RE: intersectionOf and subClassOf

> -----Original Message-----
> From: www-rdf-logic-request@w3.org
[mailto:www-rdf-logic-request@w3.org]
> On Behalf Of Peter F. Patel-Schneider
> Sent: Monday, April 07, 2003 9:28 AM
> To: geoff@sover.net
> Cc: www-rdf-logic@w3.org
> Subject: 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.

I see - since D could be empty, or a subClassOf B or C, or...
 
> > 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. 

This hits indirectly on something else I've been puzzling over. My
understanding is that the semantics of intersectionOf are if, not iff
and that as a consequence we couldn't claim:

<owl:Class rdf:about="Y">
	<owl:intersectionOf rdf:parsetype="Collection">
		<owl:Class rdf:about="B"/>
		<owl:Class rdf:about="C"/>
	</owl:intersectionOf>
</owl:Class>

just because we know (for some other reason) that Y and an intersection
of B and C have the same class extensions. But we could claim that:

<owl:Class rdf:about="Y">
	<owl:equivalentClass>
		<owl:Class>
			<owl:intersectionOf rdf:parsetype="Collection">
				<owl:Class rdf:about="B"/>
				<owl:Class rdf:about="C"/>
			</owl:intersectionOf>
		</owl:Class>
	</owl:equivalentClass>
</owl:Class>

(since equivalentClass does have iff semantics). Is this correct?

If I'm right to this point, the part I'm puzzling over is the test case
at:

http://www.w3.org/2002/03owlt/cardinality/Manifest005

which seems to me to be making a claim of class identity, not just
equivalent class extensions, based upon the fact that a class (the
restriction in the premise) has the same class extension as an
intersection of two other classes/restrictions (in the conclusion). I'm
probably interpreting it wrong, but I'm wondering what in the semantics
licenses this particular entailment.


> 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.

OK. But why not state cardinality restrictions on onProperty, etc. so
that a malformed restriction would actually be invalid? E.g. onProperty
has cardinality 1, someValuesFrom, allValuesFrom, hasValue, cardinality,
etc. all supProperties of requiredRestrictionProperty which has
cardinality of 1. Or is there some reason that won't work? 
 
> 
> peter

Thanks for your help.

Geoff

Received on Monday, 7 April 2003 10:48:04 UTC