First-Order Logic Theorem Proving and Model Building via Approximation and Instantiation

  • Andreas Teucke
  • Christoph Weidenbach
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9322)


In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The approximation extends the signature and preserves unsatisfiability: if the simplified clause set is satisfiable in some model, so is the original clause set in the same model interpreted in the original signature. A refutation generated by a decision procedure on the simplified clause set can then either be lifted to a refutation in the original clause set, or it guides a refinement excluding the previously found unliftable refutation. This way the approach is refutationally complete. We do not step-wise lift refutations but lift conflicting cores, finite unsatisfiable clause sets representing at least one refutation. The approach is dual to many existing approaches in the literature.


Automate Reasoning Horn Clause Ground Instance Lift Step Positive Literal 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Andreas Teucke
    • 1
    • 2
  • Christoph Weidenbach
    • 1
  1. 1.Max-Planck Institut for InformaticsSaarbrückenGermany
  2. 2.Graduate School of Computer ScienceSaarbrückenGermany

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