Abstract
We consider a restricted version of ordered paramodulation, called strict superposition. We show that strict superposition (together with equality resolution) is refutationally complete for Horn clauses, but not for general first-order clauses. Two moderate enrichments of the strict superposition calculus are, however, sufficient to establish refutation completeness. This strictly improves previous results. We also propose a simple semantic notion of redundancy for clauses which covers most simplification and elimination techniques used in practice yet preserves completeness of the proposed calculi. The paper introduces a new and comparatively simple technique for completeness proofs based on the use of canonical rewrite systems to represent equality interpretations.
The research described in this paper was supported in part by the National Science Foundation under grant CCR-8901322, by the ESPRIT-project PROSPECTRA (ref. no. 390), and by a travel grant from Deutsche Forschungsgemeinschaft.
This work was done while the second author was on leave at SUNY at Stony Brook.
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Bachmair, L., Ganzinger, H. (1990). On restrictions of ordered paramodulation with simplification. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_105
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DOI: https://doi.org/10.1007/3-540-52885-7_105
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