An Invitation to Knowledge Space Theory

  • Bernhard Ganter
  • Michael Bedek
  • Jürgen Heller
  • Reinhard Suck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10308)


It has been mentioned on many occasions that Formal Concept Analysis and KST, the theory of Knowledge Spaces, introduced by J.-P. Doignon and J.-C. Falmagne, are closely related in theory, but rather different in practice. It was suggested that the FCA community should learn from and contribute to KST. In a recent workshop held at Graz University of Technology, researchers from both areas started to combine their views and tried to find a common language. This article is a partial result of their effort. It invites FCA researchers to understand some ideas of KST by presenting them in the language of formal contexts and formal concepts.



This article is a partial result of an effort which has been facilitated by a workshop at Graz University of Technology. We would like to thank Dietrich Albert for hosting this workshop. It has been partly funded by the European Commission (EC) (7th Framework Programme contract no. 619762, LEA’s BOX). This document does not represent the opinion of the EC and the EC is not responsible for any use that might be made of its content.


  1. 1.
    Albert, D., Held, T.: Establishing knowledge spaces by systematical problem construction. In: Albert, D. (ed.) Knowledge Structures, pp. 78–112. Springer, New York (1994)CrossRefGoogle Scholar
  2. 2.
    Bedek, M.A., Kickmeier-Rust, M.D., Albert, D.: Formal concept analysis for modelling students in a technology-enhanced learning setting. In: ARTEL@ EC-TEL, pp. 27–33 (2015)Google Scholar
  3. 3.
    Bělohlávek, R., Vychodil, V.: Discovery of optimal factors in binary data via a novel method of matrix decomposition. J. Comput. Syst. Sci. 76(1), 3–20 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Colomb, P., Irlande, A., Raynaud, O.: Counting of moore families for n=7. In: Kwuida, L., Sertkaya, B. (eds.) ICFCA 2010. LNCS, vol. 5986, pp. 72–87. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-11928-6_6 CrossRefGoogle Scholar
  5. 5.
    Doignon, J.-P.: Knowledge spaces and skill assignments. In: Fischer, G.H., Laming, D. (eds.) Contributions to Mathematical Psychology, Psychometrics, and Methodology, pp. 111–121. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  6. 6.
    Doignon, J.-P., Falmagne, J.-C.: Knowledge Spaces. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  7. 7.
    Düntsch, I., Gediga, G.: Skills and knowledge structures. Br. J. Math. Stat. Psychol. 48(1), 9–27 (1995)CrossRefzbMATHGoogle Scholar
  8. 8.
    Falmagne, J.-C., Doignon, J.-P.: Learning Spaces. Springer, Heidelberg (2011)CrossRefzbMATHGoogle Scholar
  9. 9.
    Falmagne, J.-C., Koppen, M., Villano, M., Doignon, J.-P., Johannesen, L.: Introduction to knowledge spaces: how to build, test, and search them. Psychol. Rev. 97(2), 201 (1990)CrossRefGoogle Scholar
  10. 10.
    Ganter, B., Glodeanu, C.V.: Factors and skills. In: Glodeanu, C.V., Kaytoue, M., Sacarea, C. (eds.) ICFCA 2014. LNCS, vol. 8478, pp. 173–187. Springer, Cham (2014). doi: 10.1007/978-3-319-07248-7_13 Google Scholar
  11. 11.
    Ganter, B., Obiedkov, S.: Conceptual Exploration. Springer, Heidelberg (2016)CrossRefzbMATHGoogle Scholar
  12. 12.
    Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  13. 13.
    Gediga, G., Düntsch, I.: Skill set analysis in knowledge structures. Br. J. Math. Stat. Psychol. 55(2), 361–384 (2002)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Heller, J., Wickelmaier, F.: Minimum discrepancy estimation in probabilistic knowledge structures. Electron. Notes Discrete Math. 42, 49–56 (2013)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Korossy, K.: Modellierung von Wissen als Kompetenz und Performanz. Unpublished doctoral dissertation, see [15]. Universität Heidelberg, Germany (1993)Google Scholar
  16. 16.
    Korossy, K.: Extending the theory of knowledge spaces: a competence-performance approach. Zeitschrift für Psychol. 205(1), 53–82 (1997)Google Scholar
  17. 17.
    Korossy, K., et al.: Modeling knowledge as competence and performance. In: Albert, D., Lukas, J. (eds.) Knowledge Spaces: Theories, Empirical Research, and Applications, pp. 103–132. Lawrence Erlbaum Associates, Mahwah (1999)Google Scholar
  18. 18.
    Rusch, A., Wille, R.: Knowledge spaces and formal concept analysis. In: Bock, H.H., Polasek, W. (eds.) Data Analysis and Information Systems: Statistical and Conceptual Approaches, pp. 427–436. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  19. 19.
    Suck, R.: Parsimonious set representations of orders, a generalization of the interval order concept, and knowledge spaces. Discrete Appl. Math. 127(2), 373–386 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Suck, R.: Knowledge spaces regarded as set representations of skill structures. In: Dzhafarov, E., Perry, L. (eds.) Descriptive and Normative Approaches to Human Behavior, pp. 249–270. World Scientific, Singapore (2012)Google Scholar
  21. 21.
    Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470. Reidel, Dordrecht-Boston (1982)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Bernhard Ganter
    • 1
  • Michael Bedek
    • 2
  • Jürgen Heller
    • 3
  • Reinhard Suck
    • 4
  1. 1.Technische Universität DresdenDresdenGermany
  2. 2.Technische Universität GrazGrazAustria
  3. 3.Universität TübingenTübingenGermany
  4. 4.Universität OsnabrückOsnabrückGermany

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