The logical and probabilistic bases of the calculus of evidence

Abstract

Summary form only given. The approach proposed by R. Carnap (1962) to the development of logical bases for probability theory is applied to structures based on epistemic logic. The resulting structure, called the epistemic universe, consists of joint descriptions of possible states of the world as well as of the states of knowledge rational agents have regarding it. Special algebras of subsets of the epistemic universe are then defined. Probabilities defined over one of these classes, called the epistemic algebra (representing similar states of knowledge), are directly related to the basic functional structures of the Dempster-Shafer calculus of evidence: belief and mass assignment functions. Extensions of these probability functions to the truth algebra (representing true states of real world), must satisfy the well-known bounds of the Dempster-Shafer theory. Furthermore, these bounds are the best possible. Consideration of multiple agents leads both to more complex epistemic structures and to the derivation of a basic formula for the combination of knowledge, called the additive combination formula. From this formula and certain independence assumptions, Dempster's rule of combination is readily derived.<>