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Re: Layering bug?

From: Jeremy Carroll <jjc@hplb.hpl.hp.com>
Date: Thu, 03 Jul 2003 13:38:58 +0100
Message-ID: <3F0423E2.2090900@hplb.hpl.hp.com>
To: Mehrdad Omidvari <Mehrdad.Omidvari@networkinference.com>
CC: www-webont-wg@w3.org



Mehrdad Omidvari wrote:

> I think your new example is wrong in both OWL Full and DL.
> There is nothing stopping a "property" to be empty. For example you
> could assert that the domain of q is owl:Nothing. This would not make
> the ontology inconsistent. Property q is not necessarily equivalent to
> p, as q could be empty.
> 
> Also in your first example asserting property relations between classes
> is not OWL DL:
> 
>     <owl:ObjectProperty rdf:ID="p" />
>     <owl:Class rdf:ID="c" >
>        <p>
>          <owl:Class rdf:ID="d" />
>        </p>
>     </owl:Class>
> 



In the first example eg:ap was an annotation property, and hence can link 
classws with classes, but I have withdrawn example, since you pointed out 
that I had failed to read one part of the OWL DL semantics.

 > eg:p rdf:type owl:ObjectProperty .
 > eg:q rdf:type owl:ObjectProperty .
 > owl:Thing owl:oneOf _:b .
 >    _:b rdf:first eg:i .
 >    _:b rdf:rest rdf:nil.
 >    eg:i rdf:type owl:Thing.
 > eg:i eg:p eg:i .
 >
 >   entails
 >
 > eg:i eg:q eg:i .
 >



In the second example (above), you are quite right to say nothing stops a 
property from being empty in OWL DL, (so the DL entailment does not hold) but:
  In OWL Full, if there is an interpretation, then there is only one thing 
in the universe. Thus I(eg:p) and I(eg:q) (and I(ex:i) and I(rdf:type) and 
I(rdf:first) etc etc.) are all the same individual. The property extention 
is defined via IEXT(I(.)) thus every uriref that has an interpretation has 
the same property extension!! This extension must contain the pair 
(I(eg:i), I(eg:i)) Thus the entailment follows. (As well as very weird ones 
like eg:i rdf:type owl:oneOf .)
  There may well not be any such interpretations, in which case the 
entailment holds trivially.

(Looking at it, I can't believe that any interpretations can satisfy all 
these conditions. Since there is only one individual in the universe, we 
almost certainly violate the comprehension axioms .... this looks very messy)


> 
> I understand that you are trying to come up with an example which is a
> legal OWL DL ontology and an entailment which can be expressed in OWL DL
> but not valid in OWL DL (but valid in OWL Full) .
> As the semantics of OWL DL is stricter than that of OWL Full, it might
> not be possible to come up with such an example.


The resolution of 5.3 suggested that the semantics of OWL DL and OWL Full 
on the syntactic subset leads to the same entailments. Although my first 
example had a minor bug, it was only minor, and I think there is enough 
evidence to suggest that at best we currently have OWL DL entailment as a 
proper sub-relationship to OWL Full entailment over the OWL DL syntactic 
subset.

Jeremy
Received on Thursday, 3 July 2003 08:41:15 GMT

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