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A new method for establishing refutational completeness in theorem proving

  • Jieh Hsiang
  • Michael Rusinowitch
Term Rewriting Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)

Abstract

We present here a new technique for establishing completeness of refutational theorem proving strategies. This method employs semantic trees and, in contrast to most of the semantic tree methods, is based on proof by refutation instead of proof by induction. Thus, it works well on transfinite semantic trees as well as on finite ones. This method is particularly useful for proving the completeness of strategies with the presence of the equality predicate. We have used the method to prove the completeness of the following strategies (without the need of the functional reflexive axioms), where the precise definition of oriented paramodulation will be given later.

• Resolution + oriented paramodulation

• P1-resolution + oriented paramodulation

• Resolution with ordered predicates + oriented paramodulation using clauses only containing the equality predicate

• unfailing Knuth-Bendix-Huet algorithm

• The EN-Strategy ([Hsi85])

Keywords

Inference Rule Theorem Prove Failure Node Predicate Symbol Ground Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Jieh Hsiang
    • 1
  • Michael Rusinowitch
    • 2
  1. 1.Department of Computer ScienceSUNY at Stony BrookStony BrookUSA
  2. 2.CRINVandoeuvre-les-NancyFrance

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