# Re: OWL reasoning in rules

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 29 May 2007 10:34:35 -0400 (EDT)
Message-Id: <20070529.103435.45996988.pfps@research.bell-labs.com>

```
From: Jeremy Carroll <jjc@hpl.hp.com>
Subject: Re: OWL reasoning in rules
Date: Tue, 29 May 2007 15:07:48 +0100

>
>
>
> 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'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
>

There are lots of other ways of requiring an infinite model.

One of the simplest, using father but not exactly true-to-life:

father <= Human x Human

father is a relationship between humans

Human <=  ( =1 father) ^ ( <=1 father- )

All humans have exactly one father and at most one inverse of
father.

From this we get that every human has either an infinite chain
of fathers or is in a completely isolated cycle of fathers.
Otherwise there would be a human with more than one father
inverse.

John in Human ^ ( <=0 father- )

John is a human with no father inverse.

From this John must be the root of an infinite chain of fathers.

peter
```
Received on Tuesday, 29 May 2007 14:36:17 UTC

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