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RE: intersectionOf and subClassOf

From: Geoff Chappell <geoff@sover.net>
Date: Sun, 30 Mar 2003 17:26:30 -0500
To: "'Enrico Franconi'" <franconi@inf.unibz.it>, <www-rdf-logic@w3.org>
Message-ID: <003d01c2f70b$696e6a60$835ec6d1@GSCLAPTOP>



> -----Original Message-----
> From: www-rdf-logic-request@w3.org
[mailto:www-rdf-logic-request@w3.org]
> On Behalf Of Enrico Franconi
> Sent: Sunday, March 30, 2003 4:41 PM
> To: Geoff Chappell; www-rdf-logic@w3.org
> Subject: Re: intersectionOf and subClassOf
> 
> 
> On 30/03/2003 20:36, Geoff Chappell wrote:
> > By "etc?", I meant that there seem to be an infinite number of
> > equivalent descriptions of the same class. For example, aren't these
all
> > equivalent?
> >
> > - A is a subClassOf B and C
> > - A is a subClassOf a class that is the intersectionOf B and C
> 
> Yes, if you mean: A is a subClassOf THE class that is the
intersectionOf B
> and C

That would make sense to me, but... I modified that one from THE to A
based upon Peter Patel-Schneider's comment that "(there can be more than
one intersection in OWL)". Did I misinterpret that?

 
> > - A is a subClassOf a class that is the intersectionOf B and a class
> > that is the intersectionOf C
> 
> What is "a class that is the intersectionOf B"?


I guess I needed some parens or something there - though then you'd
likely just have asked "What is a class that is the intersectionOf C". I
meant only:

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

That's not invalid in owl full, is it? (albeit not very informative)

> 
> > - A is a subClassOf a class that is a subClassOf B and C
> 
> Yes, if you mean: there exists a class D that is a subClassOf B and C
such
> that A is a subClassOf D. For example, the class that is the
> intersectionOf
> B and C is a witness for D.
> 
> > ...
> 
> Still, I don't see a generalisation.

Only that that chain could be of infinite length - e.g.

- A is a subClassOf a class that is a subClassOf of a class that is a
subClassOf B and C

etc.
 
> > Would a reasoner be expected to decide that any one entails any of
the
> > others?
> 
> DL reasoners are in their essence just decision procedures, i.e., they
can
> only prove whether something is true or not. So, you can check whether
> some
> particular fact is entailed from some other fact, but in general you
can't
> use them to generate the deductive closure, since there are cases when
> this
> can be infinite - as you point out.
> However, there are cases when you can use a DL decision procedure to
> compute
> a deductive closure, and this is when you can prove that there is an
upper
> bound to the facts to be checked for entailment. For example, you can
use
> a
> decision procedure that checks for subsumption to compute the
> classification
> hierarchy of a set of n classes, since this involves at most n^2
> subsumption
> checks.

I'm more concerned with the answer in owl full, which I assume takes DL
reasoners out of the equation. Is that not correct?
 
> > Or just that they ultimately all result in the same subClassOf
> > relationships on A?
> 
> I don't understand this - probably because I don't see the
generalisation.

I meant that it's straight-forward to prove that the consequences of all
of them are the same wrt A's subClassOf - i.e. that A is a subClassOf B
and A is a subClassOf C - without worrying about infinite processing. 

The difficulty comes when using a rules-based approach that _does_
compute the deductive closure in order to prove that one description of
a class entails another.


> cheers
> -- e.
> 
> Enrico Franconi                  - franconi@inf.unibz.it
> Free University of Bozen-Bolzano - http://www.inf.unibz.it/~franconi/
> Faculty of Computer Science      - Phone: (+39) 0471-315-642
> I-39100 Bozen-Bolzano BZ, Italy  - Fax:   (+39) 0471-315-649

rgds,

geoff
Received on Sunday, 30 March 2003 17:30:10 GMT

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