Logical omniscience, semantics, and models of belief

Abstract

Logical omniscience may be described (roughly) as the state of affairs in which an agent explicitly believes anything which is logically entailed by that agent's beliefs. It is widely agreed that humans are not logically omniscient, and that an adequate formal model of belief, coupled with a correct semantic theory, would not entail logical omniscience. Recently, two prominent models of belief have emerged which purport both to avoid logical omniscience and to provide an intuitively appealing semantics. The first of these models is due to Levesque (1984b); the second to Fagin and Halpem (1985). It is argued herein that each of these models faces serious difficulties. Detailed criticisms are presented for each model, and a computationally oriented theory of intensions is presented which provides the foundation for a new formal model of belief. This formal model is presented in a decidable subset of first‐order logic and is shown to provide a solution to the general problem of logical omniscience. The model provides for the possibility of belief revision and places no a priori restrictions upon an agent's representation language.