Inferring Lewisian Common Knowledge using Theory of Mind Reasoning in a Forward-chaining Rule Engine

This paper presents a practical technique for inferring common knowledge based on the approach of David Lewis, who identified three conditions that are sufficient for information about the world and other agents' reasoning mechanisms to lead to chains of iterated mutual knowledge. We consider agents with theory-of-mind rules that model other agents' beliefs. We prove that only two levels of nested models of other agents are necessary to achieve common knowledge. We illustrate this approach with an implemented scenario involving information on monuments in a public forum.