Multi-Agent Epistemic Explanatory Diagnosis via Reasoning about Actions

The task of explanatory diagnosis conjectures actions to explain observations. This is a common task in real life and an essential ability of intelligent agents. It becomes more complicated in multi-agent scenarios, since agents' actions may be partially observable to other agents, and observations might involve agents' knowledge about the world or other agents' knowledge or even common knowledge of a group of agents. For example, we might want to explain the observation that p does not hold, but Ann believes p, or the observation that Ann, Bob, and Carl commonly believe p. In this paper, we formalize the multi-agent explanatory diagnosis task in the framework of dynamic epistemic logic, where Kripke models of actions are used to represent agents' partial observability of actions. Since this task is undecidable in general, we identify important decidable fragments via techniques of reducing the potentially infinite search spaces to finite ones of epistemic states or action sequences.