- From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Date: Mon, 28 Apr 2008 11:32:07 -0400 (EDT)
- To: schneid@fzi.de
- Cc: public-owl-wg@w3.org
From: "Michael Schneider" <schneid@fzi.de> Subject: RE: ISSUE-119: What can be done against the Russell paradox? Date: Mon, 28 Apr 2008 16:49:41 +0200 [...] > >The whole idea of Theorem 2 was to try to determine how close the > >semantic meanings were between OWL 1 DL and OWL 1 Full. > > I know that this was the idea, and I strongly agree that we need a > criterion for this purpose. But I do not easily accept that the > current formulation of Theorem 2 is an adequate approach to compare > the semantic expressivity of OWL Full and OWL DL. [...] > When I want to construct an OWL 2 Full, which is at least as > expressive as OWL 2 DL, then I should only ask for all those results > which OWL 2 DL produces. I should not ask OWL Full for a cow, when I > ask DL only for a glass of milk. If DL provides me from some given > premise that Alice belongs to the /set/ of all self-lovers, then I > cannot expect more than exactly this from OWL Full, too. But this is precisely what Theorem 2 does. In DL to ask whether Alice belongs to the set of all self-lovers one asks whether the KB entails Alice in SelfRestrition(loves). In an RDF-based language, one asks the same question couched in RDF-speak, i.e., does an RDF graph OWL Full-entail an RDF graph stating that Alice is in the set of self-lovers. > The asymmetric demands, which Theorem 2 puts on OWL DL and OWL Full > force OWL Full to include some very strong additional semantic conditions, > namely the comprehension principles. A comprehension principle for > self-restrictions will provide for every existing property p a class > /resource/, which has the set {x|p(x,x)} as its class extension. > Or more figuratively, comprehension principles provide me > /precautionary/ a cow for milk, a fountain for water, and a brewery > for beer, just for the case that I should ever become thirsty some > day. :) This doesn't only lead to undesirable results (as I stated > above), but also brings OWL Full near to its collapse, as one can see > from the problem with the Russell paradox. > > Bottom line: The "latent" collapse of OWL Full is not something which > is inherent to an RDFS-based language which tries to compete with > OWL DL w.r.t. semantic expressivity. Instead, this problem seems to > result solely from the strong and (technically) unfair demands > which Theorem 2 puts on OWL Full in comparison to OWL DL. I'm open to other ways of doing this, but I don't see any. [...] > Cheers, > Michael peter
Received on Monday, 28 April 2008 15:35:45 UTC