Superposition Modulo Linear Arithmetic SUP(LA)

  • Ernst Althaus
  • Evgeny Kruglov
  • Christoph Weidenbach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5749)


The hierarchical superposition based theorem proving calculus of Bachmair, Ganzinger, and Waldmann enables the hierarchic combination of a theory with full first-order logic. If a clause set of the combination enjoys a sufficient completeness criterion, the calculus is even complete. We instantiate the calculus for the theory of linear arithmetic. In particular, we develop new effective versions for the standard superposition redundancy criteria taking the linear arithmetic theory into account. The resulting calculus is implemented in SPASS(LA) and extends the state of the art in proving properties of first-order formulas over linear arithmetic.


Theory Part Implication Test Empty Clause Linear Arithmetic Completeness Criterion 
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 2009

Authors and Affiliations

  • Ernst Althaus
    • 1
  • Evgeny Kruglov
    • 1
  • Christoph Weidenbach
    • 1
  1. 1.Max Planc Institute for InformaticsSaarbrücken

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