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Emphasizing Human Techniques in Automated Geometry Theorem Proving: A Practical Realization

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Automated Deduction in Geometry (ADG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2061))

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Abstract

The underlying principles and main original techniques used in a running generic logic-based theorem prover are presented. The system (a prototype) is called HOARDATINF (Human Oriented Automated Reasoning on your Desk) and has been specialized in this work to proof learning through geometry. It is based on a new calculus, particularly suited to the class of problems we deal with. The calculus allows treatment of equality and automatic model building. HOARDATINF has some other original characteristics such as proving by analogy (using matching techniques), some possibilities of discovering lemmata (using diagrams), handling standard theories in geometry such as commutativity and symmetry (by encoding them in the unification algorithm used by the calculus), and proof verification in a rather large sense (by using capabilities of the calculus).

As this work is intended to set theoretical bases of a new logic-based approach to geometry theorem proving, a comparison of features of our system with respect to those of other important, representative logic-based systems is given. Some running examples give a good taste of the HOARDATINF capabilities. One of these examples allows us to compare qualitatively our approach with that of a powerful prover described in a recent paper [8]. Some directions of future research are mentioned.

Acknowledgements

We thank an anonymous referee for a lot of detailed and constructive remarks that helped us to improve the presentation of this paper.

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Authors and Affiliations

  1. Laboratoire LEIBNIZ-IMAG, 46, Avenue Félix Viallet, 38031, Grenoble Cedex, France

    Ricardo Caferra, Nicolas Peltier & François Puitg

Authors
  1. Ricardo Caferra
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  2. Nicolas Peltier
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  3. François Puitg
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Editors and Affiliations

  1. Zentrum Mathematik, SB4, Technische Universität München, 80290, München, Germany

    Jürgen Richter-Gebert

  2. Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie — CNRS, 4 place Jussieu, 75252, Paris Cedex 05, France

    Dongming Wang

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© 2001 Springer-Verlag Berlin Heidelberg

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Caferra, R., Peltier, N., Puitg, F. (2001). Emphasizing Human Techniques in Automated Geometry Theorem Proving: A Practical Realization. In: Richter-Gebert, J., Wang, D. (eds) Automated Deduction in Geometry. ADG 2000. Lecture Notes in Computer Science(), vol 2061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45410-1_16

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  • DOI: https://doi.org/10.1007/3-540-45410-1_16

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  • Print ISBN: 978-3-540-42598-4

  • Online ISBN: 978-3-540-45410-6

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