This paper presents a formal theory of multiple agent non-monotonic reasoning. We introduce the subject of multiple agent non-monotonic reasoning for inquiry and motivate the field in terms of its applications for con-n-nonsense reasoning. We extend Moore’s  Autoepistemic Logic to the multiple agent case, and show that the resulting logic is too weak for most applications of commonsense reasoning. We then suggest some possible sets of principles for a logic of multiple-agent non-monotonic reasoning, based on the concept of an agent’s arrogance towards his knowledge of another agent’s ignorance. While the principles of arrogance are in general too strong, we demonstrate that restricted versions of these principles can work quite well for commonsense reasoning. In particular, we show that a restricted form of the principle of arrogance yields results that are equivalent to EMAT [Morgenstern, 1989], a non-monotonic logic which was designed to reason about temporal projection in epistemic contexts.