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