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Hierarchic Superposition with Weak Abstraction

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Automated Deduction – CADE-24 (CADE 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7898))

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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.

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Author information

Authors and Affiliations

  1. NICTA, Australia

    Peter Baumgartner

  2. Australian National University, Canberra, Australia

    Peter Baumgartner

  3. MPI für Informatik, Saarbrücken, Germany

    Uwe Waldmann

Authors
  1. Peter Baumgartner
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  2. Uwe Waldmann
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Maria Paola Bonacina

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Baumgartner, P., Waldmann, U. (2013). Hierarchic Superposition with Weak Abstraction. In: Bonacina, M.P. (eds) Automated Deduction – CADE-24. CADE 2013. Lecture Notes in Computer Science(), vol 7898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38574-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-38574-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38573-5

  • Online ISBN: 978-3-642-38574-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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