FCA Examples

This webpage shows some of Rudolf Wille’s “classic” examples of formal contexts. (The references for the papers from which they are taken are below.) The examples are provided here without explanation of their background (which can be found in Wille’s papers). It is reasonably challenging to derive good layouts for these examples. Thus these examples can serve as test cases for graph layout software. The lattice diagrams which have blue lines were drawn with ConExp. All other diagrams were produced with FcaStone, which uses Graphviz for its layouts. A more detailed comparison of these examples can be found in Priss (2008) (pdf).

The focus of these examples is graph layout. Other data sets are needed for testing algorithms for buildling lattices.

Digits

Tea Ladies

Lattice of lattice properties

Bodies of water

Live in water

Sources

Digits:
Stahl, J.; Wille, R. (1986). Preconcepts and set representation of contexts. In: Gaul & Schader (eds): Classification as a tool of research. 

Bodies of water, live in water:
Wille, Rudolf (1984). Liniendiagramme hierarchischer Begriffssysteme. Studien zur Klassifikation. Indeks Verlag.

Tealadys, lattice of lattice properties:
Wille, Rudolf (1992). Concept Lattices and Conceptual Knowledge Systems. Computers Math. Applic., 23, 6-9, p 493-515.

CXT files for dowload

digits.cxt

B

10
7

0
1
2
3
4
5
6
7
8
9
a
b
c
d
e
f
g
X.XXXXX
.....XX
XXX.XX.
XXX..XX
.X.X.XX
XXXX..X
.XXXX.X
X....XX
XXXXXXX
XX.X.XX

liveinwater.cxt

B

8
9

fish leech
bream
frog
dog
water weeds
reed
bean
corn
needs water to live
lives in water
lives on land
needs chlorophyll
dicotyledon
monocotyledon
can move
has limbs
breast feeds
XX....X..
XX....XX.
XXX...XX.
X.X...XXX
XX.X.X...
XXXX.X...
X.XXX....
X.XX.X...

bodiesofwater.cxt

B

8
6

Fluss
Bach
Kanal
Graben
See
Tuempel
Teich
Becken
fliessend
stehend
natuerlich
kuenstlich
gross
klein
X.X.X.
X.X..X
X..XX.
X..X.X
.XX.X.
.XX..X
.X.XX.
.X.X.X

tealadies.cxt

B

18
14

Evelyn
Laura
Theresa
Brenda
Charlotte
Frances
Eleanor
Pearl
Ruth
Verne
Myra
Katherine
Syliva
Nora
Helen
Dorothy
Olivia
Flora
1
2
3
4
5
6
7
8
9
10
11
12
13
14
XXXXXX.XX.....
XXX.XXXX......
.XXXXXXXX.....
X.XXXXXX......
..XXX.X.......
..X.XX.X......
....XXXX......
.....X.XX.....
....X.XXX.....
......XXX..X..
.......XXX.X..
.......XXX.XXX
......XXXX.XXX
.....XX.XXXXXX
......XX.XXX..
.......XX.....
........X.X...
........X.X...

latticeoflatticeproperties.cxt

B

14
16

I
II
III
IV
1
2
3
4
5
6
7
8
9
10
Boolean lattice
CDS lattice
geometric lattice
metric lattice
atomistic
Brouwerian
complemented
distributive
dually semimodular
graded
modular
relatively complemented
sectionally complemented
semimodular
Stonean
uniquely complemented
XXXXXXXXXXXXXXXX
.X..X.X.XX..X...
..X.X.X..X.XXX..
...X....XXX..X..
...X.X.XXXX..XX.
.XXXX.X.XXXXXX..
....X.X....XX...
..X.X.X..X.XXX..
....X...XX......
...X.X.XXXX..X..
....X.X..X......
......X..X...X..
.X..X.X.XX..X...
.X..X.X.XX.XX...

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