IMG, University of Manchester 1ISWC-2003 Sanibel Island, FL  

Jeff Z. Pan1 and Ian Horrocks1,2 {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

IMG, University of Manchester 2ISWC-2003 Sanibel Island, FL  

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

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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

worksIn

Ian Horrocks horrocks@cs.man.ac.ukname email

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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.:

ParentsubClassOf

RestrictiononProperty

minCardinality

hasChild

1

equivalentClasssubPropertyOf

subClassOf

Class

subClassOf

Resource

type

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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

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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

IEXTIEXT(T)

IEXT(S)

<R,C> IEXT(I(rdf:type))<P,C> IEXT(I(rdf:type))<J,P> IEXT(I(rdf:type))

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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?

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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:typerdf:type rdfs:domain rdfs:Property

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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

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Metamodeling Architecture (Four Strata)

Stratum 0 (Instance Layer) Ian, Jeff …

Stratum 1 (Ontology Layer)

Stratum 2 (Language Layer)

Stratum 3 (Meta-Language Layer)

fa:OResourcePerson, ResearcherworkWith …

fa:LResource, fa:LClassfa:LProperty …

fa:MResource, fa:MClassfa:MProperty …

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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

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Example: Stratification

fa:LResourcefa: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-typefa:l-type fa:l-type

fa:o-type fa:o-type

eg:workWith

fa:OResourcefa:o-subClassOf

fa:MClass

fa:m-type

fa:o-domain

fa:o-range

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Interpretation of RDFS(FA)

…

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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?

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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)

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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?

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Acknowledgement

• Thanks to:

–Peter Patel-Schneider

–Peter Aczel

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Thank you for your attention!

Jeff Z. Pan1 and Ian Horrocks1,2 {pan | horrocks}@cs.man.ac.uk

1 Information Management Group

Computer Science Department

University of Manchester

2 Network Inference Ltd

London, UK