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RE: ISSUE-124 (datarange complement): The complement of a datarange is defined relative to the whole data domain

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>
Message-ID: <007301c8cbe8$da660770$4012a8c0@wolf>

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 GMT

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