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>

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, geoffReceived on Sunday, 30 March 2003 17:30:10 UTC

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