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Re: Describing Trees in OWL?

From: Uli Sattler <sattler@cs.man.ac.uk>
Date: Thu, 31 May 2012 22:28:32 +0100
Message-Id: <1A9DA02A-BD30-4AC8-9A39-988CA1D92A2C@cs.man.ac.uk>
Cc: "public-owl-dev@w3.org" <public-owl-dev@w3.org>
To: Stephan Opfer <stephan.opfer@gmx.net>
Try to build a cycle here...

Cheers, Uli

On 31 May 2012, at 18:44, Stephan Opfer <stephan.opfer@gmx.net> wrote:

> Hi Uli,
> 
> so cycles are not forbidden, right?
> 
> Best Regards,
>  Stephan
> 
> On 05/31/2012 04:10 PM, Uli Sattler wrote:
>> Hi Stephan, I think we can get a rather good approximation of a tree by
>> saying the following:
>> 
>> hasChild is a subproperty of hasOffSpring
>> 
>> hasOffSpring is transitive
>> 
>> every offSpring of  the root node (i.e., an indiviual called root) has
>> at most one incoming hasChild edge
>> (you can also say this for everything in the universe - but that would
>> be a bit strong)
>> 
>> if a node has no incoming hasChild edge, then it is the root node
>> 
>> ...now, if you want a (strict) binary tree you need to add further
>> cardinality restrictions on outgoing hasChild edges.
>> 
>> Cheers, Uli
>> 
>> On 31 May 2012, at 09:40, Stephan Opfer wrote:
>> 
>>> Hello,
>>> 
>>> I recently noticed, that although the model of an owl axiom should have
>>> tree property, it is not possible to describe a tree data structure in
>>> OWL. The way I would model it, is to create a class Node and a property
>>> hasChild and make the hasChild property transitive and irreflexive,
>>> which is not allowed in OWL-DL, because transitive properties are no
>>> simple properties.
>>> 
>>> I searched a bit on w3c websites and their citations and also made
>>> another post on the protege-owl mailing
>>> list:protege-ontology-editor-knowledge-acquisition-system.136.n4.nabble.com/Tree-Paradox-of-OWL-td4655163.html
>>> 
>>> Someone told me, that I should post this question here, too.
>>> 
>>> You don't have to read the other post. Here is a summary of my
>>> observations and the resulting question to this mailing list.
>>> 
>>> On website [0] the restriction about composite object properties are
>>> described and [1] is cited for given the reason for these restrictions.
>>> However, [1] states about irreflexivity combined with transitivity:
>>> 
>>> "For SROIQ and the remaining restrictions to simple roles in concept
>>> expressions as well as role assertions, it is part of future work to
>>> determine which of these restrictions to simple roles is strictly
>>> necessary in order to preserve decidability or practicability. This
>>> restriction, however, allows a rather smooth integration of the new
>>> constructs into existing algorithms."
>>> 
>>> So my question is: Has someone proven, that the restrictions about
>>> transitivity and irreflexivity can be loosen? Otherwise, OWL cannot
>>> describe a tree data structure on "schema level".
>>> 
>>> Best Regards,
>>> Stephan
>>> 
>>> [0]
>>> http://www.w3.org/TR/owl2-syntax/#The_Restrictions_on_the_Axiom_Closure
>>> 
>>> [1] http://www.cs.man.ac.uk/~sattler/publications/sroiq-TR.pdf
>>> 
>>> 
>> 
>> 
>> 
> 
> 
Received on Thursday, 31 May 2012 21:40:06 GMT

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