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Re: intersectionOf and subClassOf

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 08 Apr 2003 07:57:20 -0400 (EDT)
Message-Id: <20030408.075720.01449370.pfps@research.bell-labs.com>
To: geoff@sover.net
Cc: www-rdf-logic@w3.org, jjc@hpl.hp.com

From: "Geoff Chappell" <geoff@sover.net>
Subject: RE: intersectionOf and subClassOf
Date: Mon, 7 Apr 2003 10:43:55 -0400

[...]

> > 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

Incorrect.  You may be reading part of the RDFS-compatible semantics for
OWL and seeing the ``if''s there.  However, what makes the semantics for
owl:intersectionOf iff is the ``='' there.

> 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. 

This is a non-entailment.  Just because we know that Y has the same
extension as the intersection of B and C doesn't mean that it *is* an
intersection of B and C.

> 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?

Correct. This is an entailment.  

> 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.

You are correct here.  This should not be a conclusion.

> > 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? 

Yes.  This would not work.  What would instead happen is, for example, two
properties would be made the same, not that there would be a syntactic
invalidity. 

[...]

peter
Received on Tuesday, 8 April 2003 07:57:29 GMT

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