Superposition for divisible torsion-free abelian groups

  • Uwe Waldmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1421)


Variable overlaps are one of the main sources for the inefficiency of AC or ACU theorem proving calculi. In the presence of the axioms of abelian groups or at least cancellative abelian monoids, ordering restrictions allow us to avoid some of these overlaps, but inferences with unshielded variables remain necessary. In divisible torsion-free abelian groups, for instance the rational numbers, every clause can be transformed into an equivalent clause without unshielded variables. We show how such a variable elimination algorithm can be integrated into the cancellative superposition calculus. The resulting calculus is refutationally complete with respect to the axioms of divisible torsion-free abelian groups and allows us to dispense with variable overlaps altogether. If abstractions are performed eagerly, the calculus makes it furthermore possible to avoid the computation of AC unifiers and AC orderings.


Inference Rule Theorem Prove Ground Instance Automate Deduction Atomic Term 
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 1998

Authors and Affiliations

  • Uwe Waldmann
    • 1
  1. 1.Im StadtwaldMax-Planck-Institut für InformatikSaarbrückenGermany

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