All They Know: A Study in Multi-Agent Autoepistemic Reasoning

Abstract

With few exceptions the study of nonmonotonic reasoning has been confined to the single-agent case. However, it has been recognized that intelligent agents often need to reason about other agents and their ability to reason nonmonotonically. In this paper we present a formalization of multi-agent autoepistemic reasoning, which naturally extends earlier work by Levesque. In particular, we propose an n-agent modal belief logic, which allows us to express that a formula (or finite set of them) is all an agent knows, which may include beliefs about what other agents believe. The paper presents a formal semantics of the logic in the possible-world framework. We provide an axiomatization, which is complete for a large fragment of the logic and sufficient to characterize interesting forms of multi-agent autoepistemic reasoning. We also extend the stable set and stable expansion ideas of single-agent autoepistemic logic to the multi-agent case.