On generating all maximal independent sets
Information Processing Letters
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
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
Algorithms for propositional KB approximation
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
The Inverse Satisfiability Problem
SIAM Journal on Computing
Semantical and computational aspects of Horn approximations
Artificial Intelligence
Generating all maximal models of a Boolean expression
Information Processing Letters
A unified framework for structure identification
Information Processing Letters
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
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Translating between Horn representations and their characteristic models
Journal of Artificial Intelligence Research
An analysis of approximate knowledge compilation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
What makes propositional abduction tractable
Artificial Intelligence
Boolean approximation revisited
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
Information loss in knowledge compilation: A comparison of Boolean envelopes
Artificial Intelligence
Boolean affine approximation with binary decision diagrams
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
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Selman and Kautz introduced the notion of approximation of a theory and showed its usefulness for knowledge compilation and on-line reasoning. We study here the complexity of the main computational problems related to the approximation of relations (sets of possible worlds) by propositional formulas, and the semantics of reasoning with these approximations (deduction and abduction). The classes of formulas that we consider are those of (reverse-)Horn, bijunctive and affine formulas, which are the most interesting for storing knowledge.Concerning the computation of approximations, we survey and complete the results that can be found in the literature, trying to adopt a unified point of view. On the contrary, as far as we know this paper is the first real attempt to study the semantics of abduction with the bounds of a theory.