Journal of Formalized Mathematics
Volume 11, 1999
University of Bialystok
Copyright (c) 1999 Association of Mizar Users

A Characterization of Concept Lattices. Dual Concept Lattices


Christoph Schwarzweller
University of Tuebingen

Summary.

In this article we continue the formalization of concept lattices following [6]. We give necessary and sufficient conditions for a complete lattice to be isomorphic to a given formal context. As a by-product we get that a lattice is complete if and only if it is isomorphic to a concept lattice. In addition we introduce dual formal concepts and dual concept lattices and prove that the dual of a concept lattice over a formal context is isomorphic to the concept lattice over the dual formal context.

MML Identifier: CONLAT_2

The terminology and notation used in this paper have been introduced in the following articles [13] [5] [17] [8] [14] [2] [12] [18] [9] [16] [15] [1] [11] [4] [3] [19] [7] [10]

Contents (PDF format)

  1. Preliminaries
  2. The Characterization
  3. Dual Concept Lattices

Bibliography

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[6] Bernhard Ganter and Rudolf Wille. \em Formal Concept Analysis. Springer Verlag, Berlin, Heidelberg, New York, 1996. (written in German).
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[14] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[15] Andrzej Trybulec. Finite join and finite meet, and dual lattices. Journal of Formalized Mathematics, 2, 1990.
[16] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[17] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[18] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[19] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received August 17, 1999

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