categorization power of ontologies with respect to focus classes

Categorization Power of Ontologies with Respect to

Focus ClassesVojtěch Svátek, Ondřej Zamazal, Miroslav Vacura

University of Economics, PragueCzech Republic

Warning: slides go beyond the paper content!

„Categorization“?


• Not meant as DL TBox classification…

C ≡ CExp 1

D ≡ CExp 2

C ⊑ D



• … but as assignment of individuals to concepts (ABox classification)

C ≡ CExp 1

D ≡ CExp 2

C ⊑ D

I J K

CExp 1 CExp 2 CExp 3

I ∈CExp 1

J ∈CExp 2

K ∈CExp 3



• … but as assignment of individuals to concepts (ABox classification) – incl. compound CExp’s

C ≡ CExp 1

D ≡ CExp 2

C ⊑ D

I J K

CExp 1 CExp 2 CExp 3

I ∈CExp 1

J ∈CExp 2

K ∈CExp 3

Categorization power?


• Not meant as classification accuracy or similar…• Characteristic of a model / algorithm

• Measured as capability of automatically performing correct classification



• 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





• Function of the number of categories expressible using this ontology

• Categories correspond to some kind of CExp’s over the ontology signature

Why „focused“?

Why „focused“?

• We are rarely completely ignorant about the initial class of individual/s to be (further) sub-categorized

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

Even if exceptions exist…


What is the focus class for categorization?


X ∈ Thing


X ∈ Thing

Not “reasonably specific”


X ∈ CelestialBody⊔ Insect⊔ Aircraft⊔ EyeDisorder⊔ BrainDisorder⊔ …


X ∈ CelestialBody⊔ Insect⊔ Aircraft⊔ EyeDisorder⊔ BrainDisorder⊔ …

Compound, not named

…in most cases we start withalready some „light“

Helicopter icon made by Freepik from www.flaticon.com

http://www.flaticon.com/



X ∈ Helicopter




X ∈ Helicopter

“Reasonably specific” named class




X ∈ Helicopter

Focus class


What CExp’s are “categories”? Do compound ones really count?


• Named subclasses of focus class are primordialcontributors to „focused categorization power“ ofthe ontology



• Hypothesis 1: Some compound CExp’s should also count; such that a human ontologist would be willing to transform to named classes



• 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 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


Celestial Emporium of Benevolent Knowledgeby 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…




Not a valid systematic categorization by any means… but can individualcategories be viewed as ontologistic?

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 }

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 typesconsidered in the paper, beside C (named subclass): ∃ P.⊤ ∃ P.C ∃ P.{i}

Now peeping into the paper…


• Descriptive formalism considering a language Lrestricting 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.Cas category (CExp)



• 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.Cas category (CExp)

• Weighted sum of axiom pattern occurrence yields focused ontologistic categorization power (FOCP)


• 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%)




• 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)

Hypotheses revisited



Hypotheses revisited



• Both supported by the human-centric experiment (even if the sample is small)

Examples of CExp’s

• Best rated• Focus class ofrd:FridgeFreezer

category ofrd:styleOfUnit value ofrd:SingleDoori.e. type ∃ P.{i}

Examples of CExp’s

• Best rated• Focus class ofrd:FridgeFreezer

category ofrd:styleOfUnit value ofrd:SingleDoori.e. type ∃ P.{i}

• Worst rated• Focus class gr:DayOfWeek

category gr:hasNext value gr:Fridayi.e. also type ∃ P.{i}

• Focus class sigkdd:Conferencecategory sigkdd:City of conference some Thingi.e. type ∃ P.⊤

Any practical use foreseen?


• Entity reuse in ontologies/vocabularies and linkeddataset 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 reuse in ontologies/vocabularies and linkeddataset 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

Future directions

Future directions

• Test further CExp’s and corresponding patterns, e.g. possible addition of owl:inverseOf

Future directions


• Use of linguistic cues aside the logical patterns

Future directions



• Combine the expertise-based approach to “ontologistic status” prediction for CExp’s with an empirical approach, based on their population with instances

Future directions



• 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

Thanks! Questions?

categorization power of ontologies with respect to focus classes

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