Re: intersectionOf and subClassOf

From: "Geoff Chappell" <geoff@sover.net>
Subject: RE: intersectionOf and subClassOf
Date: Mon, 7 Apr 2003 08:47:59 -0400

[edited]
> > -----Original Message-----
> > From: www-rdf-logic-request@w3.org
> > On Behalf Of Peter F. Patel-Schneider
> > Sent: Monday, March 31, 2003 8:46 AM
> > To: geoff@sover.net
> > Subject: Re: intersectionOf and subClassOf
[...]
> Can you clarify a related question for me? I'll try to be a bit more
> precise this time :-) 
> 
> Given this situation:
> 
> <owl:Class rdf:about="X">
> 	<rdfs:subClassOf rdf:resource="B"/>
> 	<rdfs:subClassOf rdf:resource="C"/>
> </owl:Class>
> 
> <owl:Class rdf:about="Y">
> 	<owl:intersectionOf rdf:parsetype="Collection">
> 		<owl:Class rdf:about="B"/>
> 		<owl:Class rdf:about="C"/>
> 	</owl:intersectionOf>
> </owl:Class>
> 
> It seems to me that we can know:
> 
> <rdf:Description about="X">
> 	<rdfs:subClassOf rdf:resource="Y"/>
> </rdf:Description>

Correct.

> but not:
> 
> <rdf:Description about="X">
> 	<owl:equivalentClass rdf:resource="Y"/>
> </rdf:Description>

Correct, because Y=B^C, X<=B, X<=C, so it is not necessarily the case that
X=B^C, only that X<=B^C.

> Is that right? I'm assuming that we can take the description of Y as
> complete due to the nature of rdf:List(s) but we can never know that the
> description of X is complete (i.e. there could be another statement such
> as:
> 
> <owl:Class rdf:about="X">
> 	 <rdfs:subClassOf rdf:resource="D"/>
> </owl:Class>
> 
> lurking out there waiting to be found.

I wouldn't put it this way.  It is not the possibility of some such D but
instead is the possibility of some individual y that belongs to Y but not
to X.

> If that's right, I'm wondering about the related issue of restrictions.
> There don't seem to be cardinality restrictions on onProperty, etc. so
> I'm wondering how we can ever treat a restriction as complete? i.e. can
> we ever infer that the class extensions of two restrictions are the
> same?

Complete is probably not the right way of thinking of this (even though the
modality tag is ``partial'' or ``complete''.  What counts is whether there
is a necessary-and-sufficient condition for membership in a class.  For Y
there is, namely being in both B and C.  For X there isn't, at least from
what is given above.  For any restriction there is, namely satisfying the
condition in the restriction (for natural restrictions, that is).  

To complicate the situation, OWL restrictions are compound objects made up
of two triples (or even three if you count any rdf:type triple).  If there
are fewer triples (zero or one), or too many triples (three or more), or
just the wrong kind of triples (e.g., an owl:someValuesFrom and an
owl:minCardinality) there is still an OWL restriction of sorts.  Such OWL
restrictions have to be given some sort of meaning that fits in with the
rest of OWL.  I recommend, however, ignoring such malformed OWL
restrictions.

> Thanks,
> 
> Geoff Chappell

peter

Received on Monday, 7 April 2003 09:27:55 UTC