- From: Ian Horrocks <ian.horrocks@comlab.ox.ac.uk>
- Date: Sun, 11 Nov 2007 17:16:28 +0000
- To: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Cc: alanruttenberg@gmail.com, jjc@hpl.hp.com, schneid@fzi.de, public-owl-wg@w3.org
On 6 Nov 2007, at 17:49, Peter F. Patel-Schneider wrote: > From: Alan Ruttenberg <alanruttenberg@gmail.com> > Subject: Re: Punning and the "properties for classes" use case > (from public-owl-dev) > Date: Tue, 6 Nov 2007 12:39:34 -0500 > >> On Nov 6, 2007, at 5:14 AM, Peter F. Patel-Schneider wrote: >> >>>> But why couldn't we, with punning, for instance, have Class(C) >>>> entail >>>> Individual(C) to more closely match the OWL Full case? Then we too >>>> would have a domain size of 1 be inconsistent (because of the >>>> presence of the individuals owl:Thing and owl:Nothing)? >>> >>> But nothing says that these two individuals are different. >> >> They have different size extensions. Isn't that enough? If they were >> the same they would have to have the same extensions. > > Not enough if you have punning. Remember that having the individual > denoted by owl:Thing being the same as the individual denoted by > owl:Nothing does not imply that their denotations as classes are > equivalent. > > A slogan for punning: > The sizes of the class are not visited on the individual. :-) I find it useful to think of punning as if there were a syntactic pre- processing step that prepends INDIVIDUAL- and PROPERTY- to all individual and property names (as determined by the context in which they are used). When you look at it this way, it is easy to see that owl:INDIVIDUAL-Thing has no special status w.r.t. owl:Thing -- it is just like any other individual name. > >>>> Wouldn't the entailments match in that case? - both would be >>>> inconsistent, and hence both would entail anything. >>> >>> Nope. You can't even get away in general by using unique names >>> assumption to pump up the size of the domain. OWL Full has only >>> infinite domains (because its domains contain lots of bits of >>> syntax), >>> and this has observable consequences. For example, a spy point >>> ontology >>> that restricts the domain to maximum size 1 000 000 is >>> satisfiable in >>> OWL DL but not in OWL Full. >> >> Is there an easy way to show this (for my collection of OWL >> examples?) > > You mean prove it? OWL Full domains must be infinite, OWL DL domains > don't have to be. Both bits are easy to prove. > > You mean an ontology that is satisfiable in OWL DL but not in OWL > Full? > The same example as before with 1 replaced by 1 000 000, i.e., > > owl:Thing <= hasValue ( ex:r ex:spy ) > ex:r inverseOf ex:rinv > ex:spy in atmost(1 000 000 ex:rinv) > >>>> In order to do this, we would need to, effectively, assert an >>>> individual of the same name as each entity(class or property) >>>> in the >>>> ontology. While I can imagine why this might be considered >>>> distasteful, would it work from a technical point of view as far as >>>> getting us closer to OWL Full alignment? >>> >>> No. >> >> OK. Follows from the fact that Full domains are infinite. >> >> What about going the other way? Jeremy mentioned that David Turner >> proposed some axioms that, if I understood things correctly, would >> assert owl:Thing to be infinite even in the DL case. (he'll send a >> followup email with the details). This may not be desirable from the >> point of view of wanting DL to be able to be finite to enable certain >> types of computation, like some approximations of closed-world- >> reasoning, but I want to separate that out and understand the >> technical issues, if you will help me. > > Axioms? You mean something like > > ex:pred inverseOf ex:succ > ex:SP = exactly( 1 ex:succ ) and exactly( 1 ex:pred ) and all > ( ex:succ SP ) > ex:zero in exactly ( 1 ex:succ ) and exactly ( 0 ex:pred ) and all > ( ex:succ SP ) > > This forces the domain to infinite, but why would you ever want to > enforce that these axioms are true in all OWL DL ontologies? I guess that Alan wants to rule out the finite domain "corner cases" that lead to differences between OWL DL and OWL Full. I'm not sure how this helps. Ian > >> -Alan > > peter
Received on Sunday, 11 November 2007 17:16:53 UTC