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Hierarchic Superposition Revisited

  • Peter BaumgartnerEmail author
  • Uwe WaldmannEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11560)

Abstract

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are “reasonably complete” even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory.

Keywords

Automated deduction Superposition calculus Combinations of theories 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Data61/CSIRO, ANU Computer Science and Information Technology (CSIT)ActonAustralia
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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