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Congruence Lattices of Finite Lattices as Concept Lattices

  • Sigrid Knecht
  • Rudolf Wille

Abstract

In formal concept analysis it is of increasing interest to compute and to represent congruence lattices of finite lattices (for instance, to assist adequate drawings of concept lattices). In this note we give a representation of such congruence lattices as concept lattices which allows the use of developed computer programs to determine and to draw those congruence lattices. For basic notions and results of formal concept analysis we refer to [3] and [5].

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References

  1. [1]
    P. Crawley, R.P. Dilworth: Algebraic theory of lattices. Prentice-Hall, Englewood Cliffs 1973.zbMATHGoogle Scholar
  2. [2]
    K. Reuter, R. Wille: Complete congruence relations of concept lattices. Acta Sci. Math. 51 (1987), 319–327.MathSciNetzbMATHGoogle Scholar
  3. [3]
    R. Wille: Restructuring lattice theory: an approach based on hierarchies of concepts. In: I. Rival (ed.): Ordered Sets. Reidel, Dordrecht-Boston, 1982, 445–470.CrossRefGoogle Scholar
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    R. Wille: Subdirect decomposition of concept lattices. Algebra Universalis 17 (1983), 275–287.MathSciNetzbMATHCrossRefGoogle Scholar
  5. [5]
    R. Wille: Liniendiagramme hierarchischer Begriffssysteme. In: H.H. Bock (Hrsg.): Anwendungen der Klassifikation: Datenanalyse und numerische Klassifikation. INDEKS Verlag, Frankfurt 1984, 34–51; engl. translation: Line diagrams of hierarchical concept systems. International Classification 11 (1984), 77-86.Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Sigrid Knecht
    • 1
  • Rudolf Wille
    • 1
  1. 1.Arbeitsgruppe Allgemeine Algebra Fachbereich MathematikTechnische Hochschule DarmstadtGermany

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