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Hierarchic superposition with weak abstraction

Authors

Peter Baumgartner and Uwe Waldmann

NICTA

Max-Planck-Institute for Computer Science

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 a new completeness result for the fragment where all background-sorted terms are ground.

BibTeX Entry

  @inproceedings{Baumgartner_Waldmann_13,
    publisher        = {Springer},
    author           = {Baumgartner, Peter and Waldmann, Uwe},
    month            = jun,
    editor           = {{Maria Paola Bonacina}},
    year             = {2013},
    keywords         = {automated deduction, theorem proving, first-order logic, decision procedures, arithmetic},
    title            = {Hierarchic Superposition With Weak Abstraction},
    booktitle        = {Conference on Automated Deduction},
    pages            = {39-57},
    address          = {Lake Placid, New York, USA}
  }

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