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Formalization and Specification of Geometric Knowledge Objects

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Abstract

This paper presents our work on the identification, formalization, structuring, and specification of geometric knowledge objects for the purpose of semantic representation and knowledge management. We classify geometric knowledge according to how it has been accumulated and represented in the geometric literature, formalize geometric knowledge statements by adapting the language of first-order logic, specify knowledge objects with embedded knowledge in a retrievable and extensible data structure, and organize them by modeling the hierarchic structure of relations among them. Some examples of formal specification for geometric knowledge objects are given to illustrate our approach. The underlying idea of the approach has been used successfully for automated geometric reasoning, knowledge base creation, and electronic document generation.

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Authors and Affiliations

  1. State Key Laboratory of Software Development Environment, School of Computer Science and Engineering, Beihang University, Beijing, 100191, China

    Xiaoyu Chen

  2. Laboratoire d’Informatique de Paris 6, Université Pierre et Marie Curie, CNRS, 4 Place Jussieu, BP 169, 75252, Paris Cedex 05, France

    Dongming Wang

Authors
  1. Xiaoyu Chen
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  2. Dongming Wang
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Corresponding author

Correspondence to Xiaoyu Chen.

Additional information

This paper is a substantially revised and expanded version of a research note (by the second author with the same title) published informally in Proceedings of the 6th Asian Workshop on Foundations of Software, AWFS ’09 (Hu Z, Zhang J, eds.), National Institute of Informatics, Japan, 2009, 86–98.

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Chen, X., Wang, D. Formalization and Specification of Geometric Knowledge Objects. Math.Comput.Sci. 7, 439–454 (2013). https://doi.org/10.1007/s11786-013-0167-4

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Keywords

Mathematics Subject Classification (2010)