EVIDENCE THEORY BASED ON GENERAL CONSEQUENCE RELATIONS

Abstract

The Dempster-Shafer theory of evidence can be conceived as a theory of probability of provability. In fact, it has been shown that evidence theory can be developed on the basis of assumption-based reasoning. Taking this approach, reasoning is modeled in this paper by a consequence relation in the sense of Tarski. It is shown that it is possible to construct evidence theory on top of the very general logics defined by these consequence relations. Support functions can be derived which are, as usual, set functions, monotone of infinite order. Furthermore, plausibility functions can also be defined. However, as negation need not be defined in these general logics, the usual duality relations between support and plausibility functions of Dempster-Shafer theory do not hold in general. Nonetheless, this symmetry can be installed progressively by considering logics that enjoy more and more “structural properties”.