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Deduction with relation matching

  • Zohar Manna
  • Richard Waldinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 206)

Abstract

A new deduction rule is introduced to give streamlined treatment to relations of special importance in an automated theorem-proving system. This relation matching rule generalizes to an arbitrary binary relation the E-resolution and RUE-resolution rules for equality, and may operate within a nonclausal or clausal system. The new rule depends on an extension of the notion of polarity to apply to subterms as well as to subsentences, with respect to a given binary relation. It allows the system to draw a conclusion even if the unification algorithm fails to find a complete match, provided the polarities of the mismatched terms are auspicious. The rule allows us to eliminate troublesome axioms, such as transitivity and monotonicity, from the system; proofs are shorter and more comprehensible, and the search space is correspondingly deflated.

Keywords

Binary Relation Deduction Rule Relation Match Resolution Rule Substitutivity Property 
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 1985

Authors and Affiliations

  • Zohar Manna
    • 1
  • Richard Waldinger
    • 2
  1. 1.Computer Science DepartmentStanford UniversityUSA
  2. 2.Artificial Intelligence CenterSRI InternationalUSA

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