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The Basic Theorem of triadic concept analysis

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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.

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References

  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. Ganter, B. and Krauße, R. (1994)TRICEPT — Programm zur triadischen Begriffsanalyse, Institut für Algebra, TU Dresden.

    Google Scholar 

  3. Ganter, B. and Wille, R. (in preparation)Formale Begriffsanalyse: Mathematische Grundlagen, Springer-Verlag, Berlin-Heidelberg.

  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. Lehmann, F. and Wille, R. (1995) A triadic approach to formal concept analysis, FB4-Preprint Nr. 1738, TH Darmstadt.

  6. Peirce, Ch. S.Collected Papers, Harvard Univ. Press, Cambridge, 1931–1935.

    Google Scholar 

  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. Wille, R. (1992) Concept lattices and conceptual knowledge systems.Computers and Mathematics with Applications 23, 493–515.

    Google Scholar 

  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. 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).

  11. Wille, R. and Wille, U. (1992) Coordinatization of ordinal structures, FB4-Preprint Nr. 1454, TH Darmstadt.

  12. Wille, R. and Wille, U. (1994) Uniqueness of coordinatizations of ordinal structures, FB4-Preprint Nr. 1671, TH Darmstadt.

  13. Wille, U. (1995) Geometric representation of ordinal contexts, Doctoral Thesis, Universität Gießen.

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  1. Fachbereich Mathematik, Technishe Hochschule Darmstadt, 64289, Darmstadt, Germany

    Rudolf Wille

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  1. Rudolf Wille
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Communicated by I. Rival

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Wille, R. The Basic Theorem of triadic concept analysis. Order 12, 149–158 (1995). https://doi.org/10.1007/BF01108624

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