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Re: intersectionOf and subClassOf

From: Enrico Franconi <franconi@inf.unibz.it>
Date: Sun, 30 Mar 2003 23:40:52 +0200
To: Geoff Chappell <geoff@sover.net>, <www-rdf-logic@w3.org>
Message-ID: <BAAD3104.C618%franconi@inf.unibz.it>

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

> - 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"?

> - 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.

> 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.

> 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.

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
Received on Sunday, 30 March 2003 16:42:00 GMT

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