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Re: Punning and the "properties for classes" use case (from public-owl-dev)

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 06 Nov 2007 05:14:35 -0500 (EST)
Message-Id: <20071106.051435.206603877.pfps@research.bell-labs.com>
To: alanruttenberg@gmail.com
Cc: ian.horrocks@comlab.ox.ac.uk, jjc@hpl.hp.com, schneid@fzi.de, public-owl-wg@w3.org

From: Alan Ruttenberg <alanruttenberg@gmail.com>
Subject: Re: Punning and the "properties for classes" use case (from public-owl-dev)
Date: Tue, 6 Nov 2007 02:48:10 -0500

> On Nov 4, 2007, at 2:38 PM, Ian Horrocks wrote:
> > It is possible in OWL to restrict the size of the domain to be 1  
> > (or some other value) in all interpretations -- Peter uses the  
> > standard "spy point" trick to do this, by ensuring that every  
> > individual is related to the spy individual via the ex:s property  
> > and that the spy has at most one "incoming" ex:s edge (via a  
> > cardinality restriction in the inverse of ex:s).
> >
> > Given such a restriction, it is obviously the case that sameAs (c  
> > d) is entailed for any two individuals c and d. In OWL Full sameAs  
> > (c d) additionally entails equivalentClass (c d), so we also get  
> > that Individual ( a type ( c ) ) entails individual ( a type ( d ) ).

[...]

> > We don't get this kind of entailment in OWL DL because classes are  
> > not interpreted in the same way as individuals (i.e., as elements  
> > of the domain), so for two classes c and d we would not necessarily  
> > entail equivalentClass (c d).
> 
> But why couldn't we, with punning, for instance, have Class(C) entail  
> Individual(C) to more closely match the OWL Full case? Then we too  
> would have a domain size of 1 be inconsistent (because of the  
> presence of the individuals owl:Thing and owl:Nothing)?

But nothing says that these two individuals are different.

> Wouldn't the entailments match in that case? - both would be  
> inconsistent, and hence both would entail anything.

Nope.  You can't even get away in general by using unique names
assumption to pump up the size of the domain.  OWL Full has only
infinite domains (because its domains contain lots of bits of syntax),
and this has observable consequences.  For example, a spy point ontology
that restricts the domain to maximum size 1 000 000 is satisfiable in
OWL DL but not in OWL Full.

> In order to do this, we would need to, effectively, assert an  
> individual of the same name as  each entity(class or property) in the  
> ontology. While I can imagine why this might be considered  
> distasteful, would it work from a technical point of view as far as  
> getting us closer to OWL Full alignment?

No.

> -Alan

peter
Received on Tuesday, 6 November 2007 10:28:19 GMT

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