A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
An empirical evaluation of knowledge compilation by theory approximation
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
A class of logic problems solvable by linear programming
Journal of the ACM (JACM)
Knowledge compilation and theory approximation
Journal of the ACM (JACM)
Semantical and computational aspects of horn approximations
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
An analysis of approximate knowledge compilation
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Compilation for critically constrained knowledge bases
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
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Propositional greatest lower bounds (GLBs) are logically-defined approximations of a knowledge base. They were defined in the context of Knowledge Compilation, a technique developed for addressing high computational cost of logical inference. A GLB allows for polynomialtime complete on-line reasoning, although soundness is not guaranteed. In this paper we define the notion of k-GLB, which is basically the aggregate of several lower bounds that retains the property of polynomial-time on-line reasoning. We show that it compares favorably with a simple GLB, because it can be a "more sound" complete approximation. We also propose new algorithms for the generation of a GLB and a k-GLB. Finally, we give precise characterization of the computational complexity of the problem of generating such lower bounds, thus addressing in a formal way the question "how many queries are needed to amortize the overhead of compilation?".