Artificial Intelligence
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)
Horn approximations of empirical data
Artificial Intelligence
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
Artificial Intelligence
Semantics and complexity of abduction from default theories
Artificial Intelligence
Abduction from logic program: semantics and complexity
Theoretical Computer Science
A new method for consequence finding and compilation in restricted languages
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
On some tractable classes in deduction and abduction
Artificial Intelligence
Abduction in logic programming: a new definition and an abductive procedure based on rewriting
Artificial Intelligence
Approximation of Relations by Propositional Formulas: Complexity and Semantics
Proceedings of the 5th International Symposium on Abstraction, Reformulation and Approximation
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
Solving Advanced Reasoning Tasks Using Quantified Boolean Formulas
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
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
Preprocessing of intractable problems
Information and Computation
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Information Processing Letters
A Complete Classification of the Complexity of Propositional Abduction
SIAM Journal on Computing
Compilability of propositional abduction
ACM Transactions on Computational Logic (TOCL)
On computing all abductive explanations from a propositional Horn theory
Journal of the ACM (JACM)
Propositional independence: formula-variable independence and forgetting
Journal of Artificial Intelligence Research
A tractable class of abduction problems
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Counting complexity of propositional abduction
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Propositional abduction is almost always hard
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Complexity of default logic on generalized conjunctive queries
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Found ations of assumption-based truth maintenance systems: preliminary report
AAAI'87 Proceedings of the sixth National conference on Artificial intelligence - Volume 1
Abductive and default reasoning: a computational core
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Trichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
Solving strong-fault diagnostic models by model relaxation
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Counting complexity of propositional abduction
Journal of Computer and System Sciences
The Complexity of Handling Minimal Solutions in Logic-Based Abduction
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Troubleshooting with human-readable automated reasoning
LISA'10 Proceedings of the 24th international conference on Large installation system administration
Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs
Theory and Practice of Logic Programming
Do hard SAT-related reasoning tasks become easier in the Krom fragment?
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Abduction is a fundamental form of nonmonotonic reasoning that aims at finding explanations for observed manifestations. This process underlies many applications, from car configuration to medical diagnosis. We study here the computational complexity of deciding whether an explanation exists in the case when the application domain is described by a propositional knowledge base. Building on previous results, we classify the complexity for local restrictions on the knowledge base and under various restrictions on hypotheses and manifestations. In comparison to the many previous studies on the complexity of abduction we are able to give a much more detailed picture for the complexity of the basic problem of deciding the existence of an explanation. It turns out that depending on the restrictions, the problem in this framework is always polynomial-time solvable, NP-complete, coNP-complete, or @S"2^P-complete. Based on these results, we give an a posteriori justification of what makes propositional abduction hard even for some classes of knowledge bases which allow for efficient satisfiability testing and deduction. This justification is very simple and intuitive, but it reveals that no nontrivial class of abduction problems is tractable. Indeed, tractability essentially requires that the language for knowledge bases is unable to express both causal links and conflicts between hypotheses. This generalizes a similar observation by Bylander et al. for set-covering abduction.