1. Laboratory of Computer Science LISI National Engineering School for Mechanics and Aerotechnics ENSMA 1, avenue Clément Ader - BP 40109 - 86961 Futuroscope cedex - France ADBIS07, Varna, September 30, 2007 Stéphane JEAN jean@ensma.fr Yamine AIT-AMEURyamine@ensma.fr Guy PIERRA pierra@ensma.fr An Object-Oriented Based Algebra for Ontologies and their Instances

2. 2 Definition of an Ontology Based Database (OBDB) tA Database which contains : vLocal ontologies vPossibly, links to external ontologies vOntology-based data : extensions of ontology concepts vLinks Ontologies / Data Content System Catalog Ontology

3. 3 Motivation of our work RDB Logical model System catalog OODB System catalog Logical model Object-Oriented Data Model (Class, Property, …) Query Algebra : Encore, AQUA, QAL,... Relational Data Model (Relation) Relational Algebra Useful to study optimization, to prove semantic properties (e.g. completeness, closure) of query languages … OBDB System catalog Ontology Content Data Model ? Query Algebra ? What about OBDB ?

4. 4 Outline uContext: OBDB and OBDB Query Languages uOverall Approach uProposal: Data Model and Query Algebra for OBDB uConclusion and future work

5. 5 Existing OBDB: diversity of ontology models uOBDB use different ontology models Ontology System Catalog Content PLIB (OntoDB and OntoDB2) RDF-Schema (RDF-Suite, Sesame, RSTAR,...) OWL (DLDB, OntoMS, …) F-Logic, OWL Flight, KIF, Powerloom, KARIN, Ontolingua, … Objective 1. A data model for OBDB independent of the underlying ontology model u Context u Approach u Proposal u Conclusion

6. 6 Existing OBDB: diversity of representations tTable of triples (e.g. Jena, 3Store) system catalog contentontology tSplit ontology/data (e.g. Sesame) vbinary or vertical representation for data vfixed ontology model system catalog contentontology tOntology Meta-Schema (OntoDB) vtable-like representation for data vevolving ontology model meta-schema Objective 2. A data model for OBDB independent of the persistence DB logical model u Context u Approach u Proposal u Conclusion

7. 7 Existing Ontology Query languages SPARQL system catalog RQL system catalog contentontology OntoQL system catalog contentontology meta-schema Objective 3. Define a reference query _ _ algebra for ontology query languages u Context u Approach u Proposal u Conclusion v RDF Querying v semantics of RDF-S constructors v fixed ontology model v semantics of core ontology model constructors vevolving ontology model

8. 8 Outline uContext: OBDBs and OBDBs Query Langages uOverall Approach uProposal: Data Model and Query Algebra for OBDB uConclusion and future work

9. 9 Objective 1: Independence from ontology model u Context u Approach u Proposal u Conclusion uStorable in the ontology meta-schema part EntitiesAttributes _ Ontology _ Class _ Property _ Datatype _ code _ name _ definition _ superClasses … EntitiesAttributes _ Ontology _ Class _ Property _ Datatype _ Restriction _ code _ name _ definition _ superClasses … _ remark uDefinition of an extendable core ontology model

10. 10 Objective 2: Independence from persistence DB logical model u Each class is associated to an extent whatever is the logical model used to represent it uA view may be associated to represent the extent of a class in order to hide the specific logical model u Context u Approach u Proposal u Conclusion

11. 11 Objective 3: Define a Query algebra for OBDB uOntologies use extensively object-oriented concepts u Context u Approach u Proposal u Conclusion uBut they have their own particularities tOntology and/or Data may be queried tSolely a subset of properties are valued tMulti-instanciation t… Proposed solution Adapt and Extend the ENCORE algebra for OODB [Shaw&Zdonik, 1990] Class Property Instances

12. 12 Outline uContext: OBDBs and OBDBs Query Langages uOverall Approach uProposal: Data Model and Query Algebra for OBDB uConclusion and future work

13. 13 Proposal: formal data model of an OBDB Content: Extent, I Type I 2 Extent SchemaProp Extent 2 p Val I P I Meta-schema: E, A, OC SuperEntities E 2 E Type OC E AttDomain A E AttRange A E Val OC A OC Ontology C, P SuperClasses C 2 c propDomain P C propRange P C Model M = (E, A, OC, C, P, Extent) System catalog Ontology Content Meta Schema Nomination: C Extent Abstraction: Extent C u Context u Approach u Proposal u Conclusion

14. 14 Formal data model of an OBDB: Example Ontology Meta Schema Content System catalog u Context u Approach u Proposal u Conclusion

15. 15 OntoImage: E x 2 OC x Function E x 2 OC Apply a function to a collection of ontology elements T E, Oc 2 OC => OntoImage(T, Oc, f) = (AttRange(f), {f(i) | i Oc}) Query Algebra for OBDB: Ontology part u Context u Approach u Proposal u Conclusion u Signatures of Operators E x 2 OC x … E x 2 OC u Main Operators : OntoImage, OntoProject, OntoSelect, OntoOJoin Collection of ontology elements T E, Oc 2 OC => OntoSelect(T, Oc, pred) = (T, {i | i Oc pred(i)}) Apply a selection to a collection of ontology elements OntoSelect: E x 2 OC x Predicate E x 2 OC Ontology elements = Instance of an _ _ (Object-Oriented) Ontology model Same Semantics as OODB Operators

16. 16 Query Algebra for OBDB: Example(1) uQuery on ontologies Retrieve the URI of the ontology classes named Person OntoQL. SELECT #uri FROM #class WHERE #name = Person ontoImage name = Person ext * Class ontoSelecturi RQL. SELECT $C FROM $C WHERE label($C) = Person SPARQL. SELECT ?C WHERE { ?C rdf:type rdfs:Class. ?C rdfs:label ?n FILTER (?n=Person) } Same Semantics as OODB operators u Context u Approach u Proposal u Conclusion

17. 17 OntoImage: C x 2 I x Function C x 2 I Query Algebra for OBDB: Content part u Context u Approach u Proposal u Conclusion uSignatures of operators C x 2 I x … C x 2 I u Same Operators as on the ontology part Collection of ontology class instances OntoSelect: C x 2 I x Predicate C x 2 I OntoOJoin: C x 2 I x C x 2I x Predicate C x 2 I OntoProject: C x 2 I x 2 Function x 2 String C x 2 I Case 1: Subset of properties are valued Case 2: Multi-instanciation The Semantics of the operators needs to be adapted

18. 18 OntoImage: C x 2 I x Function C x 2 I Apply a function (e.g. a property) to a collection of ontology class instances Query Algebra for OBDB: OntoImage Operator u Context u Approach u Proposal u Conclusion u Operator signature OntoVal(i, p) = Val(i, p), if e TypeOf (i) such that p SchemaProp(e) _ else, UNKNOWN => OntoImage(C, I c, p) = (range(p), {OntoVal(i) | i I c } case 1: Property not used in the extent of a class Domain(p) = C 2 => OntoImage (C 1, I c1, p) = OntoImage( OntoOJoin ( C 1, I c1 C 2, ext*(C 2 ), λi C1 λi C2.i c1 = i c2 ), I c2.p ) case 2: Multi-instanciation u Operator semantics

19. 19 Query Algebra for OBDB: Example(2) uQuery on data Retrieve the first name of the instances of the ontology class User ontoImage first_name ext * User OntoQL. SELECT first name FROM User RQL. SELECT fn FROM User{u}.first_name{fn} SPARQL. SELECT ?fn WHERE { ?u rdf:type User OPTIONAL { ?u first_name ?fn } } Case 1: May not be used in the extent of User case2: May not be defined on User (multi-instanciation) u Context u Approach u Proposal u Conclusion

20. 20 TypeOf: I 2 C Returns the set of classes an instance belongs to Query Algebra for OBDB: Ontology and Content parts u Context u Approach u Proposal u Conclusion uSignatures of Operators (E C) x 2 (E C) x … (E C) x 2 (E C) u Same Operators with the introduction of the TypeOf function Collection of ontology elements and/or class instances _ and/or class instances Allows to join the ontology and content part of an OBDB

21. 21 Query Algebra for OBDBs: Example (3) uQuerying both ontology and data Retrieve the URI of each ontology class and the URI of its instances OntoQL. SELECT C.#uri, i.uri FROM #Class C, C as i RQL. SELECT $C, i FROM {i;$C} SPARQL. SELECT ?C ?i WHERE { ?C rdf:type rdfs:Class. ?i rdf:type ?C } OntoOJoin ext* Class CObjectC i C typeOf(i) OntoProject Join the ontology and content part of an OBDB u Context u Approach u Proposal u Conclusion

22. 22 Outline uContext: OBDBs and OBDBs Query Langages uOverall Approach uProposal: Data Model and Query Algebra for OBDB uConclusion and future work

23. 23 Conclusion u A formal work on OBDB u Context u Approach u Proposal u Conclusion tFormal Data Model vIndependent of a given ontology model nCore ontology model nExtension capabilities nCan be stored in the Meta-Schema part vIndependent of the logical model nExtent to each class nView mechanism for hiding the logical model tQuery Algebra vExtension and adaptation of the ENCORE query algebra vUsable to represent the semantics of queries on Ontology and/or data expressed in different languages

24. 24 Future work uOptimization tAdapt and reuse existing techniques tExploit specific features of OBDB u Context u Approach u Proposal u Conclusion uProperties of the algebra tCompleteness and closure of the algebra tComplexity and benchmarking uExpressive power of Ontology Query Language tExtend the notion of relational completeness to OBDB exploitation languages

25. 25 Questions