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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...
The Computational Complexity of Abduction
, 1991
"... The problem of abduction can be characterized as finding the best explanation of a set of data. In this paper we focus on one type of abduction in which the best explanation is the most plausible combination of hypotheses that explains all the data. We then present several computational complexity r ..."
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Cited by 108 (3 self)
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The problem of abduction can be characterized as finding the best explanation of a set of data. In this paper we focus on one type of abduction in which the best explanation is the most plausible combination of hypotheses that explains all the data. We then present several computational complexity results demonstrating that this type of abduction is intractable (NPhard) in general. In particular, choosing between incompatible hypotheses, reasoning about cancellation effects among hypotheses, and satisfying the maximum plausibility requirement are major factors leading to intractability. We also identify a tractable, but restricted, class of abduction problems. Thanks to B. Chandrasekaran, Ashok Goel, Jack Smith, and Jon Sticklen for their comments on the numerous versions of this paper. The referees have also made a substantial contribution. Any remaining errors are our responsibility, of course. This research has been supported in part by the National Library of Medicine, grant LM...
Representing Knowledge for Logicbased Diagnosis
, 1988
"... If one wants to use logic to build a diagnostic system, then it is not a matter of "just axiomatising" the domain; we have to understand how to use logic for diagnosis. We need some models of what diagnosis is, in order to be able to implement diagnostic systems. This paper considers 3 different "lo ..."
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Cited by 51 (10 self)
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If one wants to use logic to build a diagnostic system, then it is not a matter of "just axiomatising" the domain; we have to understand how to use logic for diagnosis. We need some models of what diagnosis is, in order to be able to implement diagnostic systems. This paper considers 3 different "logical " definitions of diagnosis. Each of these are presented in a uniform framework of hypothetical reasoning where the user provides the possible hypotheses. These are compared as to the sort of knowledge that we need to provide them, and in their expressibilty. It seems as though there is no one framework which can claim to be the logical definition of diagnosis. Each of these approaches has been implemented in the Theorist system, and used on a number of domains. This paper concentrates on the case where we have fault models. 1 Introduction Diagnosis is a problem of trying to find what is wrong with some system based on knowledge about the design /structure of the system, possible malf...
A theory of diagnosis for incomplete causal models
 In Proc. 11th IJCAI
, 1989
"... One of the problems of the recent approaches to problem solving based on deep knowledge is the lack of a formal treatment of incomplete knowledge. However, dealing with incomplete models is fundamental to many realworld domains. In this paper we propose a formal theory of causal diagnostic reasoning ..."
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Cited by 46 (4 self)
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One of the problems of the recent approaches to problem solving based on deep knowledge is the lack of a formal treatment of incomplete knowledge. However, dealing with incomplete models is fundamental to many realworld domains. In this paper we propose a formal theory of causal diagnostic reasoning, dealing with different forms of incompleteness both in the general causal knowledge (missing or abstracted knowledge) and in the data describing a specific case under examination. Different forms of nonmonotonic reasoning (hypothetical and circumscriptive reasoning) are used in order to draw and confirm conclusions from incomplete knowledge. Multiple fault solutions are treated in a natural way and parsimony criteria arc used to rank alternative solutions. 1.
Inference in Bayesian Networks
, 1999
"... A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduce ..."
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Cited by 31 (0 self)
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A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduces major current methods for exact computation, briefly surveys approximation methods, and closes with a brief discussion of open issues.
Partial abductive inference in Bayesian belief networks using a genetic algorithm
 Pattern Recognit. Lett
, 1999
"... Abstract—Abductive inference in Bayesian belief networks (BBNs) is intended as the process of generating the most probable configurations given observed evidence. When we are interested only in a subset of the network’s variables, this problem is called partial abductive inference. Both problems are ..."
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Cited by 24 (2 self)
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Abstract—Abductive inference in Bayesian belief networks (BBNs) is intended as the process of generating the most probable configurations given observed evidence. When we are interested only in a subset of the network’s variables, this problem is called partial abductive inference. Both problems are NPhard and so exact computation is not always possible. In this paper, a genetic algorithm is used to perform partial abductive inference in BBNs. The main contribution is the introduction of new genetic operators designed specifically for this problem. By using these genetic operators, we try to take advantage of the calculations previously carried out, when a new individual is evaluated. The algorithm is tested using a widely used Bayesian network and a randomly generated one and then compared with a previous genetic algorithm based on classical genetic operators. From the experimental results, we conclude that the new genetic operators preserve the accuracy of the previous algorithm, and also reduce the number of operations performed during the evaluation of individuals. The performance of the genetic algorithm is, thus, improved. Index Terms—Abductive inference, bayesian belief networks, evolutionary computation, genetic operators, most probable explanation, probabilistic reasoning. I.
Representing diagnostic knowledge for probabilistic horn abduction
 Readings in modelbased diagnosis
, 1992
"... This paper presents a simple logical framework for abduction, with probabilities associated with hypotheses. The language is an extension to pure Prolog, and it has straightforward implementations using branch and bound search with either logicprogramming technology or ATMS technology. The main fo ..."
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Cited by 20 (6 self)
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This paper presents a simple logical framework for abduction, with probabilities associated with hypotheses. The language is an extension to pure Prolog, and it has straightforward implementations using branch and bound search with either logicprogramming technology or ATMS technology. The main focus of this paper is arguing for a form of representational adequacy of this very simple system for diagnostic reasoning. It is shown how it can represent modelbased knowledge, with and without faults, and with and without nonintermittency assumptions. It is also shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. 1
Graphical Explanation in Belief Networks
 In Journal of Computational and Graphical Statistics
, 1997
"... Belief networks provide an important bridge between statistical modeling and expert systems. In this paper we present methods for visualizing probabilistic "evidence flows" in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in ..."
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Cited by 15 (4 self)
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Belief networks provide an important bridge between statistical modeling and expert systems. In this paper we present methods for visualizing probabilistic "evidence flows" in belief networks, thereby enabling belief networks to explain their behavior. Building on earlier research on explanation in expert systems, we present a hierarchy of explanations, ranging from simple colorings to detailed displays. Our approach complements parallel work on textual explanations in belief networks. GRAPHICALBELIEF, Mathsoft Inc.'s belief network software, implements the methods. 1 Introduction A fundamental reason for building a mathematical or statistical model is to foster deeper understanding of complex, realworld systems. Consequently, explanationsdescriptions of the mechanisms which comprise such modelsform an important part of model validation, exploration, and use. Early tests of rulebased expert system models indicated the critical need for detailed explanations in that setting (...
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