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Re: ACTION: task force unasserted triples

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 23 Apr 2002 11:44:13 -0400
To: connolly@w3.org
Cc: schreiber@swi.psy.uva.nl, www-webont-wg@w3.org
Message-Id: <20020423114413U.pfps@research.bell-labs.com>
OK, herein is included a completely worked out example, with the WebOnt
language stuff in something close to RDF/XML.  (I think that it is
completely-valid RDF/XML modulo the ellipses, but I'm certainly not an
expert in what is and what is not valid RDF/XML.)

peter




The Web Ontology Working Group is producing a language that can be used to
build ontologies.  This language is supposed to use the syntax of RDF and
to be compatible with the model theory of RDF.  

However, taking all three of these together results in severe problems.


Consider the following RDF graph

  John rdf:type Student .
  John rdf:type Employee .

as the WebOnt language will include an intersection construct, this graph
should entail

  John rdf:type |intersection Student Employee| .

in the WebOnt language (where |intersection Student Employee| is a short
form for a unnamed node that is connected to some other RDF triples that
carry the intersection construct applied to Student and Employee).
However, this cannot be a valid entailment unless there is an object in the
domain of discourse of the initial RDF graph that is this intersection.

Therefore the model theory for the WebOnt language will have to include
comprehension principles for these sort of classes.

Many more such examples can be constructed, together requiring a powerful
theory of classes in the WebOnt language.  This theory is so powerful that
it will contain inconsistencies, leading to a complete breakdown of the
model theory for the WebOnt language.  (Even if the WebOnt language could
be expressively limited to disallow the paradoxical classes, the same
problem will reoccur at higher expressive levels in the Semantic Web
tower.)


If, however, the triples that are used to encode the syntax of the
constructs of the WebOnt language are unasserted, then these constructs do
not need to be part of the domain of discourse.  In this case, there is no
need for comprehension axioms, and a non-trivial theory can be developed for
the WebOnt language.

One way to do this is to put WebOnt language triples into separate
documents, with a different extension.  Such a file might look like

File foo.ont

<xml ...>
<rdf:rdf xmlns:fowl="...">
<fowl:PrimitiveClass fowl:name="Student" />
<fowl:PrimitiveClass fowl:name="Employee" />
<fowl:DefinedClass fowl:name="Student-and-Employee">
 <fowl:super rdf:resource="Student" />
 <fowl:super rdf:resource="Employee" />
</fowl:DefinedClass>
</rdf:rdf>

Then information about base objects would be in .rdf files

File foo.rdf

<xml ...>
<rdf:rdf ...>
<Person rdf:about="John" />
<Student rdf:about="John" />
</rdf:rdf>


What is lost?  Well, of course, quite a number of entailments are lost, and
the details depend on which triples are unasserted.  However, if nothing is
done, the empty RDF graph will, in the WebOnt language, entail a
contradiction.
Received on Tuesday, 23 April 2002 14:36:58 GMT

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