All They Know About

We address the issue of agents reasoning about other agents’ nonmonotonic reasoning ability in the framework of a multi-agent autoepistemic logic (AEL). I n single-agent AEL, nonmonotonic inferences are drawn based on all the agent knows. In a multi-agent context such as Jill reasoning about Jack’s nonmonotonic inferences, this assumption must be abandoned since it cannot be assumed that Jill knows everything Jack knows. Given a specific subject matter like Tweety the bird, it is more realistic and sufficient if Jill only assumes to know all Jack knows about Tweety in order to arrive at Jack’s nonmonotonic inferences about Tweety. This paper provides a formalization of all an agent knows about a certain subject mutter based on possible-world semantics in a multi-agent AEL. Besides discussing various properties of the new notion, we use it to characterize formulas that are about a subject matter in a very strong sense. While our main focus is on subject matters that consist of atomic propositions, we also address the case where agents are the subject matter.