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An ordered theory resolution calculus

  • Peter Baumgartner
Session 5: Resolution Theorem Proving
Part of the Lecture Notes in Computer Science book series (LNCS, volume 624)

Abstract

In this paper we present an ordered theory resolution calculus and prove its completeness. Theory reasoning means to relieve a calculus from explicitly drawing inferences in a given theory by special purpose inference rules (e.g. E-resolution for equality reasoning). We take advantage of orderings (e.g. simplification orderings) by disallowing to resolve upon clauses which violate certain maximality constraints; stated positively, a resolvent may only be built if all the selected literals are maximal in their clauses. By this technique the search space is drastically pruned. As an instantiation for theory reasoning we show that equality can be built in by rigid E-unification.

Keywords

Automated Theorem Proving Theory Resolution 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Peter Baumgartner
    • 1
  1. 1.Institut für InformatikUniversität KoblenzKoblenz

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