Rigid unification by completion and rigid paramodulation

  • Gérard Becher
  • Uwe Petermann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 861)


This paper addresses the problem of computing complete sets of rigid-E-unifiers, initially introduced by Gallier, Narendran, Plaisted and Snyder who gave a proof of its NP-completeness. Our algorithm is based on completion and on a variant of basic paramodulation named rigid paramodulation. The crucial point of the algorithm is to ensure a constant orientation of the rules during the completion and the paramodulation process. This is achieved by defining minimal substitutions and proving that we can restrict our attention to such substitutions. This restriction allows us to use total term orderings because we don't need stability. We claim that our decision procedure becomes simpler. We prove soundness, completeness and termination of our algorithm.


Automated deduction equality rigid E-unification completion 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Gérard Becher
    • 1
  • Uwe Petermann
    • 2
  1. 1.LAIAC Université de CaenCaen CedexFrance
  2. 2.FB IMN, HTWK LeipzigLeipzigFRG

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