Re: intersectionOf and subClassOf

From: "Geoff Chappell" <geoff@sover.net>
Subject: RE: intersectionOf and subClassOf
Date: Tue, 8 Apr 2003 09:27:02 -0400

> 
> 
> > -----Original Message-----
> > From: www-rdf-logic-request@w3.org
> [mailto:www-rdf-logic-request@w3.org]
> > On Behalf Of Peter F. Patel-Schneider
> > Sent: Tuesday, April 08, 2003 7:57 AM
> > To: geoff@sover.net
> > Cc: www-rdf-logic@w3.org; jjc@hpl.hp.com
> > Subject: Re: intersectionOf and subClassOf
> > 
> > 
> [...]
> > 
> > > 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.
> 
> When you say the semantics of intersectionOf are iff, do don't mean:
> 
> owl:intersectionOf A B  iff  extension of A = intersection of extensions
> of classes in B
> 
> do you? That was the sense in which I meant it but I may be confusing
> terms or being imprecise in their use.

Because of OWL's embedding on top of RDF there are actually several
options that could arise here.

1/ One could have the semantic constraint on owl:intersectionOf	
	that if the extension of x is the same as the intersection of the
	extensions of a and b then x owl:intersectionOf [a b]   
2/ One could have the semantic constraint that if
	   x owl:intersectionOf [a b]  then the extension of x is the same
	   as the intersection of the extensions of a and b
3/ One could have the semantic constraint that if
	   x owl:intersectionOf [a b]  then the extension of x is a subset
	   of the intersection of the extensions of a and b 

Option 3 is of course wrong, as it makes owl:intersectionOf *not* be
intersection.  Both option 1 and option 2 make owl:intersectionOf be
intersection, i.e., owl:intersectionOf provides an iff condition for the
class that its subject.  Option 1, in essence, means that
owl:intersectionOf is a semantic relationship, i.e., it shows up in lots of
places.  Option 2, in essence, means that owl:intersectionOf is a syntactic
relationship, i.e., the relationship only shows up where it was stated.  

Option 2 is the one used in OWL.  Option 2 needs an extra semantic
condition to work, one that requires the existence of sufficient
intersections (roughly at least one intersection for any list of classes).

peter

Received on Tuesday, 8 April 2003 10:31:15 UTC