The Basic Theorem on Preconcept Lattices

  • Christian Burgmann
  • Rudolf Wille
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3874)


Preconcept Lattices are identified to be (up to isomorphism) the completely distributive complete lattices in which the supremum of all atoms is equal or greater than the infimum of all coatoms. This is a consequence of the Basic Theorem on Preconcept Lattices, which also offers means for checking line diagrams of preconcept lattices.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ba54]
    Balachandran, V.K.: A characterization of ΣΔ-rings of subsets. Fundamenta Mathematica 41, 38–41 (1954)zbMATHMathSciNetGoogle Scholar
  2. [BD74]
    Balbes, R., Dwinger, P.: Distributive lattices. University of Missouri Press, Columbia (1974)zbMATHGoogle Scholar
  3. [GW99]
    Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999), German version: Springer, Heidelberg (1996)zbMATHGoogle Scholar
  4. [Pi73]
    Piaget, J.: Einführung in die genetische Erkenntnistheorie. Suhrkamp taschenbuch wissenschaft 6. Suhrkamp, Frankfurt (1973)Google Scholar
  5. [Ra52]
    Raney, G.N.: Completely distributive lattices. Proc. Amer. Matm. Soc. 3, 677–680 (1952)zbMATHCrossRefMathSciNetGoogle Scholar
  6. [SW86]
    Stahl, J., Wille, R.: Preconcepts and set representations of contexts. In: Gaul, W., Schader, M. (eds.) Classification as a tool of research, pp. 431–438. North-Holland, Amsterdam (1986)Google Scholar
  7. [Wi04]
    Wille, R.: Preconcept algebras and generalized double Boolean algebras. In: Eklund, P. (ed.) ICFCA 2004. LNCS (LNAI), vol. 2961, pp. 1–13. Springer, Heidelberg (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Christian Burgmann
    • 1
  • Rudolf Wille
    • 1
  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadt

Personalised recommendations