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Automating Coherent Logic

  • Conference paper
Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3835))

Abstract

First-order coherent logic (CL) extends resolution logic in that coherent formulas allow certain existential quantifications. A substantial number of reasoning problems (e.g., in confluence theory, lattice theory and projective geometry) can be formulated directly in CL without any clausification or Skolemization. CL has a natural proof theory, reasoning is constructive and proof objects can easily be obtained. We prove completeness of the proof theory and give a linear translation from FOL to CL that preserves logical equivalence. These properties make CL well-suited for providing automated reasoning support to logical frameworks. The proof theory has been implemented in Prolog, generating proof objects that can be verified directly in the proof assistant Coq. The prototype has been tested on the proof of Hessenberg’s Theorem, which could be automated to a considerable extent. Finally, we compare the prototype to some automated theorem provers on selected problems.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Bergen, P.O. Box 7800, N-5020, Bergen, Norway

    Marc Bezem

  2. Department of Computer Science, Chalmers University of Technology and Gothenburg University, SE-412 96, Göteborg, Sweden

    Thierry Coquand

Authors
  1. Marc Bezem
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  2. Thierry Coquand
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Editor information

Editors and Affiliations

  1. University of Miami, USA

    Geoff Sutcliffe

  2. University of Manchester, UK

    Andrei Voronkov

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© 2005 Springer-Verlag Berlin Heidelberg

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Bezem, M., Coquand, T. (2005). Automating Coherent Logic. In: Sutcliffe, G., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2005. Lecture Notes in Computer Science(), vol 3835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11591191_18

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  • DOI: https://doi.org/10.1007/11591191_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30553-8

  • Online ISBN: 978-3-540-31650-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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