A FRAMEWORK FOR LOGICS OF EXPLICIT BELIEF

The epistemic notions of knowledge and belief have most commonly been modeled by means of possible worlds semantics. In such approaches an a gent knows (or believes) all logical consequences of its beliefs. Cons equently, several approaches have been proposed to model systems of ex plicit belief, more suited to modeling finite agents or computers. In this paper a general framework is developed for the specification of l ogics of explicit belief. A generalization of possible worlds, called situations, is adopted. However the notion of an accessibility relatio n is not employed; instead a sentence is believed if the explicit prop osition expressed by the sentence appears among a set of propositions associated with an agent at a situation. Since explicit propositions m ay be taken as corresponding to ''belief contexts'' or ''frames of min d'' the framework also provides a setting for investigating such appro aches to belief, The approach provides a uniform and flexible basis fr om which various issues of explicit belief may be addressed and from w hich systems may be contrasted and compared. A family of logics is dev eloped using this framework, which extends previous approaches and add resses issues raised by these earlier approaches. The more interesting of these logics are tractable, in that determining if a belief follow s from a set of beliefs, given certain assumptions, can be accomplishe d in polynomial time.