Talk at XML 2000

1
RDFS(FA) and RDF MTTwo Semantics for RDFS
Jeff Z. Pan1 and Ian Horrocks1,2 pan
horrocks_at_cs.man.ac.uk 1 Information Management
Group Computer Science Department University of
Manchester 2 Network Inference Ltd London, UK
2
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

? Semanticsreasoning
? Relational Data
? Data Exchange
3
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)

4
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.

5
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
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

ltR,Cgt ?IEXT(I(rdftype)) ltP,Cgt ?IEXT(I(rdftype))
ltJ,Pgt ?IEXT(I(rdftype))
IEXT(S)
IEXT
IEXT(T)
7
Language Layering

• More expressive ontology languages layered on top
  of RDF(S)
• E.g., OIL, DAMLOIL, 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 RDFMT gives all and
  only desired entailments
• Classes whose extension is not well defined
• Size of the MT universe

Should I use owlClass or rdfsClass?
8
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)

exmy-type rdfssubPropertyOf
rdftype rdftype rdfsdomain rdfsProperty
9
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
Metamodeling Architecture (Four Strata)
faMResource, faMClass faMProperty
Stratum 3 (Meta-Language Layer)
faLResource, faLClass faLProperty
Stratum 2 (Language Layer)
faOResource Person, Researcher workWith
Stratum 1 (Ontology Layer)
Stratum 0 (Instance Layer)
Ian, Jeff
11
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) doesnt invalidate existing RDF(S)
  syntax
• Users dont 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
Example Stratification
faMClass
fam-type
fal-subClassOf
fal-subClassOf
faLResource
faLClass
faLProperty
fal-type
fal-type
egPerson
fal-type
fao-subClassOf
faOResource
egworkWith
fao-subClassOf
fao-domain
fao-subClassOf
egResearcher
fao-range
fao-type
fao-type
egworkWith
Jeff
Ian
13
Interpretation of RDFS(FA)

14
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
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
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 faClass or rdfsClass?
17
Acknowledgement

• Thanks to
• Peter Patel-Schneider
• Peter Aczel

18

• Thank you for your attention!

Jeff Z. Pan1 and Ian Horrocks1,2 pan
horrocks_at_cs.man.ac.uk 1 Information Management
Group Computer Science Department University of
Manchester 2 Network Inference Ltd London, UK