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RE: owl:equivalentClass and rds:subClassOf

From: Bernard Vatant <bernard.vatant@mondeca.com>
Date: Mon, 12 Jan 2004 15:23:45 +0100
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: <www-rdf-logic@w3.org>, <holger@SMI.Stanford.EDU>
Message-ID: <GOEIKOOAMJONEFCANOKCKEACDBAA.bernard.vatant@mondeca.com>


Peter

> > The reciprocal rdfs:subClassOf declares a logical equivalence
> > of definition (intensional),
> > whereas owl:equivalentClass declares an equivalence at
> > instance level (extensional).

> Umm,  where did you get this impression?

>From http://www.w3.org/TR/owl-ref/#equivalentClass-def

"A class axiom may contain (multiple) owl:equivalentClass statements.
owl:equivalentClass is a built-in property that links a class description
to another class description. The meaning of such a class axiom is that the
two class descriptions involved have the same class extension (i.e., both
class extensions contain exactly the same set of individuals)..."

This is for the "extensional" definition of "equivalentClass". But I guess
your remark is about the part about rdfs:subClassOf. Well, thinking about
it, rdfs:subClassOf is also extensional, right. That's why the two
definitions are equivalent. Understood, thanks.

> > Should those declarations be kept distinct or not by a
> conformant OWL tool?
> > And if yes, what would be the logical relationship, if any, between the
> > former and the latter?
>
> As far as the logic underlying OWL is concerned they are exactly
> the same.

OK. That's what I thought before Holger asked about it and put trouble in
my mind :)
So I'm happpy to see it's a non-issue, after all

BTW since we are at it, seems it settles the debate from a while ago on
another forum about antisymmetry of subClassOf.
http://www.isotopicmaps.org/pipermail/sc34wg3/2003-February/001112.html

Where it seems I was obviously wrong :(

So, the following entailment holds :

  :A rdfs:subClassOf :B
  :B rdfs:subClassOf :A
entails
  :A owl:equivalentClass :B

But that is not antisymmetry, which would be the following :

  :A rdfs:subClassOf :B
  :B rdfs:subClassOf :A
entails
  :A owl:sameAs :B

.. and there is no such axiom in OWL, if I understand well the note.

"The use of owl:equivalentClass does not imply class equality. Class
equality means that the classes have the same intensional meaning (denote
the same concept)... Real class equality can only be expressed with the
owl:sameAs construct."

It figures rdfs:subClassOf does not define an order relation after all ...

Bernard Vatant
Senior Consultant
Knowledge Engineering
Mondeca - www.mondeca.com
bernard.vatant@mondeca.com
Received on Monday, 12 January 2004 09:23:53 GMT

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