Concept lattice

A population can be created using a collection of python objects:

[1]:

from galactic.population import Population
individuals = {48: 48, 36: 36, 64: 64, 56:56, 84: 84}
population=Population(individuals)
population

[1]:

<galactic.population.main.Population at 0x7ff1287fae80>

[2]:

list(population)

[2]:

['48', '36', '64', '56', '84']

A lattice can be created from a population using a set of strategies:

[3]:

from galactic.algebras.poset import HasseDiagram
from galactic.concepts import ConceptRenderer
from galactic.strategies import Lattice, Explorer
from galactic.examples.arithmetic import \
    MultipleStrategy, DivisorStrategy
lattice = Lattice(
    population=population,
    explorer=Explorer([
        MultipleStrategy(),
        DivisorStrategy(),
    ])
)

[4]:

list(str(concept) for concept in lattice)

[4]:

['M(4) and D(4032)',
 'M(4) and D(1008)',
 'M(4) and D(1344)',
 'M(4) and D(576)',
 'M(12) and D(1008)',
 'M(4) and D(504)',
 'M(4) and D(336)',
 'M(8) and D(1344)',
 'M(12) and D(144)',
 'M(16) and D(192)',
 'M(12) and D(252)',
 'M(12) and D(336)',
 'M(28) and D(168)',
 'M(8) and D(336)',
 'M(8) and D(448)',
 'M(48) and D(48)',
 'M(36) and D(36)',
 'M(64) and D(64)',
 'M(84) and D(84)',
 'M(56) and D(56)',
 'M(0) and D(1)']

[5]:

HasseDiagram(lattice, renderer=ConceptRenderer())

[5]:
../../_images/notebooks_concepts_notebook_7_0.png 
[6]:

HasseDiagram(lattice,renderer=ConceptRenderer(show_predicates=True))

[6]:
../../_images/notebooks_concepts_notebook_8_0.png 
[7]:

from galactic.strategies import Table
Table(lattice)

[7]:

Concept

Individuals

Predicates

0

M(4)D(4032)

1

D(1008)

2

D(1344)

3

D(576)

4

M(12)

5

D(504)

6

D(336)

7

M(8)

8

D(144)

9

M(16)D(192)

10

D(252)

12

M(28)D(168)

14

D(448)

15

48

M(48)D(48)

16

36

M(36)D(36)

17

64

M(64)D(64)

18

84

M(84)D(84)

19

56

M(56)D(56)

20

M(0)D(1)

 
[8]:

Table(lattice,all_individuals=True, all_predicates=True)

[8]:

Concept

Individuals

Predicates

0

['48', '36', '64', '56', '84']

M(4)D(4032)

1

['48', '36', '56', '84']

M(4)D(1008)

2

['48', '64', '56', '84']

M(4)D(1344)

3

['48', '36', '64']

M(4)D(576)

4

['48', '36', '84']

M(12)D(1008)

5

['36', '56', '84']

M(4)D(504)

6

['48', '56', '84']

M(4)D(336)

7

['48', '64', '56']

M(8)D(1344)

8

['48', '36']

M(12)D(144)

9

['48', '64']

M(16)D(192)

10

['36', '84']

M(12)D(252)

11

['48', '84']

M(12)D(336)

12

['56', '84']

M(28)D(168)

13

['48', '56']

M(8)D(336)

14

['64', '56']

M(8)D(448)

15

48

M(48)D(48)

16

36

M(36)D(36)

17

64

M(64)D(64)

18

84

M(84)D(84)

19

56

M(56)D(56)

20

M(0)D(1)

 
[9]:

display(*lattice)

Predicates:

  • M(4)

  • D(4032)

Individuals:

  • 48

  • 36

  • 64

  • 56

  • 84

Predicates:

  • M(4)

  • D(1008)

Individuals:

  • 48

  • 36

  • 56

  • 84

Predicates:

  • M(4)

  • D(1344)

Individuals:

  • 48

  • 64

  • 56

  • 84

Predicates:

  • M(4)

  • D(576)

Individuals:

  • 48

  • 36

  • 64

Predicates:

  • M(12)

  • D(1008)

Individuals:

  • 48

  • 36

  • 84

Predicates:

  • M(4)

  • D(504)

Individuals:

  • 36

  • 56

  • 84

Predicates:

  • M(4)

  • D(336)

Individuals:

  • 48

  • 56

  • 84

Predicates:

  • M(8)

  • D(1344)

Individuals:

  • 48

  • 64

  • 56

Predicates:

  • M(12)

  • D(144)

Individuals:

  • 48

  • 36

Predicates:

  • M(16)

  • D(192)

Individuals:

  • 48

  • 64

Predicates:

  • M(12)

  • D(252)

Individuals:

  • 36

  • 84

Predicates:

  • M(12)

  • D(336)

Individuals:

  • 48

  • 84

Predicates:

  • M(28)

  • D(168)

Individuals:

  • 56

  • 84

Predicates:

  • M(8)

  • D(336)

Individuals:

  • 48

  • 56

Predicates:

  • M(8)

  • D(448)

Individuals:

  • 64

  • 56

Predicates:

  • M(48)

  • D(48)

Individuals:

  • 48

Predicates:

  • M(36)

  • D(36)

Individuals:

  • 36

Predicates:

  • M(64)

  • D(64)

Individuals:

  • 64

Predicates:

  • M(84)

  • D(84)

Individuals:

  • 84

Predicates:

  • M(56)

  • D(56)

Individuals:

  • 56

Predicates:

  • M(0)

  • D(1)

Individuals:

Reduced context

[10]:

from galactic.algebras.lattice import ReducedContext

[11]:

context = ReducedContext(lattice, renderer=ConceptRenderer())

[12]:

context

[12]:

$1

$2

$3

$4

$5

$7

$14

64

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

48

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

36

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

84

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

56

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)

\(\checkmark\)