Formally Measuring Agreement and Disagreement in Ontologies

Mathieu d’Aquin KMi, The Open University – m.daquin@open.ac.uk

What do we mean?

Ontologies are knowledge artifacts…

…. and knowledge is subjective

What do we mean?

Therefore, two different ontologies can express two different views (=disagree)

What do we mean?

Therefore, two different ontologies can express two different view (=disagree)Or the same/similar view(s) (=agree)

What do we mean?

Similarly, an ontology can agree or disagree with a single ontology statement

Seafood subClassOf

Meat

?

No, don’t think so…

Yes, of course!

And why is that interesting?

Being able to measure these (dis)agreements could help in choosing the right ontology, in understanding what exist and in making sense of a collection of ontologies

?

A naïve approach…

To detect disagreements, one could “simply” merge ontolologies and check for incoherence/inconsitency

SeaFood disjointWith

Meat

SeaFood subClassOf

MeatDISAGREEMENT

A naïve approach, but…

… a bit limited

Animal subClassOf Human

Human subClassOf Animal

Lion type SpeciesLion subClassOf

Species

Car subClassOf Vehicle

EricCantona type FootballPlayer

?

?

?

Requirements

• R1: Ontologies agree with themselves– Kind of obvious

• R2: Covering different domains is not agreeing– Car vs Footballer example.

• R3: There are different levels of agreements and disagreements– Human subClassOf Animal vs Human disjointWith Animal– Human subClassOf Animal vs Animal subClassOf Human

• R4: (dis)agreement measures should be independent from matching techniques– Matching is necessary, but not part of the measure

• R5: It is possible to agree and disagree at the same time– Lion type Species vs Lion subClassOf Species

Basic framework

The clever bit: using 2 measures instead of one…

Agreement(s, O) [0..1]

Disagreement(s, O) [0..1]

With s a statement and O an ontology

Interpretation:A (s, O) = 1, D(s, O) = 0, O fully agrees with s

A (s, O) = 0, D(s, O) = 1, O fully disagrees with s

A (s, O) = 0, D(s, O) = 0, O doesn’t care about s

A (s, O) > 0, D(s, O) > 0, O agrees to a certain extent with s or disagrees to a certain extent with s, or both

But how to calculate that?

Considering a statement <subject, relation, object>, an ontology might agree or disagree with the relation between entities corresponding to subject and object.

Extracting information about the relation between matching entities in an ontology:

Human subClassOfAnimal

s= Human

Animal

BirdLivingBeing

O=Matching

R-Module: Human subClassOf Animal, Animal subClassOf Human, Animal equivalentClass HumanMinimal RM: Animal equivalentClass Human

Simplified representation of MRMs

With subject’ and object’ the matching entities on O to the subject and object in s, the MRM of O regarding s can be represented as a list of relations:

subject’ subClassOf object’ subClassOf

object’ subClassOf subject’ subClassOf-1

etc.

Assumptions:The MRM is non redundant (part of the definition)

{equivalenClass} OK

{equivalentClass, subClassOf, subClassOf-1} not OK

The MRM should be coherent and consistent (guarantied if O is coherent and consistent, in accordance with our 1st requirement: an ontology agrees with itself)

{subClassOf} OK

{subClassOf, disjointWith} not OK

The MRM should be homogeneous in terms of modeling, i.e., it should not imply that en entity is at the same time a class and a property for example.

{fatherOf domain Person, fatherOf range Person} OK

{fatherOf domain Person, fatherOf subClassOf Person} not OK

Nice Property and Measure definitionsThe good news:

There is a small finite set of possible MRM, whatever is are O and s

Which means?

The measures of agreement and disagreement can be entirely defined by providing explicitly the values in two matrixes

Agreement

Relation in s

MRM

0 < A1 < A2 < 1

Disagreement

So?

Animal subClassOf Human

Human subClassOf Animal

Lion type SpeciesLion subClassOf

Species

Car subClassOf Vehicle

EricCantona type FootballPlayer

A1/D1

A2/D2

0/0

What to do now…

Measuring agreement and disagreement between whole ontologies, to understand a set of ontologies

The big formulas:

Using 21 ontologies containing a concept SeaFood

Agreement

Disagreement

Camp 1: seaFood disjointWith MeatCamp 2: SeaFood subClassOf Meat

What else could we do?

Measuring consensus and controversy in a collection of ontologies

R, a repository of ontologies.

Can be positive (high agreement, low disagreement) or negative (the contrary)

High controversy means no clear cut between agreement and disagreement

Example

Watson: Thousands of ontologies automatically crawled from the Web (http://watson.kmi.open.ac.uk)

a: global agreement, d: global disagreement, cs: consensus, ct: controversy

Assessing the statements related to SeaFood in Watson

Can we use it for assessing mappings?

Using a set of 456 evaluated mappings between 2 large thesaurus in the agricultural domain (71.3% precision)

Conclusion: There is less consensus on incorrect mappings. Controversy indicates mappings that need to be investigated more.

Conclusion

We provided definitions of measures of agreement and disagreement in ontologies, including consensus and controversy in ontology repositories.

We showed that when applied on real Web ontologies, this could help assessing statements and mappings, and getting an overview of a particular set of ontologies.

We realized an implementation based on the Watson API. We intend to make it available through a Web service.

Many applications to explore: visualization of ontology collections, ontology selection and reuse, propagation of trust based on agreement, …

… and new directions: computing explanations for the (dis)agreement, different parameters and matching techniques for different applications, resolving disagreements (decide who’s right), etc.

Also, complexity and performance are still difficult issues.

Thank You!

Mathieu d’Aquin @mdaquin m.daquin@open.ac.uk http://people.kmi.open.ac.uk/mathieu