authors use a known axiomatization of card games that is extended with some new axioms that are required for the authors＇ approach. Due to a deficit in implementations grounded in theory that enable players to compute their knowledge in any state of the game, the authors show how the authors＇ approach can be used for these purposes.