Belief as Defeasible Knowledge

Abstract

We investigate the relation between the notions of knowledge and belief. Contrary to the well-known slogan about knowledge being “justified, true belief”, we propose that belief be viewed as defeasible knowledge. We offer several related definitions of belief as knowledge-relative-to-assumptions, and provide complete axiomatic systems for the resulting notions of belief. We also show a close tie between our definitions and the literature on nonmonotonic reasoning. Our definitions of belief have several advantages. First, they are short. Second, we do not need to add anything to the logic of knowledge: the “right” properties of belief fall out of our definitions and the properties of knowledge. Third, the connection between knowledge and belief is derived from one fundamental principle. Finally, a major attraction of logics of knowledge in computer science has been the concrete grounding of the mental notion in objective phenomena; by reducing belief to knowledge we obtain this grounding for a notion of belief.