- From: Boris Motik <boris.motik@comlab.ox.ac.uk>
- Date: Wed, 11 Jun 2008 18:30:33 +0100
- To: "'Web Ontology Language \(\(OWL\)\) Working Group WG'" <public-owl-wg@w3.org>

Hello, As per our decision today, I've fixed up the mapping. Here is the diff: http://www.w3.org/2007/OWL/wiki/index.php?title=Mapping_to_RDF_Graphs&diff=8468&oldid=8449 Boris > -----Original Message----- > From: public-owl-wg-request@w3.org [mailto:public-owl-wg-request@w3.org] On Behalf Of Boris Motik > Sent: 21 May 2008 20:13 > To: 'Evan Wallace'; 'Web Ontology Language ((OWL)) Working Group WG' > Subject: RE: ISSUE-124 (datarange complement): The complement of a datarange is defined relative to > the whole data domain > > > Hello, > > Complemented data ranges occur implicitly in an ontology if they occur on the LHS of implications. > Here is an example: > > (1) SubClassOf( > SomeValuesFrom( R DatatypeRestriction( xsd:integer minInclusive 5) ) > A > ) > > Here, the data range DatatypeRestriction( xsd:integer minInclusive 5) occurs on the LHS. In logic, > you can shift things from the LHS > to the RHS of implication by negating the class. Thus, this axiom is equivalent to the following > axiom: > > (2) SubClassOf( > owl:Thing > UnionOf( > AllValuesFrom( R ComplementOf( DatatypeRestriction( xsd:integer minInclusive 5) ) ) > A > ) > ) > > Here, > > (3) AllValuesFrom( R ComplementOf( DatatypeRestriction( xsd:integer minInclusive 5) ) ) > > was obtained by complementing > > (4) SomeValuesFrom( R DatatypeRestriction( xsd:integer minInclusive 5) ). > > Now here is the crux: if the semantics of data ranges were not defined w.r.t. the entire domain, then > these two concepts would not > be negations of each other. This would be bad: some straightforward and well-known transformations > that usually generate equivalent > ontologies would in our case not be applicable. > > > Furthermore, whether you like it or not, the meaning of (1) axiom is in fact equivalent to (2), even > if you don't see an explicit > negation in it. For example, assume that you also had the following assertions: > > (5) PropertyAssertion( R ind "bla" ) > (6) ClassAssertion( ComplementOf( A ) ind ) > > Axioms (1)+(5)+(6) are intuitively satisfiable: assertion (5) does not "fire" the rule (1), so we > don't derive ind to be an instance > of A, which is consistent with (6). So far so good: this is what we want. > > > Now consider what would happen if we interpreted the complemented data range in (2) w.r.t. > xsd:integer and not w.r.t. the whole > domain. Because of (6), the following axiom must hold: > > (7) ClassAssertion( > AllValuesFrom( R ComplementOf( DatatypeRestriction( xsd:integer minInclusive 5) ) ) > ind > ) > > But if we interpreted the complement w.r.t. xsd:integer, then (7) would be equivalent to the > following: > > (8) ClassAssertion( > AllValuesFrom( R DatatypeRestriction( xsd:integer maxInclusive 4) ) > ind > ) > > But this axiom is invalidated because of (5): ind is connected by R to "bla", which is not an integer > smaller than 4! Hence, (5)+(8) > is unsatisfiable, which would suggest that (5)+(6)+(2) is unsatisfiable. Thus, turning (1) into (2) - > - a quite common operation in > logic -- affects the satisfiability of our ontology; well, this IS bad! > > The moral of this is that, even though you don't see ComplementOf in (1), this complement is > implicitly present and the axiom is in > fact equivalent to (2). > > > > > > Now here is what I believe this is not an issue in practice. A typical ontology would contain an > explicit specification of the range > of R: > > (9) PropertyRange( R xsd:integer ) > > This axiom now eliminates the "not integer" possibility in (3), which effectively gives you the > desired behavior. > > In our example, (9)+(5) is unsatisfiable, which is good: the unsatisfiability is now there from the > beginning and is not affected by > equivalent transformations. > > > I hope that this clarifies this issue. > > Regards, > > Boris > > > > -----Original Message----- > > From: Evan Wallace [mailto:ewallace@cme.nist.gov] > > Sent: 21 May 2008 19:03 > > To: boris.motik@comlab.ox.ac.uk; Web Ontology Language ((OWL)) Working Group WG > > Subject: RE: ISSUE-124 (datarange complement): The complement of a datarange is defined relative to > > the whole data domain > > > > > > Boris wrote: > > > > > I really do not expect people to use complemented data ranges directly. Furthermore, if your > > ontology contains range constraints on > > > all data properties, then the complement of data ranges really becomes relative to the datatype > of > > the data range. Most ontologies > > > really do contain appropriate range constraints for data properties, so this problem will not be > > visible. > > Can you elaborate on this perhaps with an example? > > > > -Evan > >

Received on Wednesday, 11 June 2008 17:32:10 UTC