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Knuth-bendix completion of horn clause programs for restricted linear resolution and paramodulation

  • Chapter 3 Extension Of Knuth-Bendix Completion
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Conditional and Typed Rewriting Systems (CTRS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 516))

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Abstract

The aim of Knuth-Bendix completion is to transform an input specification into another, equivalent specification such that a given set of inference rules becomes complete for the transformed specification. In the classical case, the specifications consist of unconditional equations, and the inference rule is term rewriting.

Here we investigate Knuth-Bendix completion methods for full Horn clause specifications and introduce a class of inference systems defined by an abstract concept of restrictions imposed on linear resolution and paramodulation.

The usual technical ingredients of Knuth-Bendix completion methods, e.g. critical pairs, a corresponding critical pair lemma, simplification and elimination methods and critical pair criteria are generalized with respect to the concept of restrictions. We show that for any concrete restriction, our completion methods produce specifications for which linear resolution and paramodulation under the given restriction are refutationally complete. Conventional completion methods are instances of completion with respect to restrictions.

This work is partially supported by the ESPRIT-project PROSPECTRA, ref#390.

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Authors and Affiliations

  1. Fachbereich Informatik, Universität Dortmund, D-4600, Dortmund 50, Germany

    Hubert Bertling

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  1. Hubert Bertling
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S. Kaplan M. Okada

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© 1991 Springer-Verlag Berlin Heidelberg

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Bertling, H. (1991). Knuth-bendix completion of horn clause programs for restricted linear resolution and paramodulation. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_90

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  • DOI: https://doi.org/10.1007/3-540-54317-1_90

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54317-6

  • Online ISBN: 978-3-540-47558-3

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