Comments (3)
xflr6
commented on July 19, 2024
import concepts
SRC = ''',does_carry_transport,has_wheels,does_drive_is_driven,has_a_seat_seats,made_of_metal
bus0,X,X,X,,
bus1,,X,X,X,
bus2,X,X,X,,
bus3,X,,X,X,
bus4,,X,X,X,
bus5,X,,X,X,
bus6,,X,,X,X
bus7,,X,X,,X
bus8,,X,X,,X
bus9,X,X,,,X
bus10,X,X,X,,
bus11,X,,,X,X
bus12,,X,,X,X
bus13,X,X,X,,
bus14,X,X,,X,
bus15,,X,X,X,
bus16,X,X,,,X
bus17,,X,X,X,
bus18,X,X,,,X
bus19,X,X,,X,'''
c = concepts.make_context(SRC, frmat='csv')
c.lattice.graphviz()
All labels of the properties are in the topmost layer (below the supremum concept node). This is indeed expected here. The property labels are attached to the most general (highest) concept that has the property, while the object labels are attached to the most specific (lowest) concept that has the object. You can go up/down the graph collecting property/object labels to read the intent/extent of a concept (i.e. node). See an FCA itroduction for details, e.g. https://www.springer.com/de/book/9783540627715
print(c)
<Context object mapping 20 objects to 5 properties at 0x55f1a20>
|does_carry_transport|has_wheels|does_drive_is_driven|has_a_seat_seats|made_of_metal|
bus0 |X |X |X | | |
bus1 | |X |X |X | |
bus2 |X |X |X | | |
bus3 |X | |X |X | |
bus4 | |X |X |X | |
bus5 |X | |X |X | |
bus6 | |X | |X |X |
bus7 | |X |X | |X |
bus8 | |X |X | |X |
bus9 |X |X | | |X |
bus10|X |X |X | | |
bus11|X | | |X |X |
bus12| |X | |X |X |
bus13|X |X |X | | |
bus14|X |X | |X | |
bus15| |X |X |X | |
bus16|X |X | | |X |
bus17| |X |X |X | |
bus18|X |X | | |X |
bus19|X |X | |X | |
Note that from this follows that one property label can only be on a path below another one, if the higher one subsumes the lower one (equivalently, the lower property implies the higher) within the context (i.e. all objects having the lower one also have the higher one), which is not the case for the properties in this case (the properties are almost all completely orthogonal):
print(c.relations())
does_carry_transport subcontrary has_wheels
has_wheels subcontrary has_a_seat_seatsCompare this with relations.csv you cite:
import concepts
SRC = '''name,relation,transitive,symmetric,antisymmetric,reflexive,irreflexive,asymmetric,neg. trans.,connected,total,trichotomous
irrefl.,X,,,,,X,,,,,
tolerance,X,,X,,X,,,,,,
equivalence,X,X,X,,X,,,,,,
preorder,X,X,,,X,,,,,,
partial order,X,X,,X,X,,,,,,
total order,X,X,,X,X,,,X,X,X,
strict partial order,X,X,,X,,X,X,,,,
strict weak order,X,X,,X,,X,X,X,,,
strict total order,X,X,,X,,X,X,X,X,,X
R = X = {},X,X,X,X,X,X,X,X,X,X,X'''
c = concepts.make_context(SRC, frmat='csv')
print(c)
<Context object mapping 10 objects to 11 properties at 0x55dba58>
|relation|transitive|symmetric|antisymmetric|reflexive|irreflexive|asymmetric|neg. trans.|connected|total|trichotomous|
irrefl. |X | | | | |X | | | | | |
tolerance |X | |X | |X | | | | | | |
equivalence |X |X |X | |X | | | | | | |
preorder |X |X | | |X | | | | | | |
partial order |X |X | |X |X | | | | | | |
total order |X |X | |X |X | | |X |X |X | |
strict partial order|X |X | |X | |X |X | | | | |
strict weak order |X |X | |X | |X |X |X | | | |
strict total order |X |X | |X | |X |X |X |X | |X |
R = X = {} |X |X |X |X |X |X |X |X |X |X |X |E.g. all transitive relations in the context are also antisymmetric (we are still missing some relation kinds so that the graph would only show us implications that are inhertently true for all relations, but it also contains this kind such as asymmetric -> antisymmetric).
print(c.relations())
antisymmetric implication transitive
asymmetric implication transitive
neg. trans. implication transitive
connected implication transitive
total implication transitive
trichotomous implication transitive
symmetric implication reflexive
asymmetric implication antisymmetric
neg. trans. implication antisymmetric
connected implication antisymmetric
total implication antisymmetric
trichotomous implication antisymmetric
total implication reflexive
asymmetric implication irreflexive
trichotomous implication irreflexive
trichotomous implication asymmetric
connected implication neg. trans.
total implication neg. trans.
trichotomous implication neg. trans.
total implication connected
trichotomous implication connected
reflexive subcontrary irreflexivefrom concepts.
vsraptor
commented on July 19, 2024
I see. I seem to get confused because all the diagrams in papers on the subject use pair of SETS as a labels i.e. have a label/value for every point of the diagram
from concepts.
xflr6
commented on July 19, 2024
Yeah, it saves some space. AFAIK, this is the canonical way of drawing the concept graphs, see e.g. https://en.wikipedia.org/wiki/Formal_concept_analysis#/media/File:FCA_body_of_water.svg or http://www.upriss.org.uk/fca/examples.html
from concepts.
Related Issues (8)
- You cant have a context with only one Object. HOT 1
- Saving lattice visualization to a file HOT 3
- Access to concepts themselves HOT 3
- lattice_memebers.Concept vs _common.Concept API HOT 6
- Concept from pandas dataframe HOT 2
- Scalable method for deserializing lattice objects? HOT 15
- Plans for lattice reduction? HOT 4
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