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The Basic Theorem on Preconcept Lattices

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Formal Concept Analysis

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3874))

Abstract

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.

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References

  1. Balachandran, V.K.: A characterization of ΣΔ-rings of subsets. Fundamenta Mathematica 41, 38–41 (1954)

    MATH  MathSciNet  Google Scholar 

  2. Balbes, R., Dwinger, P.: Distributive lattices. University of Missouri Press, Columbia (1974)

    MATH  Google Scholar 

  3. Ganter, B., Wille, R.: Formal Concept Analysis: mathematical foundations. Springer, Heidelberg (1999), German version: Springer, Heidelberg (1996)

    MATH  Google Scholar 

  4. Piaget, J.: Einführung in die genetische Erkenntnistheorie. Suhrkamp taschenbuch wissenschaft 6. Suhrkamp, Frankfurt (1973)

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  5. Raney, G.N.: Completely distributive lattices. Proc. Amer. Matm. Soc. 3, 677–680 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  6. 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. 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)

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Authors and Affiliations

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

    Christian Burgmann & Rudolf Wille

Authors
  1. Christian Burgmann
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  2. Rudolf Wille
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Editors and Affiliations

  1. Département d’informatique et d’ingénierie, Université du Québec en Outaouais, succursale B, C.P. 1250, J8X 3X7, Gatineau, Québec, Canada

    Rokia Missaoui

  2. Mathematisches Institut, Universität Bern, Sidlerstr. 5, 3012, Bern, Switzerland

    Jürg Schmidt

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© 2006 Springer-Verlag Berlin Heidelberg

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Burgmann, C., Wille, R. (2006). The Basic Theorem on Preconcept Lattices. In: Missaoui, R., Schmidt, J. (eds) Formal Concept Analysis. Lecture Notes in Computer Science(), vol 3874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11671404_5

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  • DOI: https://doi.org/10.1007/11671404_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32203-0

  • Online ISBN: 978-3-540-32204-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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