Abstract
Recently, ordered paramodulation and Knuth-Bendix completion were shown to remain complete when using non-monotonic orderings. However, these results only implied the compatibility with too weak redundancy notions and, in particular, demodulation could not be applied at all.
In this paper, we present a complete ordered paramodulation calculus compatible with powerful redundancy notions including demodulation, which strictly improves previous results.
Our results can be applied as well to obtain a Knuth-Bendix completion procedure compatible with simplification techniques, which can be used for finding, whenever it exists, a convergent TRS for a given set of equations and a (possibly non-totalizable) reduction ordering.
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Bofill, M., Rubio, A. (2004). Redundancy Notions for Paramodulation with Non-monotonic Orderings. In: Basin, D., Rusinowitch, M. (eds) Automated Reasoning. IJCAR 2004. Lecture Notes in Computer Science(), vol 3097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25984-8_6
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DOI: https://doi.org/10.1007/978-3-540-25984-8_6
Publisher Name: Springer, Berlin, Heidelberg
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