Journal of Formalized Mathematics
Volume 10, 1998
University of Bialystok
Copyright (c) 1998 Association of Mizar Users

Introduction to Concept Lattices


Christoph Schwarzweller
University of T\"ubingen

Summary.

In this paper we give Mizar formalization of concept lattices. Concept lattices stem from the so-called formal concept analysis - a part of applied mathematics that brings mathematical methods into the field of data analysis and knowledge processing. Our approach follows the one given in [8].

MML Identifier: CONLAT_1

The terminology and notation used in this paper have been introduced in the following articles [11] [6] [14] [12] [15] [4] [3] [17] [16] [5] [13] [9] [7] [1] [10] [2]

Contents (PDF format)

  1. Formal Contexts
  2. Derivation Operators
  3. Formal Concepts
  4. Concept Lattices

Bibliography

[1] Grzegorz Bancerek. Complete lattices. Journal of Formalized Mathematics, 4, 1992.
[2] Grzegorz Bancerek. Directed sets, nets, ideals, filters, and maps. Journal of Formalized Mathematics, 8, 1996.
[3] Czeslaw Bylinski. Binary operations. Journal of Formalized Mathematics, 1, 1989.
[4] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[5] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.
[6] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.
[7] Czeslaw Bylinski. Galois connections. Journal of Formalized Mathematics, 8, 1996.
[8] Bernhard Ganter and Rudolf Wille. \em Formal Concept Analysis. Springer Verlag, Berlin, Heidelberg, New York, 1996. (written in German).
[9] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Journal of Formalized Mathematics, 8, 1996.
[10] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.
[11] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.
[12] Andrzej Trybulec. Tuples, projections and Cartesian products. Journal of Formalized Mathematics, 1, 1989.
[13] Wojciech A. Trybulec. Partially ordered sets. Journal of Formalized Mathematics, 1, 1989.
[14] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.
[15] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.
[16] Edmund Woronowicz. Relations defined on sets. Journal of Formalized Mathematics, 1, 1989.
[17] Stanislaw Zukowski. Introduction to lattice theory. Journal of Formalized Mathematics, 1, 1989.

Received October 2, 1998


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