A model-theoretic analysis of knowledge: Preliminary report

Abstract

Understanding knowledge is a fundamental issue in many disciplines. In computer science, knowledge arises not only in the obvious contexts (such as knowledge-based systems), but also in distributed systems (where the goal is to have each processor "know"something, as in Byzantine agreement). A general semantic model of knowledge is introduced, to allow reasoning about statements such as "He knows that I know whether or not she knows whether or not it is raining."This approach more naturally models a state of knowledge than previous proposals (including Kripke structures). Using this notion of model, a model theory for knowledge is developed. This theory enables one to interpret such notions as a "finite amount of information"and "common knowledge"in different contexts.