Ideal and real belief about belief: some intuitions

It is widely recognized that intelligent and autonomous agents operating in a distributed environment must be able to reason about their own and other agents' beliefs. Standard possible world semantics, usually used for such an endeavor, lead to formalization in which agents suffer the "logical omniscience problem" -- they believe all valid formulas and all the logical consequences of their own beliefs. As far as we know, no taxonomic analysis exists which describes all the possible ways in which this phenomenon can or can not arise. The goal of this paper is to fill this gap. Our approach is based on the idea of first providing a set-theoretic specification of agents' beliefs, and then to define constructors for such sets. This allows us first to provide a set of constructors modeling ideal believers, and then to analyze how such constructors can be modified to generate real believers. The constructors defined turn out to be inference rules inside a multicontext system.