From: Peter F. Patel-Schneider (pfps@research.bell-labs.com)
Date: 08/30/01
From: pat hayes <phayes@ai.uwf.edu> 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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