Categorization Power of Ontologies with Respect to Focus Classes
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Slides from the EKAW 2016 conference (content largely disjoint with the paper in proceedings) by Vojtech Svatek, Ondrej Zamazal and Miroslav Vacura
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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!
- 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
- 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
- 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
- 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
- 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