📘 Contexts#
In formal concept analysis, a context is a mathematical structure that represents the relationships between a set of objects and a set of attributes. It is typically represented as a binary relation between the objects and attributes, indicating which objects possess which attributes.
Attributes are considered as special kinds of callable objects which may return True (when the object owns the attribute), False (when the object does not own the attribute), or None (when it is unknown whether the object owns the attribute or not). To avoid confusion with the term object widely used in programming, we will use the term item to refer to the objects of a formal context.
In the galactic.algebras.concept.core module, an item is represented as an
instance of the Item class with two properties
(key and
value )
and an attribute as an instance of the Attr
class.
The galactic.algebras.concept.core module provides the
Context class to represent contexts and
several utility functions to create contexts from:
create_context_from_dataset(): Creates a context from a dataset represented as a iterable or a mapping and an iterable of attributes.create_context_from_table(): Creates a context from a binary table.create_context_from_integers(): Creates a context from a table of integers.
from galactic.algebras.concept.core import create_context_from_dataset
from galactic.algebras.concept.examples.animals.core import ANIMAL_ATTRS, ANIMAL_DATA
context = create_context_from_dataset(ANIMAL_DATA, ANIMAL_ATTRS)
context
<galactic.algebras.concept.core.Context object at 0x75ce467120c0>
A context is a binary relation between a collection of items (the domain) and a
collection of attributes (the co-domain) and therefore is also an instance of the
BinaryRelation protocol from the
galactic.algebras.relational.core module.
from galactic.algebras.relational.core import BinaryRelation
isinstance(context, BinaryRelation)
True
Each item in the context’s domain
(ItemUniverse class)
and co-domain
(AttrUniverse class)
can be accessed using indexing and
iterating over them.
display(context.domain[0])
display(context.co_domain[0])
display(context.domain[:3])
Item(key='Dove', value=<list object at 0x75ce3446c3c0>)
<function small at 0x75ce34476660>
(Item(key='Dove', value=<list object at 0x75ce3446c3c0>),
Item(key='Hen', value=<list object at 0x75ce3448c180>),
Item(key='Duck', value=<list object at 0x75ce3448c1c0>))
dove = context.domain.item(key="Dove")
small = context.co_domain.attr(name="small")
display(dove, dove.value, small, small(dove.value))
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
Cell In[4], line 3
1 dove = context.domain.item(key="Dove")
2 small = context.co_domain.attr(name="small")
----> 3 display(dove, dove.value, small, small(dove.value))
File /builds/galactic/public/src/python/algebras/galactic-algebra-concept/src/galactic/algebras/concept/core/_attribute.py:77, in member.<locals>.create_attr.<locals>.AttrWrapper.__call__(self, item)
67 def __call__(self, item: Item) -> bool | None:
68 """
69 Call the wrapped function.
70
(...) 75
76 """
---> 77 return self._func(item)
File /builds/galactic/public/src/python/algebras/galactic-algebra-concept/src/galactic/algebras/concept/core/_attribute.py:115, in member.<locals>.attr(item)
100 """
101 Compute the membership of the attribute.
102
(...) 112
113 """
114 try:
--> 115 return key in item.value # type: ignore[operator]
116 except (ValueError, TypeError):
117 return None
AttributeError: 'list' object has no attribute 'value'
Contexts are binary relations, so we can get its length, iterate over its pairs, and check for membership of a pair.
display(len(context))
for item, attr in context:
display(f"{item} has attribute {attr}")
display((dove, small) in context)
The GALACTIC framework provides methods to access to the items that possess a given attribute and the attributes owned by a given item.