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Re: OWL reasoning in rules

From: Ulrike Sattler <sattler@cs.man.ac.uk>
Date: Tue, 29 May 2007 15:27:43 +0100
Message-Id: <6D9FA419-5EB7-4BD5-B4B0-3CE18D041CCE@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>
To: Jeremy Carroll <jjc@hpl.hp.com>

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  

%% 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
> -- 
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Ulrike Sattler

Received on Tuesday, 29 May 2007 14:33:01 UTC

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