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Re: Defining cross products in OWL-1.1

From: Jeremy Carroll <jjc@hpl.hp.com>
Date: Wed, 21 Nov 2007 14:06:56 +0000
Message-ID: <47443B80.5000008@hpl.hp.com>
To: Michael Schneider <schneid@fzi.de>
CC: Owl Dev <public-owl-dev@w3.org>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

OWL does not permit an empty universe.

Michael Schneider wrote:

> 
> Task: For given classes A and B give an OWL-1.1 axiom set, by which a
> property pAXB is specified to be equivalent to the cross product A X B.
> 
> Solution:
> 
>   (A0) ClassAssertion(w owl:Thing)
>   (A1) SubClassOf(A ObjectHasValue(pA w))
>   (A2) SubClassOf(B ObjectHasValue(pB w))
>   (A3) SubObjectPropertyOf(
>          SubObjectPropertyChain(pA InverseObjectProperty(pB))
>          pAXB )
>   (A4) ObjectPropertyDomain(pAXB A)
>   (A5) ObjectPropertyRange(pAXB B)
> 

> 
> There are a several points which need some further discussion here:
> 

> Second: About the "glue instance" w. The only real requirement was that
> there is /some/ instance in the universe (denoted by owl:Thing), because
> this alone suffices to use such an instance for glueing pA and pB^-1
> together in the above sub role chain. Even the two 'ObjectHasValue' axioms
> do not seem to put a dangerous restriction on 'w'. So it seems to be
> possible for instance that I can reuse w for specifing the "glue instance"
> of a second role rCXD for other classes C and D without any problem. Also,
> if w occurs in other axioms of the ontology, this shouldn't be a big
> problem, because it does not affect the fact that such a w /exists/. Of
> course, it must not happen that in the ontology's remaining axioms one of
> the "helper roles" 'pA' and 'pB' appears, but this can always be avoided in
> practice AFAICS. So the only thing which might be considered to be at least
> a /theoretical/ problem is that it will not be possible anymore to interpret
> such an OWL ontology over the /empty/ universe. But in practice, no one will
> really care about this lacking, and I am not even certain if doing so is
> allowed at all in OWL. 
> 

In OWL 1.0, the universe is restricted to have at least one member.

http://www.w3.org/TR/owl-semantics/direct.html#3.1
[[
EC(owl:Thing) = O ⊆ R, where O is nonempty and disjoint from LV
]]

I would expect this restriction to carry through to the next version of OWL.

Jeremy
Received on Wednesday, 21 November 2007 14:16:22 GMT

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