problem with B1 B2

[[There may be some infelicities in this message, as I do not have full
internet connectivity just now. I believe that the main points are correct,
however.]]

Unfortunately, the B1-B2 extension to the mapping rules results in
incomparable mappings for OWL DL ontologies.  (One reason that I took so
long in getting to this point was that I was trying to fix details of
Jeremy's message, and thus wasn't getting to the real problem.)

The main problem is that the following assumption from Jeremy is not
correct: 

| The only possible syntactic uses of bnodes
| corresponding to descriptions in OWL DL occur
| either in triples whose OWL Full semantics
| depends only on the class extension of the bnode,
| or on rdf:first triples in lists which are the object
| of owl:unionOf and owl:intersectionOf triples.

Descriptions can, of course, be part of other descriptions, as in 

Class(A complete restriction(r allValuesFrom(restriction(r allValuesFrom(B)))))

where one restriction is part of the other restriction.

Now consider the following ontology

Ontology(
Class(B partial)
Class(A complete restriction(r allValuesFrom(restriction(r allValuesFrom(B)))))
Class(C complete restriction(r allValuesFrom(restriction(r allValuesFrom(B)))))
)

Under the current mapping results in something containing:

B rdf:type owl:Class .
A rdf:type owl:Class .
A owl:equivalentClass _:r1 .
_:r1 rdf:type owl:Restriction .
_:r1 owl:onProperty r .
:_r1 owl:allValuesFrom _:r2 .
_:r2 rdf:type owl:Restriction .
_:r2 owl:onProperty r .
:_r2 owl:allValuesFrom B .
C rdf:type owl:Class .
C owl:equivalentClass _:r3 .
_:r3 rdf:type owl:Restriction .
_:r3 owl:onProperty r .
:_r3 owl:allValuesFrom _:r4 .
_:r4 rdf:type owl:Restriction .
_:r4 owl:onProperty r .
:_r4 owl:allValuesFrom B .


Under the B1/B2 proposal there could be a mapping to:

B rdf:type owl:Class .
A rdf:type owl:Class .
A owl:equivalentClass _:r1 .
_:r1 rdf:type owl:Restriction .
_:r1 owl:onProperty r .
:_r1 owl:allValuesFrom _:r2 .
_:r2 rdf:type owl:Restriction .
_:r2 owl:onProperty r .
:_r2 owl:allValuesFrom B .
C rdf:type owl:Class .
C owl:equivalentClass _:r3 .
_:r3 rdf:type owl:Restriction .
_:r3 owl:onProperty r .
:_r3 owl:allValuesFrom _:r2 .


These two RDF graphs are not equivalent under the OWL RDFS semantics, which
causes the correspondence theorem to break down.

peter

Received on Friday, 29 August 2003 09:10:49 UTC