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Re: Open-world assumption

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Thu, 14 Sep 2006 20:17:25 +0100
Message-Id: <94026973a1ec9e71f1de5021650d56b6@cs.man.ac.uk>
Cc: public-owl-dev@w3.org
To: "Luke Steller" <Luke.Steller@infotech.monash.edu.au>

On 31 Aug 2006, at 09:56, Luke Steller wrote:

> Hello All,
> I was wondering if there is a way of explicitly saying that a set of
> object instances, given for a particular object-property, are only
> properties that can exist for this instance.
> For instance, if I have a class instance: myColours, with a property
> hasColour, containing 3 instances: {Red, Blue, Green} - is there a way
> of saying that for myColours, cardinality for hasColour is 3, where
> the instances Red, Blue, Green are all different? I am not looking to
> specify cardinality at a class level, rather I want to specify it at
> the instance level - in a sence changing from an open world assumption
> which assumes there are at least 3 colours for this property, to a
> closed world assumption by explicitly stating that there are 3 and
> only 3 for this property of this instance on the class (other
> instances might have a different cardinality)

Not sure if I quite understand the question (e.g., w.r.t. the meaning 
of "class instance"), but I will do my best.

OWL/DL restrictions *always* restrict instances rather than classes - 
in fact they define a class whose instances are just those individuals 
that satisfy the restriction. So, if you assert that myColours is is 
subClass of a suitable cardinality restriction, e.g.:

myColours subClassOf (restriction (hasColour cardinality(3))

says that instances of myColours are related to exactly 3 other 
individuals via the hasColour property (I leave it as an exercise for 
the reader to convert from this informal syntax into OWL).

If you also say:

myColours subClassOf (restriction (hasColour allValuesFrom (oneOf Red 
Blue Green)))

then you have additionally stated that all instances of myColours can 
be related via the hasColour property only to one or other of the 
individuals Red, Blue or Green. Note that Red, Blue and Green must be 
all different, otherwise the cardinality restriction could not be 
satisfied. Hopefully this gives you what you wanted.

Hope this helps.


> Is it possible?
> Thanks
> Luke Steller
> PhD Candidate
> Faculty of Information Technology
> Monash University
> A U S T R A L I A
> =============================
Received on Thursday, 14 September 2006 19:17:36 UTC

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