- From: Jeremy Carroll <jjc@hpl.hp.com>
- Date: Tue, 29 May 2007 16:19:08 +0100
- To: Ulrike Sattler <sattler@cs.man.ac.uk>
- CC: Matt Williams <matthew.williams@cancer.org.uk>, Ian Horrocks <horrocks@cs.man.ac.uk>, Owl Dev <public-owl-dev@w3.org>, Semantic Web <semantic-web@w3.org>, Bijan Parsia <bparsia@cs.man.ac.uk>
Wonderful, thanks. Jeremy Ulrike Sattler wrote: > > On 29 May 2007, at 15:07, Jeremy Carroll wrote: > >> >> >> Ulrike Sattler wrote: >>> It is not too difficult to see that we can construct an OWL ontology >>> all of whose models are infinite (let me know if you want to see an >>> example of such an ontology), e.g., where each model contains an >>> infinite chain of fathers *in addition to the fathers that are >>> explicitly present in the ontology, >> >> >> Hmmm, I would like to see a small ontology which is necessarily infinite. >> > > I meant "an ontology that is consistent (i.e., it has models) but that > has no finite models (i.e., only infinite ones)": > > so, here is one (I hope my syntax is ok): zero is an individual, Number > and Positive are classes, hasSucc and hasPred are properties --- and I > have chosen these names to help you see the structure of a model: > > %% zero is a number, but not positive > zero InstanceOf (Number And ComplementOf(Positive)) > > %% every Number has a positive number as a successor > Number SubClassOf (some hasSucc (Number And Positive)) > > %% hasPred is the inverse of hasSucc > hasPred (InversePropertyOf hasSucc) > > %% > Number SubClassOf (atmost 1 hasPred) > > Cheers, Uli > > >> I've just being looking with google, and found my own >> http://www.w3.org/TR/owl-test/dl-900-arith#description-logic-908 >> >> which I believe hinges on >> 2*3*n = 5*n & n>0 >> implies n >= aleph0, >> but I am still trying to understand it. >> >> thanks for a pointer >> >> Jeremy >> >> >> >> -- >> Hewlett-Packard Limited >> registered Office: Cain Road, Bracknell, Berks RG12 1HN >> Registered No: 690597 England >> > > Ulrike Sattler > sattler@cs.man.ac.uk <mailto:sattler@cs.man.ac.uk> > http://www.cs.man.ac.uk/~sattler/ > > -- Hewlett-Packard Limited registered Office: Cain Road, Bracknell, Berks RG12 1HN Registered No: 690597 England
Received on Tuesday, 29 May 2007 15:19:49 UTC