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

  • Phil Scott
  • Jacques Fleuriot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6877)


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.


Automate Tool Discovery Tool Proof Script Proof Language Proof Context 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Phil Scott
    • 1
  • Jacques Fleuriot
    • 1
  1. 1.Centre for Intelligent Systems and their Applications, Informatics ForumUniversity of EdinburghEdinburghUK

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