International Symposium on Frontiers of Combining Systems

Frontiers of Combining Systems pp 85-100 | Cite as

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)

Abstract

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.

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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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