- From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Date: Fri, 25 Apr 2008 19:34:01 -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: Sat, 26 Apr 2008 01:12:27 +0200 > Hi, Peter! > > Peter F. Patel-Schneider wrote: > > >From: "Michael Schneider" <schneid@fzi.de> > >Subject: ISSUE-119: What can be done against the Russell paradox? > >Date: Sat, 26 Apr 2008 00:07:50 +0200 > > > >> Dear Peter! > >> > >> Regrettably, I wasn't able to attend the last telco, so I haven't been > >able to > >> discuss the Russell problem there. > >> > >> The minutes cite you: > >> > >> Peter Patel-Schneider: one can do a patch to keep things the same... > >> Peter Patel-Schneider: that might be adequate > >> > >> Do you mean by this that you know about some method to restrict the > >semantics > >> of the self restrictions in a way that we still have all OWL 2 DL > >entailments > >> in OWL 2 Full? > > > >I thought that we already discussed this. The trick is to fiddle with > >the comprehension principle for self restrictions to not apply on > >rdf:type. > > Before I answer the rest of you mail, I will first want to make sure that I > correctly understand you in this point. > > Do you mean the following or a variant of it: > > "Guarded" Comprehension Principle: > ---------------------------------- > > IF > p rdf:type owl:ObjectProperty . > --> p owl:differentFrom rdf:type . > THEN > _:x rdf:type owl:SelfRestriction . > _:x owl:onProperty p . > > where "_:x" is an existential variable? Well that is not a comprehension principle, you need something like IF p belongs to the class extension of owl:ObjectProperty and p is not equal to the denotation of rdf:type THEN there must be a domain element x such that x belongs to the class extension of owl:SelfRestriction and x and the denotation of p is in the property extension of owl:SelfRestriction > But if you have the following two graphs G_L and G_R: > > G_L := { > :alice rdf:type owl:Thing . > :loves rdf:type owl:ObjectProperty . > :alice :loves :alice . > } > > G_R := { > :alice rdf:type _:s . > _:s rdf:type owl:SelfRestriction . > _:s owl:onProperty :loves . > } > > AFAICT, G_L entails G_R in OWL 2 DL, right? > But with the guarded comprehension principle above, this won't be an > entailment in OWL 2 Full anymore. Yes, as you state below you also need a premise of something like :loves owl:differentFrom rdf:type > The reason is that the guarded comprehension principle now only "fires" on > property :loves, if :loves can be entailed to be owl:differentFrom rdf:type. > But without giving more information in graph G_L, there will exist a > satisfying interpretation for G_L in which the URI ':loves' happens to > denote the same individual as the URI 'rdf:type' (making :alice actually > into a class, but this doesn't matter in OWL Full). So, a self restriction > class on property :loves does not exist, at least not deduced from the > guarded comprehension principle. > > The guard in the guarded comprehension principle does not only protect > against the "real" rdf:type, but also against most other properties within > an ontology. This approach is too strong for maintaining Theorem 2. Well you also have to fiddle a bit more. You could fiddle with Theorem 2, for example by adding something like ... O augmented with suitable distinctness conditions, i.e., all properties in O are distinct from rdf:type entails ... You could also fiddle with the semantic conditions, adding something like the denotation of all names that are not rdf:type are different from the denotaiton of rdf:type. But, again, what did you expect in OWL Full? OWL 1 Full was dancing right up against the cliff. Adding useful expressive power to OWL requires delicate work so that OWL Full doesn't fall into the abyss. As an alternative, I suppose that the WG could just go the N3 way with OWL Full. > Cheers, > Michael peter
Received on Friday, 25 April 2008 23:36:15 UTC