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Concept Graphs with Subdivision: A Semantic Approach

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Conceptual Structures for Knowledge Creation and Communication (ICCS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2746))

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Abstract.

The semantic approach defines a concept graph with subdivision as a mathematical structure derived from a triadic power context family. The aim of introducing concept graphs with subdivision is to represent modal information mathematically. Based on the notion of the conceptual content of a concept graph with subdivision, we can show that the concept graphs with subdivision of a triadic power context family form a complete lattice with respect to the information order. Finally, our approach is extended to existential concept graphs with subdivision.

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References

  1. Bätschmann, O., Griener, P.: Hans Holbein d. J. Die Darmstädter Madonna. Fischer Taschenbuch Verlag, Frankfurt (1998)

    Google Scholar 

  2. Biedermann, K.: A foundation of the theory of trilattices. Dissertation, TU Darmstadt 1998. Shaker Verlag, Aachen (1998)

    Google Scholar 

  3. Brandom, R.B.: Making it explicit. Reasoning, representing, and discursive commitment. Havard University Press, Cambridge (1994)

    Google Scholar 

  4. Dau, F., Wille, R.: On the modal understanding of triadic contexts. In: Decker, R., Gaul, W. (eds.) Classification and information processing at the turn of the millennium, pp. 83–94. Spinger, Heidelberg (2000)

    Google Scholar 

  5. Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1996); German version: Springer, Heidelberg (1996)

    MATH  Google Scholar 

  6. Groh, B., Wille, R.: Lattices of triadic concept graphs. In: Ganter, B., Mineau, G.W. (eds.) ICCS 2000. LNCS (LNAI), vol. 1867, pp. 332–341. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  7. Lehmann, F., Wille, R.: A triadic approach to formal concept analysis. In: Ellis, G., Rich, W., Levinson, R., Sowa, J.F. (eds.) ICCS 1995. LNCS (LNAI), vol. 954, pp. 32–43. Springer, Heidelberg (1995)

    Google Scholar 

  8. Wille, R.: The basic theorem of triadic concept analysis. Order 12, 149–158 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Wille, R.: Triadic concept graphs. In: Mugnier, M.-L., Chein, M. (eds.) ICCS 1998. LNCS (LNAI), vol. 1453, pp. 194–208. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  10. Wille, R.: Existential concept graphs of power context families. In: Priss, U., Corbett, D.R., Angelova, G. (eds.) ICCS 2002. LNCS (LNAI), vol. 2393, pp. 382–395. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Wille, R., Zickwolff, M.: Grundlagen einer triadischen Begriffsanalyse. In: Stumme, G., Wille, R. (eds.) Begriffliche Wissensverarbeitung: Methoden und Anwendungen, pp. 125–150. Springer, Heidelberg (2000)

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, D-64289, Darmstadt, Germany

    Lars Schoolmann & Rudolf Wille

Authors
  1. Lars Schoolmann
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  2. Rudolf Wille
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Editor information

Editors and Affiliations

  1. Institute of Algebra, University of Technology, Dresden, Germany

    Bernhard Ganter

  2. Semantics Technology and Applications Research Laboratory (STARLab), Department of Computer Science, Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Brussels 5, Belgium

    Aldo de Moor

  3. Institut für Algebra, Technische Universität Dresden, 01062, Dresden, Germany

    Wilfried Lex

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Schoolmann, L., Wille, R. (2003). Concept Graphs with Subdivision: A Semantic Approach. In: Ganter, B., de Moor, A., Lex, W. (eds) Conceptual Structures for Knowledge Creation and Communication. ICCS 2003. Lecture Notes in Computer Science(), vol 2746. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45091-7_19

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  • DOI: https://doi.org/10.1007/978-3-540-45091-7_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40576-4

  • Online ISBN: 978-3-540-45091-7

  • eBook Packages: Springer Book Archive

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