Generalizing the Dempster-Shafer rule of combination to Boolean algebras

Abstract

The Dempster-Shafer (D-S) theory of evidence is a significant generalization of classical Bayesian statistics which has been found to be promising for a variety of inexact reasoning applications. A number of substantial advances in the theory have been made, but no previous attempts have been made to generalize the theory to problem spaces which are not just the power sets of finite sets, which the original D-S theory addresses, but any kind of Boolean algebras. Included in this are spaces which are composed of propositions, and spaces which can be infinite. The authors generalize the theory by reworking some of the conventional D-S theorems and establish the relationships between 'weaker' forms of the familiar evidential functions. Although these relationships are not so strong as for finite sets, they show how they collapse to those stronger relations. Of particular interest is the orthogonal sum operation, and the authors generalize it so that it applies to any Boolean algebra. The potential advantages of this generalization in evidential reasoning application is discussed with the aid of a case study involving the 'Hominids of Turkana' (A. Walker, R.E.F. Leakey, 1978).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>