Chapter

Automated Deduction in Geometry

Volume 6877 of the series Lecture Notes in Computer Science pp 182-200

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

  • Phil ScottAffiliated withCentre for Intelligent Systems and their Applications, Informatics Forum, University of Edinburgh
  • , Jacques FleuriotAffiliated withCentre for Intelligent Systems and their Applications, Informatics Forum, University of Edinburgh

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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.