subclass loops, proper subclasses and so on

From: pat hayes (
Date: 08/28/01

(Im sending this to the entire JC in case anyone has anything to say 
about it. If you aren't interested, please ignore it, thanks.)

Re.  today's telecon, I would like to bring up the question of the 
connections (or lack) between the two issues of whether 'subclass' is 
understood to mean proper subclass, and whether subclass loops should 
be illegal. I confess to having conflated these in my mind, largely I 
suppose because I couldn't imagine any reason to forbid subclass 
loops other than because 'subclassOf' is understood to hold only 
between proper subclasses.

Since Peter, Ian and others all joined in a chorus of dismay when I 
said this, and since this assumption is currently embedded in the 
draft RDF/S model theory, I would like to pursue it a little more.

1. What reason can there be to forbid subclass loops, other than 
subClassOf being understood to mean proper subclass?

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?

Thanks for any input/feedback. As the RDFCore WG is on the very edge 
of adopting the model theory as a working draft, i would greatly 
appreciate any feedback asap, so we don't go public with a major bug.

(650)859 6569 w
(650)494 3973 h (until September)

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