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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 161 (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.
Explanation and Prediction: An Architecture for Default and Abductive Reasoning
 Computational Intelligence
, 1993
"... Although there are many arguments that logic is an appropriate tool for artificial intelligence, there has been a perceived problem with the monotonicity of classical logic. This paper elaborates on the idea that reasoning should be viewed as theory formation where logic tells us the consequences of ..."
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Cited by 130 (16 self)
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Although there are many arguments that logic is an appropriate tool for artificial intelligence, there has been a perceived problem with the monotonicity of classical logic. This paper elaborates on the idea that reasoning should be viewed as theory formation where logic tells us the consequences of our assumptions. The two activities of predicting what is expected to be true and explaining observations are considered in a simple theory formation framework. Properties of each activity are discussed, along with a number of proposals as to what should be predicted or accepted as reasonable explanations. An architecture is proposed to combine explanation and prediction into one coherent framework. Algorithms used to implement the system as well as examples from a running implementation are given. Key words: defaults, conjectures, explanation, prediction, abduction, dialectics, logic, nonmonotonicity, theory formation Explanation and Prediction 2 1 Introduction One way to do research i...
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
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Cited by 125 (3 self)
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. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
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...
Generic Tasks and Task Structures: History, Critique and New Directions
, 1993
"... We have for several years been working on an approach to knowledge system building that argues for the existence of a close connection between the tasks which the knowledge system is intended to solve, the methods chosen for them and the vocabulary in which knowledge is to be modeled and represent ..."
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Cited by 46 (0 self)
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We have for several years been working on an approach to knowledge system building that argues for the existence of a close connection between the tasks which the knowledge system is intended to solve, the methods chosen for them and the vocabulary in which knowledge is to be modeled and represented. We trace the historical origins of the idea that we have called Generic Tasks, and outline their evolution and accomplishments based on them. We then critique their original implementations from the perspective of flexible integration. We follow this with an outline of our current generalization of the view in the form of a theory of task structures. We describe the architectural implications of this view and outline some research directions.
Abduction from Logic Programs: Semantics and Complexity
 Theoretical Computer Science
, 1998
"... Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important pr ..."
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Cited by 36 (7 self)
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Abduction from observations and a theory, find using hypotheses an explanation for the observations  gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of commonsense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...
Using Compiled Knowledge to Guide and Focus Abductive Diagnosis
 IEEE Transactions on Knowledge and Data Engineering
, 1996
"... Several artificial intelligence architectures and systems based on "deep" models of a domain have been proposed, in particular for the diagnostic task. These systems have several advantages over traditional knowledge based systems, but they have a main limitation in their computational complexity. O ..."
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Cited by 24 (6 self)
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Several artificial intelligence architectures and systems based on "deep" models of a domain have been proposed, in particular for the diagnostic task. These systems have several advantages over traditional knowledge based systems, but they have a main limitation in their computational complexity. One of the ways to face this problem is to rely on a knowledge compilation phase, which produces knowledge that can be used more effectively with respect to the original one. In this paper we show how a specific knowledge compilation approach can focus reasoning in abductive diagnosis, and, in particular, can improve the performances of AID, an abductive diagnosis system. The approach aims at focusing the overall diagnostic cycle in two interdependent ways: avoiding the generation of candidate solutions to be discarded aposteriori and integrating the generation of candidate solutions with discrimination among different candidates. Knowledge compilation is used offline to produce operational...
Semantics and complexity of abduction from default theories
 Artificial Intelligence
, 1997
"... Since logical knowledge representation is commonly based on nonclassical formalisms like default logic, autoepistemic logic, or circumscription, it is necessary to perform abductive reasoning from theories of nonclassical logics. In this paper, we investigate how abduction can be performed from theo ..."
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Cited by 21 (2 self)
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Since logical knowledge representation is commonly based on nonclassical formalisms like default logic, autoepistemic logic, or circumscription, it is necessary to perform abductive reasoning from theories of nonclassical logics. In this paper, we investigate how abduction can be performed from theories in default logic. Different modes of abduction are plausible, based on credulous and skeptical default reasoning; they appear useful for different applications such as diagnosis and planning. Moreover, we analyze the complexity of the main abductive reasoning tasks. They are intractable in the general case; we also present known classes of default theories for which abduction is tractable. 1
Inductive Learning For Abductive Diagnosis
 In Proceedings of the Twelfth National Conference on Artificial Intelligence
, 1994
"... A new inductive learning system, Lab (Learning for ABduction), is presented which acquires abductive rules from a set of training examples. The goal is to find a small knowledge base which, when used abductively, diagnoses the training examples correctly and generalizes well to unseen examples. This ..."
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Cited by 18 (0 self)
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A new inductive learning system, Lab (Learning for ABduction), is presented which acquires abductive rules from a set of training examples. The goal is to find a small knowledge base which, when used abductively, diagnoses the training examples correctly and generalizes well to unseen examples. This contrasts with past systems that inductively learn rules that are used deductively. Each training example is associated with potentially multiple categories (disorders) , instead of one as with typical learning systems. Lab uses a simple hillclimbing algorithm to efficiently build a rule base for a setcovering abductive system. Lab has been experimentally evaluated and compared to other learning systems and an expert knowledge base in the domain of diagnosing brain damage due to stroke. Introduction Most work in symbolic concept acquisition assumes a deductive model of classification in which an example is a member of a concept if it satisfies a logical specification represented in dis...
A Neural Architecture for a Class of Abduction Problems
 IEEE Transactions on Systems Man and Cybernetics
, 1996
"... The general task of abduction is to infer a hypothesis that best explains a set of data. A typical subtask of this is to synthesize a composite hypothesis that best explains the entire data from elementary hypotheses which can explain portions of it. The synthesis subtask of abduction is computat ..."
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Cited by 10 (0 self)
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The general task of abduction is to infer a hypothesis that best explains a set of data. A typical subtask of this is to synthesize a composite hypothesis that best explains the entire data from elementary hypotheses which can explain portions of it. The synthesis subtask of abduction is computationally expensive, more so in the presence of certain types of interactions between the elementary hypotheses. In this paper, we first formulate the abduction task as a nonmonotonic constrainedoptimization problem. We then consider a special version of the general abduction task that is linear and monotonic. Next, we describe a neural network based on the Hopfield model of computation for the special version of the abduction task. The connections in this network are symmetric, the energy function contains product forms, and the minimization of this function requires a network of order greater than two. We then discuss another neural architecture which is composed of functional module...