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Ontological Engineering and Mathematical Knowledge Management: A Formalization of Projective Geometry

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Abstract

The work presented in this paper deals with the formalization of the ontology underlying projective geometry. This formalization is done by using the conceptual graph model which has been defined in the Artificial Intelligence community. Through this experiment, we endeavour to show that applying knowledge representation techniques to mathematical fields is a relevant way to improve the reliability and efficiency of tools dedicated to mathematical knowledge management. Our proposal is based on the construction of knowledge bases (defined according to ontologies) which must be considered as the core of any mathematical knowledge management tool such as mathematical search engines on the web, mathematical intelligent tutoring systems, mathematical theorem provers, etc. This paper also aims at highlighting the contributions provided by ontological engineering when dealing with mathematical knowledge management.

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Authors and Affiliations

  1. IRIN, Computer Science Research Institute (University of Nantes), 2, rue de la Houssinière, BP 92208, 44322, Nantes, France

    F. Fürst, M. Leclère & F. Trichet

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  1. F. Fürst
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  2. M. Leclère
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  3. F. Trichet
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Fürst, F., Leclère, M. & Trichet, F. Ontological Engineering and Mathematical Knowledge Management: A Formalization of Projective Geometry. Annals of Mathematics and Artificial Intelligence 38, 65–89 (2003). https://doi.org/10.1023/A:1022911730013

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