Non-Omniscient Belief as Context-Based Reasoning

This paper describes a general framework for the formalization of monotonic reasoning about belief in a multiagent environment. The agents* beliefs are modeled as logical theories. The reasoning about their beliefs is formalized in still another theory, which we call the theory of the computer. The framework is used to model non-omniscient belief and shown to have many advantages. For instance, it allows for an exhaustive classification of the "basic " forms of non logical omniscience and for their "composition" into the structure of the system modeling multiagent omniscient belief. 1 The approach This paper describes a general framework for the formalization of monotonic reasoning about belief in a multiagent environment. The most common solution is to take a first order (propositional) theory, to extend it using a set of modal operators, and to take as meaning that an agent believes A (see for instance [Halpern and Moses, 1985]). There is only one theory of the world, however this theory proves facts about the agents ' beliefs. According to a first interpretation, this theory is taken to model things how they really are. It is therefore a finite (and possibly incomplete) presentation of what is true in the world, and the fact that B i A is a theorem means that it is, in fact, the case that a i believes A. According to another interpretation, this theory is taken to be the perspective that a generic reasoner has of the world. It is therefore a finite presentation of the reasoner's beliefs, and the fact that A is a theorem means that the reasoner believes that believes A. Once one accepts the second interpretation (as we do), a mechanized theory is naturally taken as representing the beliefs of the computer where it is implemented. Moreover, in the case of multiagent belief, a further step is to have, together with the theory of the computer, one theory (at least, see later) for each agent