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