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15
Propositional information system
, 1996
"... Resolution is an often used method for deduction in propositional logic. Here a proper organization of deduction is proposed which avoids redundant computations. It is based on a generic framework of decompositions and local computations as introduced by Shenoy, Shafer [29]. The system contains the ..."
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Cited by 30 (15 self)
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Resolution is an often used method for deduction in propositional logic. Here a proper organization of deduction is proposed which avoids redundant computations. It is based on a generic framework of decompositions and local computations as introduced by Shenoy, Shafer [29]. The system contains the two basic operations with information, namely marginalization (or projection) and combination; the latter being an idempotent operation in the present case. The theory permits the conception of an architecture of distributed computing. As an important application assumptionbased reasoning is discussed. 1
Modelbased diagnostics and probabilistic assumptionbased reasoning
 Artificial Intelligence
, 1998
"... The mathematical foundations of modelbased diagnostics or diagnosis from first principles have been laid by Reiter [31]. In this paper we extend Reiter’s ideas of modelbased diagnostics by introducing probabilities into Reiter’s framework. This is done in a mathematically sound and precise way whi ..."
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Cited by 23 (17 self)
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The mathematical foundations of modelbased diagnostics or diagnosis from first principles have been laid by Reiter [31]. In this paper we extend Reiter’s ideas of modelbased diagnostics by introducing probabilities into Reiter’s framework. This is done in a mathematically sound and precise way which allows one to compute the posterior probability that a certain component is not working correctly given some observations of the system. A straightforward computation of these probabilities is not efficient and in this paper we propose a new method to solve this problem. Our method is logicbased and borrows ideas from assumptionbased reasoning and ATMS. We show how it is possible to determine arguments in favor of the hypothesis that a certain group of components is not working correctly. These arguments represent the symbolic or qualitative aspect of the diagnosis process. Then they are used to derive a quantitative or numerical aspect represented by the posterior probabilities. Using two new theorems about the relation between Reiter’s notion of conflict and our notion of argument, we prove that our socalled degree of support is nothing but the posterior probability that we are looking for. Furthermore, a model where each component may have more than two different operating modes is discussed and a new algorithm to compute posterior probabilities in this case is presented. Key words: Modelbased diagnostics; Assumptionbased reasoning; ATMS;
Modeling Uncertainty with Propositional AssumptionBased Systems
 Applications of Uncertainty Formalisms, Lecture Notes in Artifical Intelligence 1455
, 1998
"... Abstract. This paper proposes assumptionbased systems as an efficient and convenient way to encode uncertain information. Assumptionbased systems are obtained from propositional logic by including a special type of propositional symbol called assumption. Assumptions are needed to express the uncert ..."
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Cited by 14 (6 self)
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Abstract. This paper proposes assumptionbased systems as an efficient and convenient way to encode uncertain information. Assumptionbased systems are obtained from propositional logic by including a special type of propositional symbol called assumption. Assumptions are needed to express the uncertainty of the given information. Assumptionbased systems can be used to judge hypotheses qualitatively or quantitatively. This paper shows how assumptionbased systems are obtained from causal networks, it describes how symbolic arguments for hypotheses can be computed efficiently, and it presents ABEL, a modeling language for assumptionbased systems and an interactive tool for probabilistic assumptionbased reasoning. 1
Assumptionbased modeling using ABEL
 First International Joint Conference on Qualitative and Quantitative Practical Reasoning; ECSQARU–FAPR’97. Lecture Notes in Artif. Intell
, 1997
"... Abstract. Today, different formalisms exist to solve reasoning problems under uncertainty. For most of the known formalisms, corresponding computer implementations are available. The problem is that each of the existing systems has its own user interface and an individual language to model the knowl ..."
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Cited by 11 (8 self)
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Abstract. Today, different formalisms exist to solve reasoning problems under uncertainty. For most of the known formalisms, corresponding computer implementations are available. The problem is that each of the existing systems has its own user interface and an individual language to model the knowledge and the queries. This paper proposes ABEL, a new andgeneral language to express uncertain knowledge and corresponding queries. Examples from different domains show that ABEL is powerful and general enough to be used as common modeling language for the existing software systems. A prototype of ABEL is implementedin Evidenzia, a system restrictedto models based on propositional logic. A general ABEL solver is actually being implemented. 1
Reasoning with finite set constraints
 In Proc. Int. Conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems
, 1998
"... The language of propositional logic is sometimes not appropriate to model realworld problems. Therefore, finite set constraints are introduced. A variable of a finite set constraint takes exactly one value out of a given set of values whereas a propositional variable is either true or false. Althou ..."
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Cited by 9 (8 self)
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The language of propositional logic is sometimes not appropriate to model realworld problems. Therefore, finite set constraints are introduced. A variable of a finite set constraint takes exactly one value out of a given set of values whereas a propositional variable is either true or false. Although the class of realworld problems which can be described using the language of propositional logic is not enlarged, the language of finite set constraints often allows a shorter and more structured description. This additional structure can be exploited when methods of propositional logic are generalized to finite set constraint logic. Here the variable elimination method and the original algorithm of Abraham to calculate disjoint terms for formulas are generalized. Acknowledgments We wish to thank Prof. J. Kohlas for his helpful corrections and comments
a new language for assumptionbased evidential reasoning under uncertainty
, 1997
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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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Cited by 2 (1 self)
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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.
An algebraic study of argumentation systems and evidence theory
, 1995
"... Argumentation systems permit to nd arguments in favour and against hypotheses. And these hypotheses can be accepted as true or must be refuted as false according to whether the arguments supporting or refuting them are considered to be valid. Possibly the likelihood of arguments can be measured by p ..."
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Cited by 2 (1 self)
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Argumentation systems permit to nd arguments in favour and against hypotheses. And these hypotheses can be accepted as true or must be refuted as false according to whether the arguments supporting or refuting them are considered to be valid. Possibly the likelihood of arguments can be measured by probabilities. Then argumentation systems permit to de ne numerical degrees of support of hypotheses as the probability that arguments supporting the hypotheses are true. Similarly, numerical degrees of plausibility ofhypotheses can be de ned as the probability that arguments refuting the hypotheses do not hold. These probabilistic argumentation systems lead then to a DempsterShafer theory of evidence. In this paper rst an algebraic theory of argumentation systems is developped based on general logical consequence relations and the notion of an allocation of support. In particular a computational theory for argumentation systems using local computations on hypertrees is studied on the fundaments of Shafer's paper \An axiomatic study of computations in hypertrees&quot;. This is then extended to probabilistic argumentation
Assumptionbased reasoning with algebraic clauses
 EUFIT’97, 5th European Congress on Intelligent Techniques and Soft Computing
, 1997
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