Skip to main content
SpringerLink
Log in
Book cover

International Conference on Formal Concept Analysis

ICFCA 2014: Formal Concept Analysis pp 1–14Cite as

Learning Spaces, and How to Build Them

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8478))

Abstract

In Knowledge Space Theory (KST), a knowledge structure encodes a body of information as a domain, consisting of all the relevant pieces of information, together with the collection of all possible states of knowledge, identified with specific subsets of the domain. Knowledge spaces and learning spaces are defined through pedagogically natural requirements on the collection of all states. We explain here several ways of building in practice such structures on a given domain. In passing we point out some connections linking KST with Formal Concept Analysis (FCA).

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Berge, C.: Hypergraphs. Combinatorics of finite sets, Transl. from the French. North-Holland, Amsterdam (1989)

    Google Scholar 

  • Birkhoff, G.: Lattice Theory. American Mathematical Society, Providence (1967)

    MATH  Google Scholar 

  • Buekenhout, F.: Espaces à fermeture. Bull. Soc. Math. Belg. 19, 147–178 (1967)

    MATH  MathSciNet  Google Scholar 

  • Caspard, N., Monjardet, B.: Some lattices of closure systems on a finite set. Discrete Math. Theor. Comput. Sci. 6(2), 163–190 (electronic) (2004)

    Google Scholar 

  • Cosyn, E., Uzun, H.B.: Note on two necessary and sufficient axioms for a well-graded knowledge space. J. Math. Psych. 53, 40–42 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  • Doignon, J.-P., Falmagne, J.-C.: Well-graded families of relations. Discrete Math. 173, 35–44 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  • Doignon, J.-P., Falmagne, J.-C.: Knowledge Spaces. Springer, Berlin (1999)

    Book  MATH  Google Scholar 

  • Doignon, J.-P., Falmagne, J.-C.: Knowledge Spaces and Learning Spaces. To appear in: Batchelder, W.H., Colonius, H., Dzhafarov, E.N., Myung, J. (eds.) New Handbook of Mathematical Psychology (in press)

    Google Scholar 

  • Edelman, P.H., Jamison, R.E.: The theory of convex geometries. Geom. Dedicata 19, 247–270 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  • Eppstein, D., Falmagne, J.-C., Uzun, H.B.: On verifying and engineering the wellgradedness of a union-closed family. J. Math. Psych. 53, 34–39 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  • Falmagne, J.-C., Doignon, J.-P.: Learning Spaces. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  • Ganter, B., Wille, R.: Formale Begriffsanalyse: Mathematische Grundlagen. Springer, Heidelberg (1996); English translation by Franske, C.: Formal Concept Analysis: Mathematical Foundations

    Google Scholar 

  • Jamison, R.E.: Copoints in antimatroids. In: Proceedings of the Eleventh Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1980), vol. II. Congr. Numer., vol. 29, pp. 535–544 (1980)

    Google Scholar 

  • Jamison, R.E.: A perspective on abstract convexity: classifying alignments by varieties. In: Convexity and Related Combinatorial Geometry (Norman, Okla., 1980). Lecture Notes in Pure and Appl. Math., vol. 76, pp. 113–150. Dekker, New York (1982)

    Google Scholar 

  • Koppen, M.: Extracting human expertise for constructing knowledge spaces: An algorithm. J. Math. Psych. 37, 1–20 (1993)

    Article  MATH  Google Scholar 

  • Koppen, M.: On alternative representations for knowledge spaces. Math. Social Sci. 36, 127–143 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  • Koppen, M., Doignon, J.-P.: How to build a knowledge space by querying an expert. J. Math. Psych. 34, 311–331 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • Korte, B., Lovász, L., Schrader, R.: Greedoids. Algorithms and Combinatorics, vol. 4. Springer, Berlin (1991)

    Google Scholar 

  • Rusch, A., Wille, R.: Knowledge spaces and formal concept analysis. In: Bock, H.-H., Polasek, W. (eds.) Data Analysis and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg (1996)

    Google Scholar 

  • Spoto, A., Stefanutti, L., Vidotto, G.: Knowledge space theory, formal concept analysis, and computerized psychological assessment. Behavior Res. Meth. 42, 342–350 (2010)

    Article  Google Scholar 

  • van de Vel, M.L.J.: Theory of convex structures. North-Holland, Amsterdam (1993)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Université Libre de Bruxelles, c.p. 216, Bd du Triomphe, 1050, Brussels, Belgium

    Jean-Paul Doignon

Authors
  1. Jean-Paul Doignon
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technische Universität Dresden, 01062, Dresden, Germany

    Cynthia Vera Glodeanu

  2. INSA-Lyon, CNRS, LIRIS UMR 5205, 9621, 69621, Lyon, France

    Mehdi Kaytoue

  3. Babes-Bolyai University, 400084, Cluj, Romania

    Christian Sacarea

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Doignon, JP. (2014). Learning Spaces, and How to Build Them. In: Glodeanu, C.V., Kaytoue, M., Sacarea, C. (eds) Formal Concept Analysis. ICFCA 2014. Lecture Notes in Computer Science(), vol 8478. Springer, Cham. https://doi.org/10.1007/978-3-319-07248-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-07248-7_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07247-0

  • Online ISBN: 978-3-319-07248-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation