Artificial Intelligence
Design by exmple: An application of Armstrong relations
Journal of Computer and System Sciences
Making believers out of computers
Artificial Intelligence
NP is as easy as detecting unique solutions
Theoretical Computer Science
AI Magazine
Why Horn formulas matter in computer science: initial structures and generic examples
Journal of Computer and System Sciences
Explanation and prediction: an architecture for default and abductive reasoning
Computational Intelligence
An incremental method for generating prime implicants/implicates
Journal of Symbolic Computation
Hypothesis classification, abductive diagnosis and therapy
Proceedings of the international workshop on Expert systems in engineering : Principles and applications: Principles and applications
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
Information Processing Letters
Linear resolution for consequence finding
Artificial Intelligence
The complexity of logic-based abduction
Journal of the ACM (JACM)
Horn approximations of empirical data
Artificial Intelligence
The role of abduction in database view updating
Journal of Intelligent Information Systems
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Complexity of identification and dualization of positive Boolean functions
Information and Computation
Exact learning Boolean functions via the monotone theory
Information and Computation
Support set selection for abductive and default reasoning
Artificial Intelligence
Artificial Intelligence
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Defaults and relevance in model-based reasoning
Artificial Intelligence - Special issue on relevance
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
Horn clauses and database dependencies
Journal of the ACM (JACM)
On some tractable classes in deduction and abduction
Artificial Intelligence
On connected Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Horn minimization by iterative decomposition
Annals of Mathematics and Artificial Intelligence
Fixed-parameter complexity of semantics for logic programs
ACM Transactions on Computational Logic (TOCL)
Quasi-Acyclic Propositional Horn Knowledge Bases: Optimal Compression
IEEE Transactions on Knowledge and Data Engineering
New Results on Monotone Dualization and Generating Hypergraph Transversals
SIAM Journal on Computing
Monotone boolean dualization is in co-NP[log2n]
Information Processing Letters
Inferring Minimal Functional Dependencies in Horn and q-Horn Theories
Annals of Mathematics and Artificial Intelligence
Learning First-Order Acyclic Horn Programs from Entailment
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
On Horn Envelopes and Hypergraph Transversals
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
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
Learning Acyclic First-Order Horn Sentences from Entailment
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
On computing all abductive explanations
Eighteenth national conference on Artificial intelligence
The Journal of Machine Learning Research
Computational aspects of monotone dualization: A brief survey
Discrete Applied Mathematics
Bounded treewidth as a key to tractability of knowledge representation and reasoning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
New polynomial classes for logic-based abduction
Journal of Artificial Intelligence Research
Translating between Horn representations and their characteristic models
Journal of Artificial Intelligence Research
What makes propositional abduction tractable
Artificial Intelligence
A logical study of partial entailment
Journal of Artificial Intelligence Research
Debugging is-a structure in networked taxonomies
Proceedings of the 4th International Workshop on Semantic Web Applications and Tools for the Life Sciences
Deductive inference for the interiors and exteriors of horn theories
ACM Transactions on Computational Logic (TOCL)
DNF hypotheses in explanatory induction
ILP'11 Proceedings of the 21st international conference on Inductive Logic Programming
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Abduction is a fundamental mode of reasoning with applications in many areas of AI and Computer Science. The computation of abductive explanations is an important computational problem, which is at the core of early systems such as the ATMS and Clause Management Systems and is intimately related to prime implicate generation in propositional logic. Many algorithms have been devised for computing some abductive explanation, and the complexity of the problem has been well studied. However, little attention has been paid to the problem of computing multiple explanations, and in particular all explanations for an abductive query. We fill this gap and consider the computation of all explanations of an abductive query from a propositional Horn theory, or of a polynomial subset of them. Our study pays particular attention to the form of the query, ranging from a literal to a compound formula, to whether explanations are based on a set of abducible literals and to the representation of the Horn theory, either by a Horn conjunctive normal form (CNF) or model-based in terms of its characteristic models. For these combinations, we present either tractability results in terms of polynomial total-time algorithms, intractability results in terms of nonexistence of such algorithms (unless P = NP), or semi-tractability results in terms of solvability in quasi-polynomial time, established by polynomial-time equivalence to the problem of dualizing a monotone CNF expression. Our results complement previous results in the literature, and refute a longstanding conjecture by Selman and Levesque. They elucidate the complexity of generating all abductive explanations and shed light on related problems such as generating sets of restricted prime implicates of a Horn theory. The algorithms for tractable cases can be readily applied for generating a polynomial subset of explanations in polynomial time.