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A Mathematical Model for Conceptual Knowledge Systems

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Classification, Data Analysis, and Knowledge Organization

Abstract

Objects, attributes, and concepts are basic notions of conceptal knowledge; they are linked by the following four basic relations : an object has an attribute, an object belongs to a concept, an attribute abstracts from a concept, and a concept is a subconcept of another concept. These structural elements are well mathematized in formal concept analysis. Therefore, conceptual knowledge systems can be mathematically modelled in the frame of formal concept analysis. How such modelling may be performed is indicated by an example of a conceptual knowledge system. The formal definition of the model finally clarifies in which ways representation, inference, acquisition, and communication of conceptual knowledge can be mathematically treated.

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Author information

Authors and Affiliations

  1. Forschungsgruppe Begriffsanalyse Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstr. 7, D-6100, Darmstadt, Germany

    Peter Luksch & Rudolf Wille

Authors
  1. Peter Luksch
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  2. Rudolf Wille
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Editor information

Editors and Affiliations

  1. Institut für Statistik und Wirtschaftsmathematik, Rheinisch-Westfälische Technische Hochschule Aachen, Wüllnerstraße 3, D-5100, Aachen, Germany

    Hans-Hermann Bock

  2. Institut für Medizinische Biometrie, Philipps-Universität Marburg, Bunsenstraße 3, D-3500, Marburg, Germany

    Peter Ihm

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© 1991 Springer-Verlag Berlin · Heidelberg

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Luksch, P., Wille, R. (1991). A Mathematical Model for Conceptual Knowledge Systems. In: Bock, HH., Ihm, P. (eds) Classification, Data Analysis, and Knowledge Organization. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76307-6_21

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  • DOI: https://doi.org/10.1007/978-3-642-76307-6_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53483-9

  • Online ISBN: 978-3-642-76307-6

  • eBook Packages: Springer Book Archive

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