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Abduction in Logic Programming
"... Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over th ..."
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Cited by 600 (74 self)
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Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application. The paper attempts to expose some of the challenges and prospects for the further development of the field.
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 184 (28 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.
On The Relationship Between Abduction And Deduction
, 1991
"... this paper is at analyzing from various points of view the relationships betwee ..."
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Cited by 174 (9 self)
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this paper is at analyzing from various points of view the relationships betwee
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 131 (6 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...
Theory Refinement Combining Analytical and Empirical Methods
 Artificial Intelligence
, 1994
"... This article describes a comprehensive approach to automatic theory revision. Given an imperfect theory, the approach combines explanation attempts for incorrectly classified examples in order to identify the failing portions of the theory. For each theory fault, correlated subsets of the examples a ..."
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Cited by 123 (7 self)
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This article describes a comprehensive approach to automatic theory revision. Given an imperfect theory, the approach combines explanation attempts for incorrectly classified examples in order to identify the failing portions of the theory. For each theory fault, correlated subsets of the examples are used to inductively generate a correction. Because the corrections are focused, they tend to preserve the structure of the original theory. Because the system starts with an approximate domain theory, in general fewer training examples are required to attain a given level of performance (classification accuracy) compared to a purely empirical system. The approach applies to classification systems employing a propositional Hornclause theory. The system has been tested in a variety of application domains, and results are presented for problems in the domains of molecular biology and plant disease diagnosis. 1 INTRODUCTION 2 1 Introduction One of the most difficult problems in the develo...
Tractable Reasoning via Approximation
 Artificial Intelligence
, 1995
"... Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantical ..."
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Cited by 104 (0 self)
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Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantically wellfounded logic for approximate reasoning, which is justifiable from the intuitive point of view, and to provide fast algorithms for dealing with it even when using expressive languages. We also want our logic to be useful to perform approximate reasoning in different contexts. We define a method for the approximation of decision reasoning problems based on multivalued logics. Our work expands and generalizes in several directions ideas presented by other researchers. The major features of our technique are: 1) approximate answers give semantically clear information about the problem at hand; 2) approximate answers are easier to compute than answers to the original problem; 3) approxim...
Concept abduction and contraction for semanticbased discovery of matches and negotiation spaces in an emarketplace
, 2005
"... ..."
Approaches to Abductive Reasoning  An Overview
 ARTIFICIAL INTELLIGENCE REVIEW
, 1993
"... Abduction is a form of nonmonotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule
$$O = \mathop C\limits_  N = \mathop P\limits_^  O  \mathop C\limits_^  .$$
i.e., from an occurrence of ohgr an ..."
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Cited by 43 (1 self)
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Abduction is a form of nonmonotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule
$$O = \mathop C\limits_  N = \mathop P\limits_^  O  \mathop C\limits_^  .$$
i.e., from an occurrence of ohgr and the rule ldquophiv implies ohgrrdquo, infer an occurrence of phiv as aplausible hypothesis or explanation for ohgr. Thus, in contrast to deduction, abduction is as well as induction a form of ldquodefeasiblerdquo inference, i.e., the formulae sanctioned are plausible and submitted to verification.
In this paper, a formal description of current approaches is given. The underlying reasoning process is treated independently and divided into two parts. This includes a description of methods for hypotheses generation and methods for finding the best explanations among a set of possible ones. Furthermore, the complexity of the abductive task is surveyed in connection with its relationship to default reasoning. We conclude with the presentation of applications of the discussed approaches focusing on plan recognition and plan generation.
Configuration As Model Construction: The Constructive Problem Solving Approach
, 1994
"... . Configuration is distinguished by two important aspects: the inherent wellstructuredness of the problem description, and the synthetic type of problem solving. Up to now there is quite a number of (more or less) ad hoc approaches to configuration  but we are still missing a comprehensive formal ..."
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Cited by 21 (3 self)
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. Configuration is distinguished by two important aspects: the inherent wellstructuredness of the problem description, and the synthetic type of problem solving. Up to now there is quite a number of (more or less) ad hoc approaches to configuration  but we are still missing a comprehensive formal treatment. In order to be adequate a formalization of configuration has to take both aspects into account: the wellstructuredness and the synthetic problem solving type. In this paper we introduce a formalisation of configuration, called the Constructive Problem Solving (CPS). CPS formalizes the task to construct for a given specification, which is described as a finite set of logical formulas, a semantical model that satisfies the specification. In this approach, a specification consists of two parts. One part describes the domain, the possible components, and their interdependencies. The other part specifies the particular object that is to be configured. We give a sound CPS calculus, wh...
Abductive plan recognition and diagnosis: A comprehensive empirical evaluation
 In Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning
, 1992
"... While it has been realized for quite some time within AI that abduction is a general model of explanation for a variety of tasks, there have been no empirical investigations into the practical feasibility of a general, logicbased abductive approach to explanation. In this paper we present extensive ..."
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Cited by 20 (4 self)
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While it has been realized for quite some time within AI that abduction is a general model of explanation for a variety of tasks, there have been no empirical investigations into the practical feasibility of a general, logicbased abductive approach to explanation. In this paper we present extensive empirical results on applying a general abductive system, Accel, to moderately complex problems in plan recognition and diagnosis. In plan recognition, Accel has been tested on 50 short narrative texts, inferring characters ' plans from actions described in a text. In medical diagnosis, Accel has diagnosed 50 realworld patient cases involving brain damage due to stroke (previously addressed by setcovering methods). Accel also uses abduction to accomplish modelbased diagnosis of logic circuits (a full adder) and continuous dynamic systems (a temperature controller and the water balance system of the human kidney). The results indicate that general purpose abduction is an e ective and e cient mechanism for solving problems in plan recognition and diagnosis. 1