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Employing Theory Formation to Guide Proof Planning

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Artificial Intelligence, Automated Reasoning, and Symbolic Computation (AISC 2002, Calculemus 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2385))

Abstract

The invention of suitable concepts to characterise mathematical structures is one of the most challenging tasks for both human mathematicians and automated theorem provers alike. We present an approach where automatic concept formation is used to guide non-isomorphism proofs in the residue class domain. The main idea behind the proof is to automatically identify discriminants for two given structures to show that they are not isomorphic. Suitable discriminants are generated by a theory formation system; the overall proof is constructed by a proof planner with the additional support of traditional automated theorem provers and a computer algebra system.

The author’s work is supported by EPSRC grant GR/M98012 and European Union IHP grant CALCULEMUS HPRN-CT-2000-00102. He is also affiliated with the Department of Computer Science at the University of York.

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Author information

Authors and Affiliations

  1. Fachbereich Informatik, Universität des Saarlandes, Germany

    Andreas Meier

  2. School of Computer Science, University of Birmingham, UK

    Volker Sorge

  3. Division of Informatics, University of Edinburgh, UK

    Simon Colton

Authors
  1. Andreas Meier
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  2. Volker Sorge
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  3. Simon Colton
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Editor information

Editors and Affiliations

  1. University of Karlsruhe (TH), Am Fasanengarten 5, Postfach 6980, D-76128, Karlsruhe, Germany

    Jacques Calmet

  2. CMI, Université de Provence, 39 rue F. Juliot-Curie, 13453, Marseille Cedex 13, France

    Belaid Benhamou

  3. Research Institute for Symbolic Computation (RISC-Linz), Johannes Kepler University, A-4040, Linz, Austria

    Olga Caprotti

  4. ESIL, Université de la Méditerannée, 163 Avenue de Luminy, Marseille Cedex 09, France

    Laurent Henocque

  5. School of Computer Science, University of Birmingham, Birmingham, B15 2TT, UK

    Volker Sorge

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© 2002 Springer-Verlag Berlin Heidelberg

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Meier, A., Sorge, V., Colton, S. (2002). Employing Theory Formation to Guide Proof Planning. In: Calmet, J., Benhamou, B., Caprotti, O., Henocque, L., Sorge, V. (eds) Artificial Intelligence, Automated Reasoning, and Symbolic Computation. AISC Calculemus 2002 2002. Lecture Notes in Computer Science(), vol 2385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45470-5_25

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  • DOI: https://doi.org/10.1007/3-540-45470-5_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43865-6

  • Online ISBN: 978-3-540-45470-0

  • eBook Packages: Springer Book Archive

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