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 http://www.cs.man.ac.uk/~sattler/Received on Tuesday, 29 May 2007 14:33:01 UTC
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