1. 1 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Jeff Z. Pan 1 and Ian Horrocks 1,2 {pan | horrocks}@cs.man.ac.uk 1 Information Management Group Computer Science Department University of Manchester 2 Network Inference Ltd London, UK RDFS(FA) and RDF MT: Two Semantics for RDFS

2. 2 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Semantic Web Vision Semantic Web (SW) aims at machine understandability –SW languages describe content/function of Web resources RDF(S) is proposed as the base for SW languages –(In)famous “layer cake”:  Data Exchange  Semantics+reasoning  Relational Data ??? ? ?

3. 3 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Dual Roles of RDF(S) - I RDF(S) is used to add metadata annotations to Web resources –Subject-predicate-object triples used to link resources –i.e., triples represent knowledge about domain (such as Ian Horrocks worksWith Jeff Pan) worksWith worksIn Ian Horrocks horrocks@cs.man.ac.uk name email

4. 4 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Dual Roles of RDF(S) - II RDF(S) also used to define syntax and semantics of subsequent language layers (and even of itself), e.g.: Parent subClassOf Restriction onProperty minCardinality hasChild 1 equivalentClass subPropertyOf subClassOf Class subClassOf Resource type

5. 5 ISWC-2003 Sanibel Island, FL IMG, University of Manchester RDF(S) Features/Limitations Not clear that RDF(S) is appropriate for both functions (at once) –Limited set of syntax constructs (triples) –Not possible to extend syntax (as it is, e.g., when using XML) –Uniform semantic treatment of triple syntax i.e., “syntax” and “knowledge” triples have same semantics –Confusing (for some) cyclical meta-model –Semantics given by “non-standard” Model Theory

6. 6 ISWC-2003 Sanibel Island, FL IMG, University of Manchester RDF(S) Model Theory (RDF MT) Let V be a set of vocabulary, IR the universe of discourse –I is a mapping from V to IR –IP is the set of property objects –IEXT (x), the extension of a property object x, is a set of pairs IEXT IEXT(T) IEXT(S)  IEXT(I(rdf:type))

7. 7 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Language Layering More expressive ontology languages layered on top of RDF(S) –E.g., OIL, DAML+OIL, and now OWL –Include logical connectives, quantifiers, transitive properties, etc. –Need to extend RDF MT to “RDF+ MT” to give semantics to them However … –Several known problems with the “RDF+ MT” approach Difficult to ensure that RDF+MT gives all and only desired entailments Classes whose extension is not well defined Size of the MT universe Should I use owl:Class or rdfs:Class?

8. 8 ISWC-2003 Sanibel Island, FL IMG, University of Manchester RDF(S) Features/Limitations (reprise) Problems stem from features/limitations of RDF(S) –Triples, all triples and nothing but triples! –Classes and properties are treated as objects in the domain Including RDF/OWL/… built-in classes and properties –No restrictions on the use of built-in vocabularies E.g. the users can write triples as follows: Can lead to unwanted/unexpected consequences, particularly with more expressive langauges (like OWL) ex:my-type rdfs:subPropertyOf rdf:type rdf:type rdfs:domain rdfs:Property

9. 9 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Proposed Solution: RDFS(FA) RDFS(FA) is a sub-language of RDF(S) –It stands for “RDFS with Fixed layer metamodeling Architecture” –Has a First Order/Description Logic style semantics The universe of discourse is divided up into a series of strata –User defined facts/vocabulary and RDF/OWL built-in vocabulary are (typically) in different strata –Each modelling primitive belongs to a certain stratum (layer) Labelled with different prefix to indicate the stratum

10. 10 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Metamodeling Architecture (Four Strata) Stratum 0 (Instance Layer) Ian, Jeff … Stratum 1 (Ontology Layer) Stratum 2 (Language Layer) Stratum 3 (Meta-Language Layer) fa:OResource Person, Researcher workWith … fa:LResource, fa:LClass fa:LProperty … fa:MResource, fa:MClass fa:MProperty …

11. 11 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Syntax and Semantics RDFS(FA) introduces some new syntax to RDF(S) –Disallows arbitrary use of built-in vocabulary –Supports meta-classes and meta-properties (in specified strata) RDFS(FA) doesn’t invalidate existing RDF(S) syntax –Users don’t need to change their RDF(S) data sets Classes and Properties are not objects in RDFS(FA) –Classes interpreted as sets of resources in the adjacent lower stratum –Properties interpreted as sets of pairs of resources in the adjacent lower stratum The only exception is “type” property

12. 12 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Example: Stratification fa:LResource fa:LClass eg:Person eg:Researcher fa:LProperty eg:workWith Jeff Ian fa:l-subClassOf fa:o-subClassOf fa:l-subClassOf fa:o-subClassOf fa:l-type fa:o-type eg:workWith fa:OResource fa:o-subClassOf fa:MClass fa:m-type fa:o-domain fa:o-range

13. 13 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Interpretation of RDFS(FA) …

14. 14 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Advantages of RDF MT RDF(S) (RDF MT) is more expressive than RDFS(FA) –No stratification restrictions Anyone can say anything about anything –Properties can be defined between any two resources –Any resource can be defined as an instance of any resource (including itself) Be careful: an object can become a class or a property some time later What are the motivations of the extra expressive power?

15. 15 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Advantages of RDFS(FA) No problems layering FO languages on top of RDFS(FA) –Bottom two layers form standard FO models RDFS(FA) supports use of meta-classes and meta-properties –In stratum above classes and properties RDFS(FA) metamodel very similar to that of UML Possible to define a new sub-language of OWL: OWL FA –Extends OWL DL with meta-classes/properties and support for annotation properties –Fully compatible with OWL DL semantics –Amenable to reasoning (even for meta-classes/properties)

16. 16 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Conclusion RDF(S) is proposed as base for SW languages –Language architecture may be too complex for base layer –Known problems layering FO languages on top of RDF(S) We propose RDFS(FA) as a sub-language of RDF(S) Users can choose between –Layered style: RDFS(FA) –Non-layered style: full RDF(S) Should I use fa:Class or rdfs:Class?

17. 17 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Acknowledgement Thanks to: –Peter Patel-SchneiderPeter Patel-Schneider –Peter AczelPeter Aczel

18. 18 ISWC-2003 Sanibel Island, FL IMG, University of Manchester Thank you for your attention! Jeff Z. Pan 1 and Ian Horrocks 1,2 {pan | horrocks}@cs.man.ac.uk 1 Information Management Group Computer Science Department University of Manchester 2 Network Inference Ltd London, UK