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Probabilistic AssumptionBased Reasoning
 PROC. 9TH CONF. ON UNCERTAINTY IN ARTIFICIAL INTELLIGENCE
, 1993
"... In this paper the classical propositional assumptionbased model is extended to incorporate probabilities for the assumptions. Then the whole model is placed into the framework of the DempsterShafer theory of evidence. Laskey, Lehner [1] and Provan [2] have already proposed a similar point of view ..."
Abstract

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In this paper the classical propositional assumptionbased model is extended to incorporate probabilities for the assumptions. Then the whole model is placed into the framework of the DempsterShafer theory of evidence. Laskey, Lehner [1] and Provan [2] have already proposed a similar point of view but these papers do not emphasize the mathematical foundations of the probabilistic assumptionbased reasoning paradigm. These foundations are thoroughly exposed in the rst part of this paper. Then we address the computational problems related to the assumptionbased model. The idea is to translate evidence theory problems into propositional logic problems and then use the powerful techniques of logic to solve them. In particular, advanced consequence nding algorithms developed by Inoue [3] and Siegel [4] will be used. These logicbased techniques can be considered as alternatives to the classical method of local propagation in Markov trees. Finally, we switch back from logic to the theory of evidence in order to compute degrees of support of hypotheses. We show that some recently proposed methods for computing simple disjunctive normal forms can be used to compute these degrees of support.
Theory of evidence  a survey of its mathematical foundations, applications and computational aspects
 ZOR MATHEMATICAL METHODS OF OPERATIONS RESEARCH
, 1994
"... The mathematical theory of evidence has been introduced by Glenn Shafer in 1976 as a new approach to the representation of uncertainty. This theory can be represented under several distinct but more or less equivalent forms. Probabilistic interpretations of evidence theory have their roots in Arthur ..."
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The mathematical theory of evidence has been introduced by Glenn Shafer in 1976 as a new approach to the representation of uncertainty. This theory can be represented under several distinct but more or less equivalent forms. Probabilistic interpretations of evidence theory have their roots in Arthur Dempster's multivalued mappings of probability spaces. This leads to random set and more generally to random lter models of evidence. In this probabilistic view evidence is seen as more or less probable arguments for certain hypotheses and they can be used to support those hypotheses to certain degrees. These degrees of support are in fact the reliabilities with which the hypotheses can be derived from the evidence. Alternatively, the mathematical theory of evidence can be founded axiomatically on the notion of belief functions or on the allocation of belief masses to subsets of a frame of discernment. These approaches aim to present evidence theory as an extension of probability theory. Evidence theory has been used to represent uncertainty in expert systems, especially in the domain of diagnostics. It can be applied to decision analysis and it gives a new perspective for statistical analysis. Among its further applications are image processing, project planing and scheduling and risk analysis. The computational problems of evidence theory
ALLOCATION OF ARGUMENTS AND EVIDENCE THEORY
, 1996
"... The DempsterShafer 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 ..."
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The DempsterShafer 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 assumptionbased 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 DempsterShafer 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.