Superposition for Fixed Domains

  • Matthias Horbach
  • Christoph Weidenbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5213)

Abstract

Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a perfect term-generated model for the theory. Proving universal properties with respect to a saturated theory directly leads to a modification of the perfect model’s term-generated domain, as new Skolem functions are introduced. For many applications, this is not desired. Therefore, we propose the first superposition calculus that can explicitly represent existentially quantified variables and can thus compute with respect to a given domain. This calculus is sound and complete for a first-order fixed domain semantics. For some classes of formulas and theories, we can even employ the calculus to prove properties of the perfect model itself, going beyond the scope of known superposition based approaches.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Matthias Horbach
    • 1
  • Christoph Weidenbach
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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