Re: subclass loops, proper subclasses and so on

From: Peter F. Patel-Schneider (
Date: 08/30/01

From: pat hayes <>
Subject: Re: subclass loops, proper subclasses and so on
Date: Wed, 29 Aug 2001 15:25:39 -0700

> > > 2. Suppose Subclass is the subclass relation, Psubclass the
> > > proper-subclass relation, and R is any binary irreflexive relation
> > > between classes; then (R intersect Subclass) = (R intersect
> > > PSubclass). From which is follows that if some formal relation symbol
> > > on classes is loop-free, then if it can be interpreted as meaning
> > > subclass then it can also be interpreted as meaning proper subclass,
> > > without changing the truthvalues of any expressions in the language.
> > > So, what justification can there be for asserting that
> > > rdfs:subClassOf does *not* mean proper subclass?
> >
> >I don't see how this can be true.
> >
> >Suppose R is ``has a different ID than'',
> That is not an irreflexive relation on classes, since the same class 
> may have two distinct IDs (ie two IDs may denote the same class.)

Ahh.  This depends on what you mean by ``class''.  If by ``class'' you
indeed mean ``the extension in all models'' then fine.  If, however, a
class is a node (in an RDF graph) or a name (in a description logic KB),
then it makes sense to distinguish between the class and its extension.  

I believe that your model theory for RDF makes this distinction in the
model theory itself.   A class is a resource.  The extension of two classes
may be the same in all models.  (There is, of course, few or no ways to
enforce this in RDF, but DAML+OIL can easily state that two classes have
the same extension in all models.)


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