The computational complexity of abduction
Artificial Intelligence - Special issue on knowledge representation
Artificial Intelligence - Special volume on natural language processing
The complexity of logic-based abduction
Journal of the ACM (JACM)
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
On some tractable classes in deduction and abduction
Artificial Intelligence
Diagnosing tree-structured systems
Artificial Intelligence
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Consistency restoriation and explanations in dynamic CSPs----application to configuration
Artificial Intelligence
A unified framework for structure identification
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Inference Problem for Propositional Circumscription of Affine Formulas Is coNP-Complete
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of Restricted Consequence Finding and Abduction
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
On computing all abductive explanations
Eighteenth national conference on Artificial intelligence
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
New polynomial classes for logic-based abduction
Journal of Artificial Intelligence Research
What makes propositional abduction tractable
Artificial Intelligence
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
The union of minimal hitting sets: Parameterized combinatorial bounds and counting
Journal of Discrete Algorithms
Complexity of default logic on generalized conjunctive queries
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Counting complexity of propositional abduction
Journal of Computer and System Sciences
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Abduction is a fundamental form of nonmonotonic reasoning that aims at finding explanations for observed manifestations. Applications of this process range from car configuration to medical diagnosis. We study here its computational complexity in the case where the application domain is described by a propositional theory built upon a fixed constraint language and the hypotheses and manifestations are described by sets of literals. We show that depending on the language the problem is either polynomial-time solvable, NP-complete, or ΣP2-complete. In particular, we show that under the assumption P≠NP, only languages that are affine of width 2 have a polynomial algorithm, and we exhibit very weak conditions for NP-hardness.