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International Workshop on Automated Deduction in Geometry

ADG 2010: Automated Deduction in Geometry pp 182–200Cite as

An Investigation of Hilbert’s Implicit Reasoning through Proof Discovery in Idle-Time

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6877))

Abstract

In this paper, we describe how we captured and investigated incidence reasoning in Hilbert’s Foundations of Geometry by using a new discovery tool integrated into an interactive proof assistant. Our tool exploits concurrency, inferring facts independently of the user with the incomplete proof as a guide. It explores the proof space, contributes tedious lemmas and discovers alternative proofs. We show how this tool allowed us to write readable formalised proof-scripts that correspond very closely to Hilbert’s prose arguments.

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Author information

Authors and Affiliations

  1. Centre for Intelligent Systems and their Applications, Informatics Forum, University of Edinburgh, 10 Crichton Street, Edinburgh, UK, EH8 9AB

    Phil Scott & Jacques Fleuriot

Authors
  1. Phil Scott
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  2. Jacques Fleuriot
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Editor information

Editors and Affiliations

  1. LSIIT, Pôle API, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cédex, France

    Pascal Schreck  & Julien Narboux  & 

  2. Technische Universität München, Zentrum Mathematik (M10), Lehrstuhl für Geometrie und Visualisierung, Boltzmannstraße 3, 85748, Garching, Germany

    Jürgen Richter-Gebert

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Scott, P., Fleuriot, J. (2011). An Investigation of Hilbert’s Implicit Reasoning through Proof Discovery in Idle-Time. In: Schreck, P., Narboux, J., Richter-Gebert, J. (eds) Automated Deduction in Geometry. ADG 2010. Lecture Notes in Computer Science(), vol 6877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25070-5_11

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  • DOI: https://doi.org/10.1007/978-3-642-25070-5_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25069-9

  • Online ISBN: 978-3-642-25070-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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