DOOR ontology

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

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Why do weneed DOOR? 1/2

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Why do weneed 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.

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Which Methodology isDOOR 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;

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Main steps ofthe 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;

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Main steps ofthe 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.

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

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

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Main steps ofthe 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.

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Main steps ofthe 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.

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The DOOR Ontology g

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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

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

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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

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

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Agree and Disagree1/3 ”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

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Agree and Disagree2/3 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 ).

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Agree and Disagree3/3 the taxonomic structure is agreesWith BackwardCompatibleWith semanticallyEquivalentTo semanticallySimilarTo explanationEvolution syntacticallyEquivalentTo syntactiallySimilarTo

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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;

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KANNEL...

DOOR ontology

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