Allocation of arguments and evidence theory

Abstract

The Dempster-Shafer theory of evidence is developed here in a very general setting. First, its symbolic or algebraic part is discussed as a body of arguments which contains an allocation of support and an allowment of possibility for each hypothesis. It is shown how such bodies of arguments arise in the theory of hints and in assumption-based reasoning in logic. A rule of combination of bodies of arguments is then defined which constitutes the symbolic counterpart of Dempster's rule. Bodies of evidence are next introduced by assigning probabilities to arguments. This leads to support and plausibility functions on some measurable hypotheses. As expected in Dempster-Shafer theory, they are shown to be set functions, monotone or alternating of infinite order, respectively. It is shown how these support and plausibility functions can be extended to all hypotheses. This constitutes then the numerical part of evidence theory. Finally, combination of evidence based on the combination of bodies of arguments is discussed and a generalized version of Dempster's rule is derived. The approach to evidence theory proposed is general and is not limited to finite frames.