Reasoning about Failure

In this paper we investigate a modal logic of believing and saying to reason about unreliable agents in a system of communicating agents. We suppose that communication is reliable and semi-public: an agent's utterances are communicated to all the adjacent agents. We suppose that to each agent is associated some set of facts that he monitors, and that his perception is perfect in what concerns these facts. We show how an agent can detect failure of another agent by deduction in our logic. To that end we use a tableau theorem prover for our logic.