- From: Jeremy Carroll <jjc@hpl.hp.com>
- Date: Wed, 21 Nov 2007 14:06:56 +0000
- 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 UTC