Superposition Modulo Non-linear Arithmetic

  • Andreas Eggers
  • Evgeny Kruglov
  • Stefan Kupferschmid
  • Karsten Scheibler
  • Tino Teige
  • Christoph Weidenbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6989)


The first-order theory over non-linear arithmetic including transcendental functions (NLA) is undecidable. Nevertheless, in this paper we show that a particular combination with superposition leads to a sound and complete calculus that is useful in practice. We follow basically the ideas of the SUP(LA) combination, but have to take care of undecidability, resulting in “unknown” answers by the NLA reasoning procedure. A pipeline of NLA constraint simplification techniques related to the SUP(NLA) framework significantly decreases the number of “unknown” answers. The resulting approach is implemented as SUP(NLA) by a system combination of Spass and iSAT. Applied to various scenarios of traffic collision avoidance protocols, we show by experiments that Spass(iSAT) can fully automatically proof and disproof safety properties of such protocols using the very same formalization.


Horn Clause Empty Clause Linear Arithmetic Arithmetic Constraint Uninterpreted Function 
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-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Eggers
    • 1
  • Evgeny Kruglov
    • 2
  • Stefan Kupferschmid
    • 3
  • Karsten Scheibler
    • 3
  • Tino Teige
    • 1
  • Christoph Weidenbach
    • 2
  1. 1.Dept. of Computing ScienceCarl von Ossietzky Universität OldenburgOldenburgGermany
  2. 2.Universität des Saarlandes, Max-Planck-Institut für InformatikSaarbrückenGermany
  3. 3.Institute of Computer ScienceAlbert-Ludwigs-UniversityFreiburg im BreisgauGermany

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