On the Combination of the Bernays–Schönfinkel–Ramsey Fragment with Simple Linear Integer Arithmetic

  • Matthias HorbachEmail author
  • Marco VoigtEmail author
  • Christoph WeidenbachEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10395)


In general, first-order predicate logic extended with linear integer arithmetic is undecidable. We show that the Bernays-Schönfinkel-Ramsey fragment (\(\exists ^* \forall ^*\)-sentences) extended with a restricted form of linear integer arithmetic is decidable via finite ground instantiation. The identified ground instances can be employed to restrict the search space of existing automated reasoning procedures considerably, e.g., when reasoning about quantified properties of array data structures formalized in Bradley, Manna, and Sipma’s array property fragment. Typically, decision procedures for the array property fragment are based on an exhaustive instantiation of universally quantified array indices with all the ground index terms that occur in the formula at hand. Our results reveal that one can get along with significantly fewer instances.


Bernays–Schönfinkel–Ramsey fragment Linear integer arithmetic Complete instantiation 


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Max Planck Institute for InformaticsSaarbrückenGermany
  2. 2.Saarbrücken Graduate School of Computer ScienceSaarbrückenGermany

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