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Integrating Boolean and Mathematical Solving: Foundations, Basic Algorithms, and Requirements

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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))

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Abstract

In the last years we have witnessed an impressive advance in the efficiency of boolean solving techniques, which has brought large previously intractable problems at the reach of state-of-the-art solvers. Unfortunately, simple boolean expressions are not expressive enough for representing many real-world problems, which require handling also integer or real values and operators. On the other hand, mathematical solvers, like computer-algebra systems or constraint solvers, cannot handle efficiently problems involving heavy boolean search, or do not handle them at all. In this paper we present the foundations and the basic algorithms for a new class of procedures for solving boolean combinations of mathematical propositions, which combine boolean and mathematical solvers, and we highlight the main requirements that boolean and mathematical solvers must fulfill in order to achieve the maximum benefits from their integration. Finally we show how existing systems are captured by our framework.

This work is sponsored by the CALCULEMUS! IHP-RTN EC project, contract code HPRN-CT-2000-00102, and has thus benefited of the financial contribution of the Commission through the IHP programme.

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Author information

Authors and Affiliations

  1. ITC-IRST, Povo, Trento, Italy

    Gilles Audemard, Piergiorgio Bertoli, Alessandro Cimatti, Artur Korniłowicz & Roberto Sebastiani

  2. LSIS, University of Provence, Marseille, France

    Gilles Audemard

  3. Institute of Computer Science, University of Białystok, Poland

    Artur Korniłowicz

  4. DIT, Università di Trento, Povo, Trento, Italy

    Roberto Sebastiani

Authors
  1. Gilles Audemard
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  2. Piergiorgio Bertoli
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  3. Alessandro Cimatti
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  4. Artur Korniłowicz
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  5. Roberto Sebastiani
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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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Audemard, G., Bertoli, P., Cimatti, A., Korniłowicz, A., Sebastiani, R. (2002). Integrating Boolean and Mathematical Solving: Foundations, Basic Algorithms, and Requirements. 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_22

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  • DOI: https://doi.org/10.1007/3-540-45470-5_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43865-6

  • Online ISBN: 978-3-540-45470-0

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