Belief, Awareness, and Limited Reasoning: Preliminary Report

Abstract

Several new logics for belief and knowledge are introduced and studied, all of which have the property that agents are not logically omniscient. In particular, in these logics, the set of beliefs of an agent does not necessarily contain all valid formulas. Thus, these logics are more suitable than traditional logics for modelling beliefs of humans (or machines) with limited reasoning capabilities. Our first logic is essentially an extension of Levesque's logic of implicit and explicit belief, where we extend to allow multiple agents and higher-level belief (i.e., beliefs about beliefs). Our second logic deals explicitly with "awareness", where, roughly speaking, it is necessary to be aware of a concept before one can have beliefs about it. Our third logic gives a model of "local reasoning", where an agent is viewed as a "society of minds", each with its own cluster of beliefs, which may contradict each other.