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25
Probabilistic Horn abduction and Bayesian networks
 Artificial Intelligence
, 1993
"... This paper presents a simple framework for Hornclause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete Bayesia ..."
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Cited by 298 (37 self)
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This paper presents a simple framework for Hornclause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete Bayesian belief network can be represented in this framework. The main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning. This provides a useful representation language in its own right, providing a compromise between heuristic and epistemic adequacy. It also shows how Bayesian networks can be extended beyond a propositional language. This paper also shows how a language with only (unconditionally) independent hypotheses can represent any probabilistic knowledge, and argues that it is better to invent new hypotheses to explain dependence rather than having to worry about dependence in the language. Scholar, Canadian Institute for Advanced...
Probabilistic argumentation systems
 Handbook of Defeasible Reasoning and Uncertainty Management Systems, Volume 5: Algorithms for Uncertainty and Defeasible Reasoning
, 2000
"... Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [42]. More general approaches are the DempsterShafer theory of evidence [51], and possibility theory [16], which is closely re ..."
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Cited by 53 (33 self)
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Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [42]. More general approaches are the DempsterShafer theory of evidence [51], and possibility theory [16], which is closely related to fuzzy systems.
Current Approaches to Handling Imperfect Information in Data and Knowledge Bases
, 1996
"... This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering ..."
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Cited by 52 (1 self)
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This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.
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 29 (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 22 (16 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;
A Review of Uncertainty Handling Formalisms
, 1998
"... Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one ..."
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Cited by 21 (1 self)
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Many different formal techniques, both numerical and symbolic, have been developed over the past two decades for dealing with incomplete and uncertain information. In this paper we review some of the most important of these formalisms, describing how they work, and in what ways they differ from one another. We also consider heterogeneous approaches which incorporate two or more approximate reasoning mechanisms within a single reasoning system. These have been proposed to address limitations in the use of individual formalisms.
Costbounded argumentation
 International Journal of Approximate Reasoning
"... The purpose of this paper is to present new computational techniques for probabilistic argumentation systems. It shows that instead of computing intractable large sets of arguments, it is also possible to find good approximations of the exact solutions in reasonable time. The technique presented is ..."
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Cited by 20 (13 self)
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The purpose of this paper is to present new computational techniques for probabilistic argumentation systems. It shows that instead of computing intractable large sets of arguments, it is also possible to find good approximations of the exact solutions in reasonable time. The technique presented is based on cost functions, which are used to measure the relevance of arguments.
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 ..."
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Cited by 15 (5 self)
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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.
Representing Bayesian networks within probabilistic Horn abduction
 In Proc. Seventh Conf. on Uncertainty in Artificial Intelligence
, 1991
"... This paper presents a simple framework for Hornclause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions are in finding a relationship between logic ..."
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Cited by 13 (4 self)
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This paper presents a simple framework for Hornclause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The main contributions are in finding a relationship between logical and probabilistic notions of evidential reasoning. This can be used as a basis for a new way to implement Bayesian Networks that allows for approximations to the value of the posterior probabilities, and also points to a way that Bayesian networks can be extended beyond a propositional language. 1
Belief Maintenance with Probabilistic Logic
 In Proceedings of the AAAI Fall Symposium on Automated Deduction in Non Standard Logics
, 1993
"... Belief maintenance systems are natural extensions of truth maintenance systems that use probabilities rather than boolean truthvalues. This paper introduces a general method for belief maintenance, based on (the propositional fragment of) probabilistic logic, that extends the Boolean Constraint Pro ..."
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Cited by 13 (9 self)
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Belief maintenance systems are natural extensions of truth maintenance systems that use probabilities rather than boolean truthvalues. This paper introduces a general method for belief maintenance, based on (the propositional fragment of) probabilistic logic, that extends the Boolean Constraint Propagation method used by the logicbased truth maintenance systems. From the concept of probabilistic entailment, we derive a set of constraints on the (probabilistic) truthvalues of propositions and we prove their soundness. These constraints are complete with respect to a welldefined set of clauses, and their partial incompleteness is compensated by a gain in computational efficiency. 1 Introduction Truth maintenance systems (tmss) are independent reasoning modules which incrementally maintain the beliefs of a general problem solving system, enabling it to reason with temporary assumptions in the growth of incomplete information. The concept of truth maintenance system is due to Doyle ...