Logic & Philosophy of Science

Though mutual belief and reasoning about the beliefs of others have achieved a great deal of attention over the last fifteen years, I would contend that there is as yet no very good theory of the reasoning that goes into modeling the beliefs of other agents, or more generally their attitudes (their beliefs, desires, presuppositions, intentions, etc.), and that the reason for the problem is an inadequate model of single-agent attitudes.

This paper takes its departure from the idea that we model others' beliefs by imagining what we would believe if we were in their shoes. This requires, first, that we impose a much richer structure on our own beliefs than is usually imagined in formalizations of belief, a structure involving multiple modalities, indexed by the conditions under which the belief was acquired. With such an organization of belief, we can (by default) attribute a belief to another agent if the belief has an index that applies to that agent.

I develop a formalization of these ideas, called Intra-Agent Modal Logic, and show how to extend it to an Inter-Agent Modal Logic in which reasoning about others' beliefs can be formalized. I indicate how to formalize specific examples in this logic, and discuss the solution it offers to the problem of acquiring mutual beliefs.