Implicational systemΒΆ

[1]:

from galactic.rules import DirectImplicationalSystem
from galactic.population import Population
from galactic.characteristics import Key
from galactic.examples.arithmetic.strategies import \
    MultipleStrategy, DivisorStrategy
individuals = [
    {"x": 48, "y": 15},
    {"x": 36, "y": 3},
    {"x": 64, "y": 10}
]
population = Population(individuals)
strategies = [
    MultipleStrategy(Key(name="x")),
    DivisorStrategy(Key(name="x")),
    MultipleStrategy(Key(name="y")),
    DivisorStrategy(Key(name="y")),
]

[2]:

from galactic.algebras.poset.collections import HasseDiagram
from galactic.concepts.lattice import Lattice
lattice = Lattice(
    population=population,
    strategies=strategies
)

[3]:

HasseDiagram(lattice)

[3]:
../../_images/notebooks_rules_notebook_3_0.png 
[4]:

display(*lattice)

Predicates:

  • M(x,4)

  • D(x,576)

  • M(y,1)

  • D(y,30)

Individuals:

  • 0

  • 1

  • 2

Predicates:

  • M(x,16)

  • D(x,192)

  • M(y,5)

  • D(y,30)

Individuals:

  • 0

  • 2

Predicates:

  • M(x,12)

  • D(x,144)

  • M(y,3)

  • D(y,15)

Individuals:

  • 0

  • 1

Predicates:

  • M(x,64)

  • D(x,64)

  • M(y,10)

  • D(y,10)

Individuals:

  • 2

Predicates:

  • M(x,48)

  • D(x,48)

  • M(y,15)

  • D(y,15)

Individuals:

  • 0

Predicates:

  • M(x,36)

  • D(x,36)

  • M(y,3)

  • D(y,3)

Individuals:

  • 1

Predicates:

  • M(x,0)

  • D(x,1)

  • M(y,0)

  • D(y,1)

Individuals:

[5]:

system = DirectImplicationalSystem(
    population=population,
    strategies=strategies
)
system

[5]: