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Mechanical Theorem Proving in Tarski’s Geometry

  • Julien Narboux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4869)

Abstract

This paper describes the mechanization of the proofs of the first height chapters of Schwabäuser, Szmielew and Tarski’s book: Metamathematische Methoden in der Geometrie. The proofs are checked formally using the Coq proof assistant. The goal of this development is to provide foundations for other formalizations of geometry and implementations of decision procedures. We compare the mechanized proofs with the informal proofs. We also compare this piece of formalization with the previous work done about Hilbert’s Grundlagen der Geometrie. We analyze the differences between the two axiom systems from the formalization point of view.

Keywords

Decision Procedure Formal Proof Axiom System Proof Assistant Transitivity Property 
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 2007

Authors and Affiliations

  • Julien Narboux
    • 1
  1. 1.Équipe LogiCal, LIX, École Polytechnique, 91128 Palaiseau CedexFrance

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