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Paramodulation with Non-Monotonic Orderings and Simplification

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Abstract

Ordered paramodulation and Knuth-Bendix completion are known to remain complete when using non-monotonic orderings. However, these results do not imply the compatibility of the calculus with essential redundancy elimination techniques such as demodulation, i.e., simplification by rewriting, which constitute the primary mode of computation in most successful automated theorem provers. In this paper we present a complete ordered paramodulation calculus for non-monotonic orderings which is compatible with powerful redundancy notions including demodulation, hence strictly improving the previous results and making the calculus more likely to be used in practice. As a side effect, we obtain a Knuth-Bendix completion procedure compatible with simplification techniques, which can be used for finding, whenever it exists, a convergent term rewrite system for a given set of equations and a (possibly non-totalizable) reduction ordering.

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Authors and Affiliations

  1. Dept. Informàtica i Matemàtica Aplicada, Universitat de Girona, Campus Montilivi, Ed. P4, 17071, Girona, Spain

    Miquel Bofill

  2. Dept. Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, C/ Jordi Girona, 1-3, 08034, Barcelona, Spain

    Albert Rubio

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  1. Miquel Bofill
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  2. Albert Rubio
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Correspondence to Miquel Bofill.

Additional information

This work has been partially supported by the Spanish MEC/MICINN under grants TIN2008-04547 and TIN 2010-68093-C02-01. A preliminary version of this work was presented at the IJCAR 2004 conference [10].

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Bofill, M., Rubio, A. Paramodulation with Non-Monotonic Orderings and Simplification. J Autom Reasoning 50, 51–98 (2013). https://doi.org/10.1007/s10817-011-9244-z

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