Presented by Jie Bao RPI Sept 11, 2008 Part 2 of RDF/OWL Semantics Tutorial

1. OWL Full Semantics-- RDF-Compatible Model-Theoretic Semanticsby Peter F. Patel-Schneider, Patrick Hayes and Ian HorrocksW3C Recommendation, 2004http://www.w3.org/TR/owl-semantics/rdfs.html Presented by Jie Bao RPI Sept 11, 2008 Part 2 of RDF/OWL Semantics Tutorial http://tw.rpi.edu/wiki/index.php/RDF_and_OWL_Semantics

2. Disclaimer • The semantics and inference rules about RDFS Plus /RDFS 3.0 are rolely Jie Bao’s own and do not reflect the positions of either W3C (or any of its working group) or any of the RDFS Plus /RDF 3.0 proposals (citation on the page RDFS Plus: a Rule Subset of OWL ).

3. A Layer Cake of Languages You Are Here

4. Not Covered in the Talk • Datatype • Annotation • Ontology house keeping (e.g., imports) • OWL comprehension conditions

5. Outline • Review of RDF Semantics • OWL Overview • RDFS 3.0 Semantics • OWL Full Universe • OWL Full Interpretation Conditions

6. RDF(S) Vocabulary

7. RDFS Interpretation V vocabulary extension of classes IS ICEXT IP IC rdf:Property IEXT rdfs:Class IR rdfs:Resource IR x IR extension of properties

8. Outline • Review of RDF Semantics • OWL Overview • RDFS Plus Semantics • OWL Full Universe • OWL Full Interpretation Conditions

9. OWL Family

10. From RDF to OWL 2 Full OWL 2 Full RDFS+ RDFS OWL 2 RL OWL Full RDF

11. OWL Extensions to RDFS • Constructing classes: • e.g.,     • Constructing properties: • e.g., inverseOf • Property characteristics: • e.g., transitive, functional, symmetric • Mapping • Equality, non-equality (between classes, properties, ind.)

12. Direct MT Sem. vs RDF MT Sem. • Direct Model-Theoretical Semantics • For OWL DL (thus also OWL Lite) • Simpler than the RDF MT Semantics • Corresponds to the semantics of DL SHOIN(D) • Decidability guaranteed • RDF-Compatible Model-Theoretical Semantics • For OWL Full (thus also OWL DL and OWL Lite) • Extends RDFS Semantics

13. Outline • Review of RDF Semantics • OWL Overview • RDFS Plus Semantics • OWL Full Universe • OWL Full Interpretation Conditions

14. RDFS Plus: a Rule Subset of OWL Design intuition: Scalable, easier to implement using rule inference • RDFS Plus / OWL Prime / RDFS 3.0 • Dean Allemang, James Hendler. Semantic Web for the Working Ontologist, Chapter 7 • Oracle: OWL Prime http://www.w3.org/2007/OWL/wiki/OracleOwlPrime • Related proposals • AllegroGraph RDFS++: http://agraph.franz.com/support/learning/Overview-of-RDFS++.lhtml • OWL 2 RL http://www.w3.org/2007/OWL/wiki/Profiles#OWL_2_RL

15. RDFS Plus Vocabulary

16. RDFS Plus Semantics

17. RDFS Plus Semantics

18. RDFS Plus Semantics * By default, RDFS uses “only if”, OWL 1 Full and OWL 2 Full uses “iff”

19. Inference Rules Some examples: Complete rule set is in backup slides

20. Outline • Review of RDF Semantics • OWL Overview • RDFS Plus Semantics • OWL Full Universe • OWL Full Interpretation Conditions

21. OWL Vocabulary

22. Recall: RDFS Interpretation V vocabulary extension of classes IS ICEXT IP IC rdf:Property IEXT rdfs:Class IR rdfs:Resource IR x IR extension of properties

23. OWL Full Interpretation V vocabulary extension of classes IS ICEXT rdf:Property = {owl:ObjectProperty, owl:DatatypeProperty, owl:AnnotationProperty, owl:OntologyProperty} IP IC IEXT rdfs:Class =owl:Class IR rdfs:Resource =owl:Thing IR x IR extension of properties

24. OWL Full vs OWL DL P is the union of owl:ObjectProperty, owl:DatatypeProperty, owl:AnnotationProperty, and owl:OntologyProperty Note: in OWL Full, an element can be an individual (owl:Thing element), a class (owl:Class element) and an property (P element) at the same time.

25. True or False? In OWL Full • owl:Thing rdfs:subClassOf owl:Class • owl:Class rdfs:subClassOf owl:Thing • owl:Thing rdf:type owl:Class • owl:Class rdf:type owl:Class • rdf:Property rdf:type owl:Class Refer: • OWL RDF Schema: http://www.w3.org/2002/07/owl • Thing and Class: http://ontolog.cim3.net/forum/ontolog-forum/2008-09/threads.html#00004

26. Outline • Review of RDF Semantics • OWL Overview • RDFS Plus Semantics • OWL Full Universe • OWL Full Interpretation Conditions

27. OWL Classes and Properties

28. Boolean Operations and Enumeration

29. Restriction (Anonymous Class) Note: Content on this page is simplified by omitting datatype properties

30. Non-equality More: Comprehension conditions (which require the existence of appropriate OWL descriptions and data ranges ) – not covered

31. Conclusions RDFS Plus • A scalable rule subset of OWL Full, with MT semantics • Equality + Property Characteristics • Has extensional semantic conditions (while RDFS has not) OWL Full • Extends RDFS Plus, with MT semantics • OWL Full universe = RDFS universe • rdfs:Class = owl:Class ; rdfs:Resource = owl:Thing; owl:ObjectProperty <= rdf:Property • No distinction between classes, properties and individuals Next talk: OWL 2Full

32. Further Reading • Ian Horrocks, Peter F. Patel-Schneider, Frank van Harmelen - From SHIQ and RDF to OWL: the making of a Web Ontology Language. In J. Web Sem. 1(1):7-26, 2003.(URL) • Turner, David; Carroll, Jeremy J. Comparing OWL Semantics. Technical Reports HPL-2007-146. HP Lab, 2007. (URL)

33. Backup

34. Other OWL Vocabulary • owl:DatatypeProperty, owl:DataRange • owl:Ontology • owl:imports, owl:priorVersion, owl:backwardCompatibleWith, and owl:incompatibleWith, owl:versionInfo • owl:OntologyProperty • owl:DeprecatedClass, owl:DeprecatedProperty • owl:AnnotationProperty

35. Exercise • Prove tautology in RDFS: • rdfs:subPropertyOf rdfs:subPropertyOf rdfs:subPropertyOf • rdfs:domain rdfs:domain rdf:Property • rdfs:doman rdfs:range rdf:Class • rdf:Property rdf:type rdfs:Class • Prove tautology in OWL Full: • owl:sameAs owl:sameAs owl:sameAs

36. d RDFS Plus Rules (1) Equality rules

37. RDFS Plus Rules (2) Equality rules

38. RDFS Plus Rules (3) Property characteristic rules

39. RDFS Plus Rules (4) OWL Class and Property Declaration

40. RDFS Plus Rules (5) RDFS Rules

41. RDFS Plus Rules (6) RDFS Rules (domain & range)