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27
The Complexity of LogicBased Abduction
, 1993
"... Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minima ..."
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Cited by 162 (26 self)
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Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logicbased abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.
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 109 (4 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...
On the Role of Coherence in Abductive Explanation
 AAAI90
"... Abduction is an important inference process underlying much of human intelligent activities, including text understanding, plan recognition, disease diagnosis, and physical device diagnosis. In this paper, we describe some problems encountered using abduction to understand text, and present some sol ..."
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Cited by 46 (6 self)
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Abduction is an important inference process underlying much of human intelligent activities, including text understanding, plan recognition, disease diagnosis, and physical device diagnosis. In this paper, we describe some problems encountered using abduction to understand text, and present some solutions to overcome these problems. The solutions we propose center around the use of a different criterion, called explanatory coherence, as the primary measure to evaluate the quality of an explanation. In addition, explanatory coherence plays an important role in the construction of explanations, both in determining the appropriate level of specificity of a preferred explanation, and in guiding the heuristic search to efficiently compute explanations of sufficiently high quality.
Diagnosis and Debugging as Contradiction Removal
 PROCEEDINGS OF THE 2ND INTERNATIONAL WORKSHOP ON LOGIC PROGRAMMING AND NONMONOTONIC REASONING
, 1993
"... ..."
Horn Approximations of Empirical Data
 Artificial Intelligence
, 1995
"... Formal AI systems traditionally represent knowledge using logical formulas. Sometimes, however, a modelbased representation is more compact and enables faster reasoning than the corresponding formulabased representation. The central idea behind our work is to represent a large set of models by a s ..."
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Cited by 33 (2 self)
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Formal AI systems traditionally represent knowledge using logical formulas. Sometimes, however, a modelbased representation is more compact and enables faster reasoning than the corresponding formulabased representation. The central idea behind our work is to represent a large set of models by a subset of characteristic models. More specifically, we examine modelbased representations of Horn theories, and show that there are large Horn theories that can be exactly represented by an exponentially smaller set of characteristic models. We show that deduction based on a set of characteristic models requires only polynomial time, as it does using Horn theories. More surprisingly, abduction can be performed in polynomial time using a set of characteristic models, whereas abduction using Horn theories is NPcomplete. Finally, we discuss algorithms for generating efficient representations of the Horn theory that best approximates a general set of models. 1 Introduction Logical formulas are...
On Tests for Hypothetical Reasoning
 Readings in ModelBased Diagnosis
, 1992
"... Suppose that HY P is a set of hypotheses which we currently entertain about some state of affairs represented by a propositional sentence \Sigma. In a diagnostic setting, HY P might consist of all the diagnoses of some device whose description is given by \Sigma, although our analysis is not restric ..."
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Cited by 24 (4 self)
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Suppose that HY P is a set of hypotheses which we currently entertain about some state of affairs represented by a propositional sentence \Sigma. In a diagnostic setting, HY P might consist of all the diagnoses of some device whose description is given by \Sigma, although our analysis is not restricted to diagnosis. Our concern is with tests  how they can be designed, and what conclusions can be drawn about the hypotheses in HY P as a result of performing tests. Specifically, we define the concept of a test and the concept of the outcome of a test. We characterize those tests whose outcomes refute or confirm an hypothesis, and discriminate between competing hypotheses. These characterizations are in terms of the prime implicates of \Sigma, and hence are implementable using assumptionbased truth maintenance systems. In addition, we characterize the impact of a test outcome on consistencybased and abductive hypothesis spaces. Finally, we provide a characterization of differential dia...
A complete classification of the complexity of propositional abduction
 SIAM Journal on Computing
, 2006
"... Abstract. Abduction is the process of explaining a given query with respect to some background knowledge. For instance, p is an explanation for the query q given the knowledge p → q. This problem is wellknown to have many applications, in particular in Artificial Intelligence, and has been widely s ..."
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Cited by 19 (4 self)
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Abstract. Abduction is the process of explaining a given query with respect to some background knowledge. For instance, p is an explanation for the query q given the knowledge p → q. This problem is wellknown to have many applications, in particular in Artificial Intelligence, and has been widely studied from both an AI and a complexitytheoretic point of view. In this paper we completely classify the complexity of propositional abduction in Schaefer’s famous framework. We consider the case where knowledge bases are taken from a class of formulas in generalized conjunctive normal form. This means that the propositional formulas considered are conjunctions of constraints taken from a fixed finite language. We show that according to the properties of this language, deciding whether at least one explanation exists is either polynomial, NPcomplete or ΣP 2complete. Our results are stated for a query consisting of a single, positive literal and for assumptionbased solutions, i.e., the solutions must be formed upon a distinguished subset of the variables that is part of the input. We however show that our results can be interpreted “dually ” for negative queries, and thus also for unrestricted (positive or negative) queries.
Controlling the Complexity in ModelBased Diagnosis
 Annals of Mathematics and Artificial Intelligence
, 1993
"... We present IDA  an Incremental Diagnostic Algorithm which computes minimal diagnoses from diagnoses, and not from conflicts. As a consequence of this, and by using different models, one can control the computational complexity. In particular, we show that by using a model of the normal behavior, ..."
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Cited by 12 (3 self)
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We present IDA  an Incremental Diagnostic Algorithm which computes minimal diagnoses from diagnoses, and not from conflicts. As a consequence of this, and by using different models, one can control the computational complexity. In particular, we show that by using a model of the normal behavior, the worstcase complexity of the algorithm to compute the k + 1st minimal diagnosis is O(n 2k ), where n is the number of components. On the practical side, an experimental evaluation indicates that the algorithm can efficiently diagnose devices consisting of a few thousand components. We propose to use a hierarchy of models: first a structural model to compute all minimal diagnoses, then a normal behavior model to find the additional diagnoses if needed, and only then a fault model for their verification. IDA separates model interpretation from the search for minimal diagnoses in the sense that the model interpreter is replaceable. In particular, we show that in some domains it is advan...
New Polynomial Classes for LogicBased Abduction
, 2003
"... We address the problem of propositional logicbased abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based on the notion of projection; then we study restrictions ..."
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Cited by 9 (5 self)
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We address the problem of propositional logicbased abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based on the notion of projection; then we study restrictions over the representations of the knowledge base and of the query, and find new polynomial classes of abduction problems. We also show that our algorithm unifies several previous results.
Complexity of abduction in the el family of lightweight description logics
 in KR, G. Brewka and J. Lang, Eds. AAAI Press
"... The complexity of logicbased abduction has been extensively studied for the case in which the background knowledge is represented by a propositional theory, but very little is known about abduction with respect to description logic knowledge bases. The purpose of the current paper is to examine the ..."
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Cited by 8 (0 self)
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The complexity of logicbased abduction has been extensively studied for the case in which the background knowledge is represented by a propositional theory, but very little is known about abduction with respect to description logic knowledge bases. The purpose of the current paper is to examine the complexity of logicbased abduction for the EL family of lightweight description logics. We consider several minimality criteria for explanations (set inclusion, cardinality, prioritization, and weight) and three decision problems: deciding whether an explanation exists, deciding whether a given hypothesis appears in some acceptable explanation, and deciding whether a given hypothesis belongs to every acceptable explanation. We determine the complexity of these tasks for general TBoxes and also for EL and EL + terminologies. We also provide results concerning the complexity of computing abductive explanations.