On restrictions of ordered paramodulation with simplification

  • Leo Bachmair
  • Harald Ganzinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 449)


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.


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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Leo Bachmair
    • 1
  • Harald Ganzinger
    • 2
  1. 1.Department of Computer ScienceSUNY at Stony BrookStony BrookU.S.A.
  2. 2.FB InformatikUniversität DortmundDortmund 50F.R.G.

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