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Extending resolution for model construction

  • Ricardo Caferra
  • Nicolas Zabel
Selected Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 478)

Abstract

A method is proposed to systematize the simultaneous search for a refutation and Herbrand models of a given conjecture. It is based on an extension of resolution using equational problems and the inference system included in the method is proved to be sound and refutational complete. For some classes of formulae the method is indeed a decision procedure. Some examples of model construction — including one for which other resolution based decision procedures fail to detect satisfiability — are developed in detail.

Models are built by constructing relations on Herbrand universe. The relationship between these models and finite ones is established. The class of these constructible relations is precisely characterized. Some of the rules introduced, in order to extend resolution, are essentially new. Their necessity in constructing models is proved. A brief comparison with existing methods which bear similarity with ours, either in the use of constraints (a particular case of equational problems) or in the search of a model, shows the originality of our proposal.

Keywords

Theorem Proving Model Construction Equational Problems Unification Disunification Decision Procedures 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Ricardo Caferra
    • 1
  • Nicolas Zabel
    • 1
  1. 1.Laboratoire d'Informatique Fondamentale et d'Intelligence ArtificielleImag-CnrsGrenobleFrance

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