- From: Bijan Parsia <bparsia@cs.man.ac.uk>
- Date: Mon, 19 Nov 2012 10:36:07 +0000
- To: public-owl-comments@w3.org
Where's the transitivity?
Consider the following interpretation of P
P : {<a, b>, <b,c>}
Given your range and domain restrictions we have:
A: {a, b...}
B: {b, c...}
But A and B are disjoint so this isn't a model.
I suppose this is vacuously transitive...since you can't have a chain, every chain has all the intermediate links. But then the empty property is also transitive, in this sense. Such transitivity is harmless since, e.g., it can't be used in grid construction. (It can't be used at all, really :)).
----
In a general way, the answer to your question is "sort of" and "that's the wrong way to think about it". The point of these restrictions is to enforce decidability of key inference services including entailment. If we had to perform entailment in order to check the conditions, we'd have a bit a problem, eh!
However, it is true that if we consider entailment of *OWL DL ontologies* then we are only considering entailments which adhere to the restrictions. But then we'd just not check that entailment. There could be entailments that follow (in first order logic) that are outside OWL DL (indeed, there always will be).
Cheers,
Bijan.
Received on Monday, 19 November 2012 10:36:34 UTC