RE: Nonstructural Restrictions on Axioms (OWL/1.1 Syntax Section 7)

Hi all,

I hope this message is not too controversial.

> -----Original Message-----
> From: Ulrike Sattler [mailto:sattler@cs.man.ac.uk]
> Sent: 09 March 2007 18:37
> >> Finally, there's something a little troubling about not having a 
> >> wellfoundedness constraint on the role hierarchy, which means that 
> >> checking for simplicity could not be decidable.
> 
> ah, well spotted, but there is! The definition of regularity makes use

> of a partial order < (which works on both properties and inverse 
> properties and thus must also be "regular"), and thus everything is 
> fine (assuming that we have only finitely many property names).

I think that assumption needs to be explicit; although a single ontology
can only mention finitely many property names, its imports-closure may
not. 

In OWL/1.0, the definition of satisfaction (of an ontology, by an
interpretation) only covers ontologies at the top of a wellfounded
fragment of the graph of owl:imports: the spec says that I satisfies O
if [some conditions] hold and I satisfies the imports of O. A possible
interpretation of this is that the spec implicitly assumes that
ontologies are at the top of wellfounded fragments of the graph of
owl:imports, and this would be sufficient to ensure that there are only
finitely many property names.

However I'm not sure that this was what was intended, and in particular
this interpretation does not cover ontologies whose imports graph
contains cycles, which do occur in practice. The generally-accepted
reading (and intended meaning?) seems to be to check the conjunction
over all ontologies in the imports closure of the [some conditions]
mentioned above, and this reading imposes no wellfoundedness
constraints; perhaps OWL DL would rather the imports graph were finite
but OWL Full probably doesn't care (and we can think of use cases where
it might be handy).

Cheers,

Dave

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Received on Monday, 2 April 2007 14:06:53 UTC