NRCL - A Model Building Approach to the Bernays-Schönfinkel Fragment

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


We combine constrained literals for model representation with key concepts from first-order superposition and propositional conflict-driven clause learning (CDCL) to create the new calculus Non-Redundant Clause Learning (NRCL) deciding the Bernays-Schönfinkel fragment. We use first-order literals constrained by disequalities between tuples of terms for compact model representation. From superposition, NRCL inherits the abstract redundancy criterion and the monotone model operator. CDCL adds the dynamic, conflict-driven search for a model. As a result, NRCL finds a false clause modulo the current model candidate effectively. It guides the derivation of a first-order ordered resolvent that is never redundant. Similar to 1UIP-learning in CDCL, the learned resolvent induces backtracking and, by blocking the previous conflict state via propagation, it enforces progress towards finding a model or a refutation. The non-redundancy result also implies that only finitely many clauses can be generated by NRCL on the Bernays-Schönfinkel fragment, which proves termination.


Horn Clause Ground Atom Ground Instance Constraint Language Empty Clause 
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 International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Saarbrücken Graduate School of Computer ScienceSaarbrückenGermany
  2. 2.Saarland UniversitySaarbrückenGermany
  3. 3.Max-Planck-Institut für InformatikSaarbrückenGermany

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