Categorization Power of Ontologies with Respect to Focus Classes
1. Categorization Power of
Ontologies with Respect to
Focus Classes
Vojtěch Svátek, Ondřej Zamazal, Miroslav Vacura
University of Economics, Prague
Czech Republic
6. „Categorization“?
• Not meant as DL TBox classification…
• … but as assignment of individuals to concepts
(ABox classification)
C ≡ CExp1
D ≡ CExp2
C ⊑ D
I J K
CExp1 CExp2 CExp3
I ∈CExp1
J ∈CExp2
K ∈CExp3
7. „Categorization“?
• Not meant as DL TBox classification…
• … but as assignment of individuals to concepts
(ABox classification) – incl. compound CExp’s
C ≡ CExp1
D ≡ CExp2
C ⊑ D
I J K
CExp1 CExp2 CExp3
I ∈CExp1
J ∈CExp2
K ∈CExp3
9. Categorization power?
• Not meant as classification accuracy or similar…
• Characteristic of a model / algorithm
• Measured as capability of automatically performing
correct classification
10. Categorization power?
• Not meant as classification accuracy or similar…
• Characteristic of a model / algorithm
• Measured as capability of automatically performing
correct classification in a specific task
11. Categorization power?
• Not meant as classification accuracy or similar…
• Characteristic of a model / algorithm
• Measured as capability of automatically performing
correct classification in a specific task
• … but as
• Task-independent characteristic of an ontology
12. Categorization power?
• Not meant as classification accuracy or similar…
• Characteristic of a model / algorithm
• Measured as capability of automatically performing
correct classification in a specific task
• … but as
• Task-independent characteristic of an ontology
• Function of the number of categories expressible using
this ontology
13. Categorization power?
• Not meant as classification accuracy or similar…
• Characteristic of a model / algorithm
• Measured as capability of automatically performing
correct classification in a specific task
• … but as
• Task-independent characteristic of an ontology
• Function of the number of categories expressible using
this ontology
• Categories correspond to some kind of CExp’s over the
ontology signature
14. Categorization power?
• Not meant as classification accuracy or similar…
• Characteristic of a model / algorithm
• Measured as capability of automatically performing
correct classification in a specific task
• … but as
• Task-independent characteristic of an ontology
• Function of the number of categories expressible using
this ontology
• Categories correspond to some kind of CExp’s over the
ontology signature
16. Why „focused“?
• We are rarely completely ignorant about the initial
class of individual/s to be (further) sub-categorized
17. Why „focused“?
• We are rarely completely ignorant about the initial
class of individual/s to be (further) sub-categorized
• Mostly there exists a
• initial reasonably specific named class – focus class
• …that is trivially assigned to the individual
• …prior to its non-trivial (focused) sub-categorization
18. Why „focused“?
• We are rarely completely ignorant about the initial
class of individual/s to be (further) sub-categorized
• Mostly there exists a
• initial reasonably specific named class – focus class
• …that is trivially assigned to the individual
• …prior to its non-trivial (focused) sub-categorization
19. Why „focused“?
• We are rarely completely ignorant about the initial
class of individual/s to be (further) sub-categorized
• Mostly there exists a
• initial reasonably specific named class – focus class
• …that is trivially assigned to the individual
• …prior to its non-trivial (focused) sub-categorization
27. …in most cases we start with
already some „light“
Helicopter icon made by Freepik from www.flaticon.com
28. …in most cases we start with
already some „light“
Helicopter icon made by Freepik from www.flaticon.com
X ∈ Helicopter
29. …in most cases we start with
already some „light“
Helicopter icon made by Freepik from www.flaticon.com
X ∈ Helicopter
“Reasonably specific”
named class
30. …in most cases we start with
already some „light“
Helicopter icon made by Freepik from www.flaticon.com
X ∈ Helicopter
Focus class
31. What CExp’s are “categories”?
Do compound ones really count?
32. What CExp’s are “categories”?
Do compound ones really count?
• Named subclasses of focus class are primordial
contributors to „focused categorization power“ of
the ontology
33. What CExp’s are “categories”?
Do compound ones really count?
• Named subclasses of focus class are primordial
contributors to „focused categorization power“ of
the ontology
• Hypothesis 1: Some compound CExp’s should also
count; such that a human ontologist would be
willing to transform to named classes
34. What CExp’s are “categories”?
Do compound ones really count?
• Named subclasses of focus class are primordial
contributors to „focused categorization power“ of
the ontology
• Hypothesis 1: Some compound CExp’s should also
count; such that a human ontologist would be
willing to transform to named classes
• proposed term: ontologistic category
35. What CExp’s are “categories”?
Do compound ones really count?
• Named subclasses of focus class are primordial
contributors to „focused categorization power“ of
the ontology
• Hypothesis 1: Some compound CExp’s should also
count; such that a human ontologist would be
willing to transform to named classes
• proposed term: ontologistic category
• Hypothesis 2: The likelihood of a CExp to be
considered as ontologistic category is correlated
with its internal structure
36. What CExp’s are “categories”?
Do compound ones really count?
37. What CExp’s are “categories”?
Do compound ones really count?
Celestial Emporium of Benevolent Knowledge
by J. L. Borges in essay "The Analytical Language of John Wilkins (1942)
ako sub-categorization of focus class Animal:
• Those that belong to the emperor
• Embalmed ones
• Those that are trained
• Sucking pigs
• Mermaids (or Sirens)
• Fabulous ones
• Stray dogs
• Those that are included in this classification
• Those that tremble as if they were mad
• Innumerable ones
• Those drawn with a very fine camel hair brush
• Et cetera
• Those that have just broken the flower vase
• Those that, at a distance, resemble flies
38. What CExp’s are “categories”?
Do compound ones really count?
Celestial Emporium of Benevolent Knowledge
by J. L. Borges in essay "The Analytical Language of John Wilkins (1942)
ako sub-categorization of focus class Animal:
• Those that belong to the emperor
• Embalmed ones
• Those that are trained
• Sucking pigs
• Mermaids (or Sirens)
• Fabulous ones
• Stray dogs
• Those that are included in this classification
• Those that tremble as if they were mad
• Innumerable ones
• Those drawn with a very fine camel hair brush
• Et cetera
• Those that have just broken the flower vase
• Those that, at a distance, resemble flies
Not a valid systematic categorization by
any means…
39. What CExp’s are “categories”?
Do compound ones really count?
Celestial Emporium of Benevolent Knowledge
by J. L. Borges in essay "The Analytical Language of John Wilkins (1942)
ako sub-categorization of focus class Animal:
• Those that belong to the emperor
• Embalmed ones
• Those that are trained
• Sucking pigs
• Mermaids (or Sirens)
• Fabulous ones
• Stray dogs
• Those that are included in this classification
• Those that tremble as if they were mad
• Innumerable ones
• Those drawn with a very fine camel hair brush
• Et cetera
• Those that have just broken the flower vase
• Those that, at a distance, resemble flies
Not a valid systematic categorization by
any means… but can individual
categories be viewed as ontologistic?
40. What CExp’s are “categories”?
Do compound ones really count?
Celestial Emporium of Benevolent Knowledge
by J. L. Borges in essay "The Analytical Language of John Wilkins (1942)
ako sub-categorization of focus class Animal:
• Those that belong to the emperor
• Embalmed ones
• Those that are trained
• Sucking pigs
• Mermaids (or Sirens)
• Fabulous ones
• Stray dogs
• Those that are included in this classification
• Those that tremble as if they were mad
• Innumerable ones
• Those drawn with a very fine camel hair brush
• Et cetera
• Those that have just broken the flower vase
• Those that, at a distance, resemble flies
41. Intuitive rewriting to DL CExp’s
• “Those that are trained”
∃ trainedBy . ⊤
• “Those that have just broken the flower vase”
∃ broke . Vase
• “Those that belong to the emperor”
∃ belongsTo . { Emperor }
42. Intuitive rewriting to DL CExp’s
• “Those that are trained”
∃ trainedBy . ⊤
• “Those that have just broken the flower vase”
∃ broke . Vase
• “Those that belong to the emperor”
∃ belongsTo . { Emperor }
• This is exactly the 3 compound CExp types
considered in the paper, beside C (named subclass):
∃ P.⊤ ∃ P.C ∃ P.{i}
44. Now peeping into the paper…
• Descriptive formalism considering a language L
restricting the form of CExp’s
45. Now peeping into the paper…
• Descriptive formalism considering a language L
restricting the form of CExp’s
• Axiom patterns with mapping to CExp’s
• E.g.,
P rdfs:domain FC
P rdfs:range D
C rdfs:subClassOf D
(P,C) prun3(FC)
yielding
∃ P.C
as category (CExp)
46. Now peeping into the paper…
• Descriptive formalism considering a language L
restricting the form of CExp’s
• Axiom patterns with mapping to CExp’s
• E.g.,
P rdfs:domain FC
P rdfs:range D
C rdfs:subClassOf D
(P,C) prun3(FC)
yielding
∃ P.C
as category (CExp)
• Weighted sum of axiom pattern occurrence yields
focused ontologistic categorization power (FOCP)
47. Now peeping into the paper…
• Survey on axiom pattern occurrence in two
ontology collections (LOV and OntoFarm)
• Pattern for ∃ P.⊤ most widespread, followed by C and
then ∃ P.C, while ∃ P.{i} is the rarest
48. Now peeping into the paper…
• Survey on axiom pattern occurrence in two
ontology collections (LOV and OntoFarm)
• Pattern for ∃ P.⊤ most widespread, followed by C and
then ∃ P.C, while ∃ P.{i} is the rarest
• Assessment of a sample of 59 compound CExp’s by
human ontologists (3 experts and 27 students)
• ∃ P.{i} accepted as “ontologistic” most often (appr. 70%),
followed by ∃ P.C (appr. 50%);
∃ P.⊤ was least successful (appr. 30%)
49. Now peeping into the paper…
• Survey on axiom pattern occurrence in two
ontology collections (LOV and OntoFarm)
• Pattern for ∃ P.⊤ most widespread, followed by C and
then ∃ P.C, while ∃ P.{i} is the rarest
• Assessment of a sample of 59 compound CExp’s by
human ontologists (3 experts and 27 students)
• ∃ P.{i} accepted as “ontologistic” most often (appr. 70%),
followed by ∃ P.C (appr. 50%);
∃ P.⊤ was least successful (appr. 30%)
• Interesting insights drawn from disagreement cases
(cf. Chris’ keynote)
50. Hypotheses revisited
• Hypothesis 1: Some compound CExp’s should also
count; such that a human ontologist would be
willing to transform to named classes
• Hypothesis 2: The likelihood of a CExp to be
considered as ontologistic category is correlated
with its internal structure
51. Hypotheses revisited
• Hypothesis 1: Some compound CExp’s should also
count; such that a human ontologist would be
willing to transform to named classes
• Hypothesis 2: The likelihood of a CExp to be
considered as ontologistic category is correlated
with its internal structure
• Both supported by the human-centric experiment
(even if the sample is small)
52. Examples of CExp’s
• Best rated
• Focus class ofrd:FridgeFreezer
category ofrd:styleOfUnit value ofrd:SingleDoor
i.e. type ∃ P.{i}
53. Examples of CExp’s
• Best rated
• Focus class ofrd:FridgeFreezer
category ofrd:styleOfUnit value ofrd:SingleDoor
i.e. type ∃ P.{i}
• Worst rated
• Focus class gr:DayOfWeek
category gr:hasNext value gr:Friday
i.e. also type ∃ P.{i}
• Focus class sigkdd:Conference
category sigkdd:City of conference some Thing
i.e. type ∃ P.⊤
55. Any practical use foreseen?
• Entity reuse in ontologies/vocabularies and linked
dataset schemas
• Reuse strategies are now a widely researched topic in LD
• Estimated FOCP can serve as additional criterion to
those already described in literature
56. Any practical use foreseen?
• Entity reuse in ontologies/vocabularies and linked
dataset schemas
• Reuse strategies are now a widely researched topic in LD
• Estimated FOCP can serve as additional criterion to
those already described in literature
• Entity transformation
• Some applications may only allow to pick named classes
in an entity categorization task
• Unnamed ontologistic categories can be transformed to
named ones so as to become considered by these
applications
58. Future directions
• Test further CExp’s and corresponding patterns, e.g.
possible addition of owl:inverseOf
59. Future directions
• Test further CExp’s and corresponding patterns, e.g.
possible addition of owl:inverseOf
• Use of linguistic cues aside the logical patterns
60. Future directions
• Test further CExp’s and corresponding patterns, e.g.
possible addition of owl:inverseOf
• Use of linguistic cues aside the logical patterns
• Combine the expertise-based approach to
“ontologistic status” prediction for CExp’s with an
empirical approach, based on their population with
instances
61. Future directions
• Test further CExp’s and corresponding patterns, e.g.
possible addition of owl:inverseOf
• Use of linguistic cues aside the logical patterns
• Combine the expertise-based approach to
“ontologistic status” prediction for CExp’s with an
empirical approach, based on their population with
instances
• Implementation of the approach in tools