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RE: SEM: semantics for current proposal (why R disjoint V?) (sameState TEST)

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Thu, 2 May 2002 19:01:50 +0100
Message-ID: <15569.32526.368827.417304@merlin.oaklands.net>
To: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>
Cc: "Dan Connolly" <connolly@w3.org>, "Pat Hayes" <phayes@ai.uwf.edu>, <www-webont-wg@w3.org>
On April 29, Jeremy Carroll writes:
> > Unfortunately, the interaction of UnambiguousProperty and datatypes
> > makes this problematical. Imagine, for example, that a datatype
> > consisting of integers in the range 0-999 is used as a unique-id/key
> > for instances of the class Person such that all persons have exactly
> > one unique-id, all unique-ids are integers in the range 0-999, and
> > unique-id is an UnambiguousProperty.  In order to function correctly,
> > a reasoner is now required to understand the properties of datatypes,
> > e.g., that the cardinality of this particular datatype is 1,000, and
> > that as a result no model can contain more than 1,000 instances of
> > Person (note that this would not be the case if unique-ids were reals
> > in the range 0-999).
> 

You are missing the crucial point that the reasoner has to know about
the properties of the datatype (i.e., that there are exactly 1,000
integers in the range 0-999, neither more nor less) and may also need
to consider complex interactions resulting from the predicates defined
on the datatypes. This is what makes the formal properties unclear and
could lead to decidability problems.

In contrast, the maxCardinality of the class of one-thousand URIs is
inherent in its definition, and there are no additional predicates to
worry about.

You are right in saying that the intractability problem would still be
there with the 1,000 individuals class.

Ian

> Can't I set up this example without any recourse to datatypes at all.
> 
> e.g.
> 
> I form one thousand URIs.
> For each one I form the class: oneOf[x] (giving me 1000 classes).
> 
> I form the disjoint union of these 1000 classes, giving me oneOf 1000
> distinct URIs.
> 
> i.e.
> 
> <daml:Class rdf:ID="Thousand">
>   <daml:disjointUnionOf rdf:parseType="daml:collection">
>     <daml:Class>
>       <daml:oneOf rdf:parseType="daml:collection>
>         <rdf:Description rdf:about="#000"/>
>       </daml:oneOf>
>     </daml:Class>
>     <daml:Class>
>       <daml:oneOf rdf:parseType="daml:collection>
>         <rdf:Description rdf:about="#001"/>
>       </daml:oneOf>
>     </daml:Class>
> ...
>     <daml:Class>
>       <daml:oneOf rdf:parseType="daml:collection>
>         <rdf:Description rdf:about="#999"/>
>       </daml:oneOf>
>     </daml:Class>
>   </daml:disjointUnionOf>
> </daml:Class>
> 
> 
> I now define an UnambiguousProperty whose range is that Thousand class
> 
> <daml:UnambiguousProperty rdf:ID="p">
>    <daml:range rdf:resource="#Thousand"/>
> </daml:UnambiguousProperty>
> 
> >
> > The formal properties of the resulting logic are not well understood
> > (e.g., it is not clear yet if the language would be
> > decidable).
> 
> pass
> 
> >  Moreover, it would cause severe problems for implementors
> > and might be a source (admittedly not the only possible source) of
> > crippling intractability: remember that, unlike a database, the
> > existence of 2,000 individual names would not be an error, but would
> > lead to the inference that the names must be partitioned into 1,000
> > sets of "sameIndividuals". Check out the number of ways that 2,000
> > elements can be partitioned into 1,000 sets - it is a big number!
> 
> snap?
> 
> >
> > This is an irresistible opportunity for a very nice citation [1] :-).
> > Sadly, Stirling does not seem to have made this work available on
> > his web site.
> >
> > Regards, Ian
> >
> > [1] Stirling, J. Methodus differentialis, sive tractatus de summation
> > et interpolation serierum infinitarium. London, 1730. English
> > translation by Holliday, J. The Differential Method: A Treatise of the
> > Summation and Interpolation of Infinite Series. 1749.
> 
> Jeremy
> 
Received on Thursday, 2 May 2002 14:05:05 GMT

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