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Automatic Verification of Regular Constructions in Dynamic Geometry Systems

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Automated Deduction in Geometry (ADG 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4869))

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Abstract

We present an application of automatic theorem proving (ATP) in the verification of constructions made with dynamic geometry software (DGS). Given a specification language for geometric constructions, we can use its processor to deal with syntactic errors. The processor can also detect semantic errors — situations when, for a given concrete set of geometrical objects, a construction is not possible. However, dynamic geometry tools do not test if, for a given set of geometrical objects, a construction is geometrically sound, i.e., if it is possible in a general case. Using ATP, we can do this last step by verifying the geometric constructions deductively. We have developed a system for the automatic verification of regular constructions (made within DGSs GCLC and Eukleides), using our ATP system, GCLCprover. This gives a real-world application of ATP in dynamic geometry tools.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia

    Predrag Janičić

  2. Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal

    Pedro Quaresma

Authors
  1. Predrag Janičić
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  2. Pedro Quaresma
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Francisco Botana Tomas Recio

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Janičić, P., Quaresma, P. (2007). Automatic Verification of Regular Constructions in Dynamic Geometry Systems. In: Botana, F., Recio, T. (eds) Automated Deduction in Geometry. ADG 2006. Lecture Notes in Computer Science(), vol 4869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77356-6_3

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  • DOI: https://doi.org/10.1007/978-3-540-77356-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77355-9

  • Online ISBN: 978-3-540-77356-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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