1. An Extensible Approach for Modeling Ontologies in RDF(S) Steffen Staab, Michael Erdmann, Alexander Mädche, & Stefan Decker Research Group Knowledge Management Institute AIFB, University of Karlsruhe, & DB Group, Stanford University Lisbon, September 21, 2000

2. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 2 What is an Ontology? n Light-weight Ontology –concepts, atomic types –is-a hierarchy among concepts –associations between concepts n Heavy-weight Ontology –cardinality constraints –taxonomy of relations –reified statements –Axioms / semantic entailments of various tastes expressiveness (DL, propositional, horn, or first order logic, higher order) inferences n RDF(S)

3. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 3 Tools for Ontologies n Light-weight –uncontroversial –all Tools support light-weight Protege, Stanford OntoEdit, Karlsruhe UML-Tools, several n Heavy-weight –no consensus yet –layering seems appropriate/necessary

4. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 4 Concepts, Relations,....

5. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 5 Modeling Ideal Modeling (WYMIWYG) n Modeling not constrained by any language n All appropriate epistemological primitives and modeling styles should be usable Real Modeling n A particular language always restricts allowed primitives (modeling language) n A particular language is needed in applications (application language) => distinguish modeling language from final application language translate automatically

6. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 6 Axioms n For Semantic Web and DAML more than light-weight is needed! –Axioms n Framework for conceptual modeling of axioms –Ontology of axiom patterns –language specific axiom-schemata can work with that knowledge n Interoperability is an issue –RDF / RDFS seem appropriate next slide next but one slide

7. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 7 Axiom Patterns n 1. Axioms for a relational algebra (a) Reflexivity of relations (b) Symmetry of relations (c) Asymmetry of relations (d) Transitivity of relations (e) Inverse relations (f) Irreflexivity of relations (g) Antisymmetry of relations n 2. Composition of relations n 3. (Exhaustive) Partitions of Concepts

8. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 8 Axiom Patterns n 4. Axioms for subrelation relationships n 5. Axioms for part-whole reasoning [Winston 87] [Chaffin 92] PhysicalPartOf MemberOf PortionOf PhaseOf FeatureOf SubRegionOf n 6. Nonmonotonicity n 7. Axioms for temporal and modal contexts n 8. (General axioms (application specific, ad hoc))

9. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 9 Application- specific actual data http://www.foo.com/W.Smith WilliamSmith appl:lastName appl:firstName http://www.foo.com/S.Smith SmithSusan appl:firstName appl:lastName appl:marriedWith rdfs:Resource rdfs:Classrdf:Property RDF/RDFS layer and namespace subClassOf instanceOf Application-specific schema and namespace appl:Person appl:Manappl:Womanappl:fatherInLawappl:marriedWithappl:fatherOf appl:Organisation o:secondComponent o:firstComponent o:composee o:Relationo:Partition o:PartOfRel o:isInverseRelationOf o:Composition ontology meta layer and namespace o:Reflexiveo:Irreflexiveo:Asymmetrico:Transitiveo:Symmetric o:Partonomic- RolePropagation

10. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 10 Example of Composition of Relations appl:marriedWith appl:fatherOfappl:fatherInLawOf o:composee o:firstComponent o:secondComponent o:Composition rdfs:Property o:Relation o:IrreflexiveRel rdf:Class Composition(fatherInLawOf, fatherOf, marriedWith). forall R,Q,S,X,Y,Z X[R ->> Z] <- Composition(R, Q, S) and X[Q ->> Y] and Y[S ->> Z]. forall X,Y,Z X[fatherInLawOf ->> Z] <- X[fatherOf ->> Y] and Y[marriedWith ->> Z].

11. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 11 OntoEdit supports Axiom Classification fatherInLawOffatherOfmarriedWith

12. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 12 Ontology Engineering using OntoEdit n Interaction with the user on a conceptual level n Multiple views for concepts, relations and axioms n Multilinguality n Linkable to NLP domain lexicon n Exports ontology (incl. axioms) into several formats F-Logic (main language) RDF/RDFS DTDs (as far as possible) ORDB-Schema (as far as possible) OIL (partially and in RDF) UML/XMI (planned) the DAML language (when specified ;-)

13. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 13 Ontoedit

14. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 14 Automatically Derived from Axiom views Debugging Instances + Rule Debugging Pure F-Logic Frame-Logic Inference Engine Access

15. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 15 1.Generate FaCT LISP KB (future: OIL) 2.Call FaCT Client, transform ontology on FaCT server 3.Ask server FaCT DL Engine Interface

16. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 16 o:Relationo:isInverseRelationOf o:Composition o:ReflexiveRel o:IrreflexiveRel o:AsymmetricRel o:TransitiveRel o:PartOfRel o:SymmetricRel o:Partition o:PhysicalPartOfRel o:MemberOfRel o:SubRegionOfRel Ontological meta layer for kinds of relations with own namespace rdfs:Resource rdf:Class rdfs:Property rdfs:ConstraintProperty rdfs:rangerdfs:domainrdfs:subPropertyOf rdf:type rdfs:subClassOf subClassOf instanceOf RDF/RDFS layer and namespace Flexible Epistemological Level XRDF OIL DAML XRDFDAMLOIL Application

17. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 17 Conclusion n ‘‘No Method fits all‘‘ –Different applications need different representation languages with their underlying reasoning services –Ontology development must be aware of this conceptual modeling mechanisms to access/integrate several ontologies –distributed on the web –identified by (XML-) namespaces

18. Axioms in RDF OntoEdit Ontology Modelling Axioms conceptually Conclusion 18 Thank You!