Allocation of Arguments and Evidence Theory

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 de ned 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 in nite 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 nite frames