Implicational system

[1]:

from galactic.rules import HasseDiagramOrderedBasis, CanonicalDirectBasis
from galactic.rules import RuleTable
from galactic.population import Population
from galactic.characteristics import Key
from galactic.examples.arithmetic import (
    MultipleStrategy,
    DivisorStrategy,
    MultipleDescription,
    DivisorDescription,
    Integer,
)

individuals = [{"x": 48, "y": 15}, {"x": 36, "y": 3}, {"x": 64, "y": 10}]
population = Population(individuals)
strategies = [
    MultipleStrategy(Integer(Key(name="x"))),
    DivisorStrategy(Integer(Key(name="x"))),
    MultipleStrategy(Integer(Key(name="y"))),
    DivisorStrategy(Integer(Key(name="y"))),
]
descriptions = [
    MultipleDescription(Integer(Key(name="x"))),
    DivisorDescription(Integer(Key(name="x"))),
    MultipleDescription(Integer(Key(name="y"))),
    DivisorDescription(Integer(Key(name="y"))),
]

[2]:

from galactic.algebras.poset import HasseDiagram
from galactic.concepts import ConceptRenderer, ConceptLattice

lattice = ConceptLattice(population=population, descriptions=descriptions)
lattice.apply(strategies)

[3]:

HasseDiagram(lattice, domain_renderer=ConceptRenderer())

[3]:

../../_images/notebooks_rules_notebook_3_0.png

[4]:

display(*lattice.domain)

Predicates:

M(x,4)
D(x,576)
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]:

RuleTable(HasseDiagramOrderedBasis(lattice=lattice), support=0.0)

[5]:

Premises	Conclusions	Support	Confidence
	`$0`	1	1
`$0`	`M(x,4)D(x,576)D(y,30)`	1	1
`M(x,16)`	`$1`	0.666667	1
`D(x,192)`	`$1`	0.666667	1
`M(y,5)`	`$1`	0.666667	1
`$1`	`M(x,16)D(x,192)M(y,5)D(y,30)`	0.666667	1
`M(x,12)`	`$2`	0.666667	1
`D(x,144)`	`$2`	0.666667	1
`M(y,3)`	`$2`	0.666667	1
`D(y,15)`	`$2`	0.666667	1
`$2`	`M(x,12)D(x,144)M(y,3)D(y,15)`	0.666667	1
`M(x,64)`	`$3`	0.333333	1
`D(x,64)`	`$3`	0.333333	1
`M(y,10)`	`$3`	0.333333	1
`D(y,10)`	`$3`	0.333333	1
`$3`	`M(x,64)D(x,64)M(y,10)D(y,10)`	0.333333	1
`$1$2`	`$4`	0.333333	1
`$4`	`M(x,48)D(x,48)M(y,15)D(y,15)`	0.333333	1
`M(x,36)`	`$5`	0.333333	1
`D(x,36)`	`$5`	0.333333	1
`D(y,3)`	`$5`	0.333333	1
`$5`	`M(x,36)D(x,36)M(y,3)D(y,3)`	0.333333	1

[6]:

RuleTable(CanonicalDirectBasis(lattice=lattice), support=0.0)

[6]:

Premises	Conclusions	Support	Confidence
	`M(x,4)D(x,576)D(y,30)`	1	1
`M(x,16)`	`D(x,192)M(y,5)D(y,30)`	0.666667	1
`D(x,192)`	`M(x,16)M(y,5)D(y,30)`	0.666667	1
`M(y,5)`	`M(x,16)D(x,192)D(y,30)`	0.666667	1
`M(x,12)`	`D(x,144)M(y,3)D(y,15)`	0.666667	1
`D(x,144)`	`M(x,12)M(y,3)D(y,15)`	0.666667	1
`M(y,3)`	`M(x,12)D(x,144)D(y,15)`	0.666667	1
`D(y,15)`	`M(x,12)D(x,144)M(y,3)`	0.666667	1
`M(x,64)`	`D(x,64)M(y,10)D(y,10)`	0.333333	1
`D(x,64)`	`M(x,64)M(y,10)D(y,10)`	0.333333	1
`M(y,10)`	`M(x,64)D(x,64)D(y,10)`	0.333333	1
`D(y,10)`	`M(x,64)D(x,64)M(y,10)`	0.333333	1
`M(x,36)`	`D(x,36)M(y,3)D(y,3)`	0.333333	1
`D(x,36)`	`M(x,36)M(y,3)D(y,3)`	0.333333	1
`D(y,3)`	`M(x,36)D(x,36)M(y,3)`	0.333333	1