Mathematics in Computer Science

, Volume 7, Issue 4, pp 439–454 | Cite as

Formalization and Specification of Geometric Knowledge Objects

  • Xiaoyu ChenEmail author
  • Dongming Wang


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.


Embedded knowledge Formal specification Semantic representation Knowledge management 

Mathematics Subject Classification (2010)

68T30 68P05 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.State Key Laboratory of Software Development Environment, School of Computer Science and EngineeringBeihang UniversityBeijingChina
  2. 2.Laboratoire d’Informatique de Paris 6Université Pierre et Marie Curie, CNRSParis Cedex 05France

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