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Propositional Lower Bounds: Generalization and Algorithms

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Logics in Artificial Intelligence (JELIA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1489))

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Abstract

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 polynomial-time complete on-line reasoning, although soundness is not guaranteed. In this paper we define the notion of k-GLB, which is basically the aggre-gate 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?”

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© 1998 Springer-Verlag Berlin Heidelberg

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Cadoli, M., Palopoli, L., Scarcello, F. (1998). Propositional Lower Bounds: Generalization and Algorithms. In: Dix, J., del Cerro, L.F., Furbach, U. (eds) Logics in Artificial Intelligence. JELIA 1998. Lecture Notes in Computer Science(), vol 1489. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49545-2_24

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  • DOI: https://doi.org/10.1007/3-540-49545-2_24

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  • Print ISBN: 978-3-540-65141-3

  • Online ISBN: 978-3-540-49545-1

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