Order

, Volume 12, Issue 2, pp 149–158 | Cite as

The Basic Theorem of triadic concept analysis

  • Rudolf Wille
Article

Abstract

Experiences with applications of concept lattices and the pragmatic philosophy founded by Ch. S. Peirce have suggested a triadic approach to formal concept analysis. It starts with the notion of atriadic context combiningobjects, attributes, andconditions under which objects may have certain attributes.The Basic Theorem of triadic concept analysis clarifies the class of structures which are formed by thetriadic concepts of triadic contexts: These structures are exactly thecomplete trilattices up to isomorphism.

Mathematics Subject Classifications (1991)

06A23 62-07 

Key words

Triordered sets complete trilattices formal concept analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ganter, B. (1987) Algorithmen zur Formalen Begriffsanalyse, in B. Ganter, R. Wille, and K. E. Wolff (eds),Beiträge zur Begriffsanalyze, B.I.-Wissenschaftsverlag, Mannheim, pp. 241–254.Google Scholar
  2. 2.
    Ganter, B. and Krauße, R. (1994)TRICEPT — Programm zur triadischen Begriffsanalyse, Institut für Algebra, TU Dresden.Google Scholar
  3. 3.
    Ganter, B. and Wille, R. (in preparation)Formale Begriffsanalyse: Mathematische Grundlagen, Springer-Verlag, Berlin-Heidelberg.Google Scholar
  4. 4.
    Krolak-Schwerdt, S., Orlik, P., and Ganter, B. (1994) TRIPAT: a model for analyzing threemode binary data, in H.-H. Bock, W. Lenski, and M. M. Richter (eds),Information Systems and Data Analysis, Springer, Berlin-Heidelberg, pp. 298–307.Google Scholar
  5. 5.
    Lehmann, F. and Wille, R. (1995) A triadic approach to formal concept analysis, FB4-Preprint Nr. 1738, TH Darmstadt.Google Scholar
  6. 6.
    Peirce, Ch. S.Collected Papers, Harvard Univ. Press, Cambridge, 1931–1935.Google Scholar
  7. 7.
    Wille, R. (1982) Restructuring lattice theory: an approach based on hierarchies of concepts, in I. Rival (ed.)Ordered Sets, Reidel, Dordrecht-Boston 1982, pp. 445–470.Google Scholar
  8. 8.
    Wille, R. (1992) Concept lattices and conceptual knowledge systems.Computers and Mathematics with Applications 23, 493–515.Google Scholar
  9. 9.
    Wille, R. (1994) Plädoyer für eine philosophische Grundlegung der Begrifflichen Wissensverarbeitung, in R. Wille and M. Zickwolff (Hrsg.),Begriffliche Wissensverarbeitung: Grundfragen und Aufgaben. B.I.-Wissenschaftsverlag, Mannheim 1994, pp. 11–25.Google Scholar
  10. 10.
    Wille, R. (1994) Restructuring mathematical logic: an approach based on Peirce's pragmatism, in P. Agliano and A. Ursini (eds),International Conference on Logic and Algebra, Siena (to appear).Google Scholar
  11. 11.
    Wille, R. and Wille, U. (1992) Coordinatization of ordinal structures, FB4-Preprint Nr. 1454, TH Darmstadt.Google Scholar
  12. 12.
    Wille, R. and Wille, U. (1994) Uniqueness of coordinatizations of ordinal structures, FB4-Preprint Nr. 1671, TH Darmstadt.Google Scholar
  13. 13.
    Wille, U. (1995) Geometric representation of ordinal contexts, Doctoral Thesis, Universität Gießen.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Rudolf Wille
    • 1
  1. 1.Fachbereich MathematikTechnishe Hochschule DarmstadtDarmstadtGermany

Personalised recommendations