From: Peter F. Patel-Schneider ([email protected])
Date: 08/30/01
From: pat hayes <[email protected]>
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.)
peter
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