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

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 UTC