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Thomas Eiter and Georg Gottlob. The complexity of logic-based abduction. Journal of the ACM, 42(1):3-42, January 1995. [BibTeX entry]

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 logic-based abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subset-minimality, minimal cardinality, minimal weight, or minimalityunder prioritization of individual hypotheses. This paper present 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. Copyright 1995 by ACM, Inc.

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Categories and Subject Descriptors: I.2.3 [Artificial Intelligence]: Deduction and Theorem Proving; I.2.4 [Artificial Intelligence]: Knowledge Representation Formalisms and Methods; F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic

General Terms: Theory

Additional Key Words and Phrases: Abduction, Complexity Analysis, Diagnosis, Reasoning, Propositional Logic

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