An ontology of ontology relationships

1. DOOR:
Descriptive Ontology of Ontology Relations
Carlo Allocca
Mathieu d’Aquin, Enrico Motta
Knowledge Media Institute
The Open University
Milton Keynes, UK

2. Why do we need DOOR? 1/2

3. Why do we need DOOR? 2/2
1 We are investigating:
implicit relationships
between ontologies
and how to make them
explicit on the SW;
2 Our approach:
It is based on a formal
characterization of relations
between ontologies.

4. Which Methodology is DOOR based on?
Three main sources are taken into consideration to identify
relevant ontology relations:
OWL
Three important requirements to build DOOR are:
the relations have to be general enough to be applied to multiple
domains;
the relations have to be sufficiently intuitive to reflect general meaning;
the relations have to be formally defined.
A Top-Down approach is used to analyze and formalize
ontology relations;

5. Main steps of the Approach 1/5
1 The outcome is a list of relevant relations e.g.:
1 Identifying the top relations,
includedIn, equivalentTo, similarTo,
w.r.t. the three resources.
previousVersion, import, etc;

6. Main steps of the Approach 2/5
2 Distinguishing relevant varieties/sub-relations, 2 e.g. includedIn and equivalentTo
looking at ontologies (and their relations) from carlodakbjgfsjkgfs
five different perspectives: Ivettdakbjgfsjkgfs
a. Lexicographic level which concerns with the a. none.
vocabularies of the ontologies.
b. Syntactic level which concerns with the sets b. syntacticallyIncludedIn, import
of the ontology axioms. syntacticallyEquivalentTo
c. Structural level which concerns with the c. isHomomorphicTo
graph structures formed by the axioms of the isIsomorphicTo
ontologies.
d. Semantic level which concerns with the d. semanticallyIncludedIn
formal models of the ontologies, looking in semanticallyEquivalentTo
particular at their logical consequences. isAConservativeExtentionOf
e. Temporal level which concerns with the e. none.
evolution of ontologies in time.

7. Main steps of the Approach 2/5
2 Distinguishing relevant varieties/sub-relations, 2 e.g. includedIn and equivalentTo
looking at ontologies (and their relations) from carlodakbjgfsjkgfs
five different perspectives: Ivettdakbjgfsjkgfs
a. Lexicographic level which concerns with the a. none.
vocabularies of the ontologies.
b. Syntactic level which concerns with the sets b. syntacticallyIncludedIn, import
of the ontology axioms. syntacticallyEquivalentTo
c. Structural level which concerns with the c. isHomomorphicTo
graph structures formed by the axioms of the isIsomorphicTo
ontologies.
d. Semantic level which concerns with the d. semanticallyIncludedIn
formal models of the ontologies, looking in semanticallyEquivalentTo
particular at their logical consequences. isAConservativeExtentionOf
e. Temporal level which concerns with the e. none.
evolution of ontologies in time.

8. Main steps of the Approach 2/5
2 Distinguishing relevant varieties/sub-relations, 2 e.g. includedIn and equivalentTo
looking at ontologies (and their relations) from carlodakbjgfsjkgfs
five different perspectives: Ivettdakbjgfsjkgfs
a. Lexicographic level which concerns with the a. none.
vocabularies of the ontologies.
b. Syntactic level which concerns with the sets b. syntacticallyIncludedIn, import
of the ontology axioms. syntacticallyEquivalentTo
c. Structural level which concerns with the c. isHomomorphicTo
graph structures formed by the axioms of the isIsomorphicTo
ontologies.
d. Semantic level which concerns with the d. semanticallyIncludedIn
formal models of the ontologies, looking in semanticallyEquivalentTo
particular at their logical consequences. isAConservativeExtentionOf
e. Temporal level which concerns with the e. none.
evolution of ontologies in time.

9. Main steps of the Approach 2/5
2 Distinguishing relevant varieties/sub-relations, 2 e.g. includedIn and equivalentTo
looking at ontologies (and their relations) from carlodakbjgfsjkgfs
five different perspectives: Ivettdakbjgfsjkgfs
a. Lexicographic level which concerns with the a. none.
vocabularies of the ontologies.
b. Syntactic level which concerns with the sets b. syntacticallyIncludedIn, import
of the ontology axioms. syntacticallyEquivalentTo
c. Structural level which concerns with the c. isHomomorphicTo
graph structures formed by the axioms of the isIsomorphicTo
ontologies.
d. Semantic level which concerns with the d. semanticallyIncludedIn
formal models of the ontologies, looking in semanticallyEquivalentTo
particular at their logical consequences. isAConservativeExtentionOf
e. Temporal level which concerns with the e. none.
evolution of ontologies in time.

10. Main steps of the Approach 2/5
2 Distinguishing relevant varieties/sub-relations, 2 e.g. includedIn and equivalentTo
looking at ontologies (and their relations) from carlodakbjgfsjkgfs
five different perspectives: Ivettdakbjgfsjkgfs
a. Lexicographic level which concerns with the a. none.
vocabularies of the ontologies.
b. Syntactic level which concerns with the sets b. syntacticallyIncludedIn, import
of the ontology axioms. syntacticallyEquivalentTo
c. Structural level which concerns with the c. isHomomorphicTo
graph structures formed by the axioms of the isIsomorphicTo
ontologies.
d. Semantic level which concerns with the d. semanticallyIncludedIn
formal models of the ontologies, looking in semanticallyEquivalentTo
particular at their logical consequences. isAConservativeExtentionOf
e. Temporal level which concerns with the e. none.
evolution of ontologies in time.

11. Main steps of the Approach 2/5
2 Distinguishing relevant varieties/sub-relations, 2 e.g. includedIn and equivalentTo
looking at ontologies (and their relations) from carlodakbjgfsjkgfs
five different perspectives: Ivettdakbjgfsjkgfs
a. Lexicographic level which concerns with the a. none.
vocabularies of the ontologies.
b. Syntactic level which concerns with the sets b. syntacticallyIncludedIn, import
of the ontology axioms. syntacticallyEquivalentTo
c. Structural level which concerns with the c. isHomomorphicTo
graph structures formed by the axioms of the isIsomorphicTo
ontologies.
d. Semantic level which concerns with the d. semanticallyIncludedIn
formal models of the ontologies, looking in semanticallyEquivalentTo
particular at their logical consequences. isAConservativeExtentionOf
e. Temporal level which concerns with the e. none.
evolution of ontologies in time.

12. Main steps of the Approach 3/5
3
3 includedIn: reflexive , transitive;
Characterizing each relation by its algebraic
equivalentTo: reflexive , symmetric
properties.
transitive.

13. Main steps of the Approach 4/5
includedIn
4 Establishing the
taxonomic
structure equivalentTo semanticallyIncludedIn isHomomorphicTo
between the
identified
isIsomorphicTo semanticallyEquivalentTo syntacticallyIncludedIn isIsomorphicTo
relations.
syntacticallyEquivalentTo imports isAConservativeExtensionOf

14. Main steps of the Approach 5/5
5 Introducing rules to define complex relations 5 e.g.: equivalentTo(O1 , O2 ):-
combining relations. includedIn(O1 , O2 ), includedIn(O2 , O1 ).
6 Repeating steps 1-5 we analyze all the other
relations.

15. Main steps of the Approach 5/5
5 Introducing rules to define complex relations 5 e.g.: equivalentTo(O1 , O2 ):-
combining relations. includedIn(O1 , O2 ), includedIn(O2 , O1 ).
6 Repeating steps 1-5 we analyze all the other
relations.

16. The DOOR Ontology
g

17. SimilarTo 1/2
”how many ways two ontologies overlap to each other”
SimilarTo
Semantic semanticallySimilarTo
MappingSimilarTo
Syntactic syntacticallySimilarTo
Lexicographic LexicographicSimilarTo
|Voc(O1 ) Voc(O2 )| |S A(O1 ) S A(O2 )| |LC (O1 ,O2 ) LC (O2 ,O1 )|
max(|Voc(O1 )|,|Voc(O2 )|) ≥T max(|S A(O1 |,|S A(O2 |) ≥T max(|S A(O1 |,|S A(O2 |) ≥T

18. SimilarTo 2/2
It is reflexive and symmetric;
The taxonomic structure:

19. Versioning 1/2
” O1 is a previous version of O2 ”
” O2 is a latter version of O1 ”
isLatterVersionOf isPreviousVersionOf
Temporal conceptualEvolutionOf priorVersion
explanationEvolutionOf
backwardCompatibleWith
owl:IncompatibleWith
Semantic conceptualEvolutionOf
Syntactic explanationEvolutionOf
conceptualEvolutionOf(O1 , O2 ) if O1 is a latter version that is not
semantically equivalent to O2 .
explanationEvolutionOf(O1 , O2 ) if O1 is a latter version that is semantically
equivalent to O2

20. Versioning 2/2
It is reflexive and transitive;
The taxonomic structure:

21. Agree and Disagree 1/3
”O1 expresses the same opinion as O2 about...”
”O1 and O2 contradict each other on...”
agreeWith disagreeWith
Temporal backwardCompatibleWith owlIncompatibleWith
Semantic semanticallyEquivalentTo hasDisparateModeling
semanticallySimilarTo incompatibleWith
incoherentWith
inconsistentWith
Syntactic syntacticallyEquivalentTo
syntacticallySimilarTo
explanationEvolution

22. Agree and Disagree 2/3
the taxonomic structure is
disagreeWith
hasDisparateModelling incompatibleWith
incoherentWith inconsistentWith owlIncompatibleWith
incoherentWith(O1 , O2 ) if the union of O1 and O2 generates an
unsatisfiable concept.
inconsistentWith(O1 , O2 ) if the union of O1 and O2 generates a new
ontology which has no model.
hasDisparateModeling(O1 , O2 ) if O1 and O2 represent corresponding
entities in different ways (e.g. as an instance in O1 and a
class O2 ).

23. Agree and Disagree 3/3
the taxonomic structure is
agreesWith
BackwardCompatibleWith semanticallyEquivalentTo semanticallySimilarTo
explanationEvolution syntacticallyEquivalentTo syntactiallySimilarTo

24. Conclusion and Future
We designed the DOOR ontology, which formalizes relations
existing between ontologies on the SW;
We presented the methodology on which DOOR is based on;
What is next:
keep developing DOOR;
Using the DOOR Ontology
KANNEL;

25. KANNEL...