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

2. Warning: slides go beyond the paper content!

3. „Categorization“?

4. „Categorization“? • Not meant as DL TBox classification… C ≡ CExp1 D ≡ CExp2 C ⊑ D

5. „Categorization“? • Not meant as DL TBox classification… C ≡ CExp1 D ≡ CExp2 C ⊑ D

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

8. Categorization power?

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

15. Why „focused“?

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

20. Even if exceptions exist…

21. Even if exceptions exist… What is the focus class for categorization?

22. Even if exceptions exist… X ∈ Thing

23. Even if exceptions exist… X ∈ Thing Not “reasonably specific”

24. Even if exceptions exist… X ∈ CelestialBody ⊔ Insect ⊔ Aircraft ⊔ EyeDisorder ⊔ BrainDisorder ⊔ …

25. Even if exceptions exist… X ∈ CelestialBody ⊔ Insect ⊔ Aircraft ⊔ EyeDisorder ⊔ BrainDisorder ⊔ … Compound, not named

26. Even if exceptions exist…

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}

43. Now peeping into the paper…

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.⊤

54. Any practical use foreseen?

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

57. Future directions

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

62. Thanks! Questions?

Categorization Power of Ontologies with Respect to Focus Classes

Categorization Power of Ontologies with Respect to Focus Classes

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