📘 Predicates

The galactic.algebras.convex.predicates.core module provides the foundation for creating and evaluating predicates on item data. It defines the Predicate protocol, which combines characteristics with truth evaluation logic through an abstract _truth() method. Predicates handle imprecision by returning None when truth values cannot be determined, such as when characteristics return empty lists or exceptions occur during evaluation.

The module includes basic comparison predicates and a membership predicate for set containment checks. Each predicate uses a template-based string representation with the format() mechanism, allowing flexible display of predicates with their parameters and characteristics.

• Equality

• Different

• LessEqual

• GreaterEqual

• LessThan

• GreaterThan

• Membership

Special predicates are also provided:

• Absurd (always returns False)

• Tautology (always returns True)

• Degenerated (combines multiple predicates using conjunction, requiring all sub-predicates to share the same characteristic space)

Predicates are hashable and comparable based on their characteristics and parameters, enabling efficient storage in sets and use as dictionary keys. They serve as extended attributes in classical Formal Concept Analysis, created on demand to precisely describe groups of items.

from galactic.algebras.concept.core import Item
from galactic.algebras.convex.characteristics.core import Integer
from galactic.algebras.convex.predicates.core import GreaterEqual

characteristic = Integer()
predicate = GreaterEqual((characteristic,), value=10)
display(str(characteristic), str(predicate))
display(
    predicate(Item(value=15)),
    predicate(Item(value=10)),
    predicate(Item(value=0)),
    predicate(Item(value=None))
)

'int(@)'

'int(@) ≥ 10'

True

True

False

None