bug in semantics (was Re: intersectionOf and subClassOf)

Jeremy has pointed out a problem with the semantics.

The semantics assumes that intersectionOf is a ``syntactic'' relationship,
i.e., there are no sufficient conditions for it.  This was fine once upon a
time, but is now, due to recent changes in the mapping to triples, the
correspondence theorem is now not correct.

There are several possible changes:

1/ Change the mapping back to the way it was, so that, for example, classes
   are not related to their ``definition'' by owl:intersectionOf
   relationships.  Instead there would be an anonymous intersection class
   related to the named class by an equivalence link.  This would be the
   safest course.

2/ Leave the mapping the way it is and upgrade owl:intersectionOf from a
   syntactic relationship to a semantic one.  This would require
   significant work on the correspondence proofs.  (If this course is taken
   I would withdraw my action to look into B1 and B2.)

3/ 

peter





From: "Jeremy Carroll" <jjc@hplb.hpl.hp.com>
Subject: RE: intersectionOf and subClassOf
Date: Thu, 10 Apr 2003 17:12:51 +0200

> 
> I think S&AS may be wrong about this.
> 
> Peter:
> [[
> Because of OWL's embedding on top of RDF there are actually several
> options that could arise here.
> 
> 1/ One could have the semantic constraint on owl:intersectionOf
> 	that if the extension of x is the same as the intersection of the
> 	extensions of a and b then x owl:intersectionOf [a b]
> 2/ One could have the semantic constraint that if
> 	   x owl:intersectionOf [a b]  then the extension of x is the same
> 	   as the intersection of the extensions of a and b
> 3/ One could have the semantic constraint that if
> 	   x owl:intersectionOf [a b]  then the extension of x is a subset
> 	   of the intersection of the extensions of a and b
> ]]
> 
> Option 1 might have been a better choice than option 2 (if I understood
> Peter's earlier message)
> 
> E.g.
> 
> Consider
> 
> <owl:Class rdf:about="#AandB">
>    <owl:equivalentClass>
>      <owl:Class>
>         <owl:intersectionOf rdf:parseType="Collection">
>           <owl:Class rdf:about="#A"/>
>           <owl:Class rdf:about="#B"/>
>         </owl:intersectionOf>
>      </owl:Class>
>    </owl:equivalentClass>
> </owl:Class>
> 
> This corresponds to the abstract syntax form
> 
> EquivalentClasses(<#AandB> intersectionOf(<#A> <#B>) )
> 
> which directly entails
> 
> Class( <#AandB> complete <#A> <#B> )
> 
> which corresponds to
> 
> 
> <owl:Class rdf:about="#AandB">
>    <owl:intersectionOf rdf:parseType="Collection">
>           <owl:Class rdf:about="#A"/>
>           <owl:Class rdf:about="#B"/>
>     </owl:intersectionOf>
> </owl:Class>
> 
> 
> i.e. option 1
> 
> but the rdfs compatible semantics has taken option 2.
> 
> Is this a bug?
> Does someone need to make a last call comment?
> Or have I misunderstood?
> 
> Jeremy
>

Received on Friday, 9 May 2003 18:53:25 UTC