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RE: Describing Trees in OWL?

From: Marco Colombetti <colombet@elet.polimi.it>
Date: Fri, 1 Jun 2012 10:40:16 +0200
To: "'Uli Sattler'" <sattler@cs.man.ac.uk>, "'Stephan Opfer'" <stephan.opfer@gmx.net>
Cc: <public-owl-dev@w3.org>
Message-ID: <003f01cd3fd2$2b1faa70$815eff50$@elet.polimi.it>
Here:

   A1.  hasChild(a,b)
   A2.  hasChild(b,a)

   A3.  hasOffspring(root,a)
   A4.  hasOffspring(root,b)

By inference:

   A5.  hasOffspring(a,b)            (from A1)
   A6.  hasOffspring(b,a)            (from A2)
   A7.  hasOffspring(a,a)            (from A5, A6)
   A8.  hasOffspring(b,b)           (from A6, A5)

I think you cannot forbid cycles if you cannot state that hasOffspring is
irreflexive.

Marco

-----Original Message-----
From: Uli Sattler [mailto:sattler@cs.man.ac.uk] 
Sent: giovedý 31 maggio 2012 23:29
To: Stephan Opfer
Cc: public-owl-dev@w3.org
Subject: Re: Describing Trees in OWL?

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.nab
>>> ble.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_Clos
>>> ure
>>> 
>>> [1] http://www.cs.man.ac.uk/~sattler/publications/sroiq-TR.pdf
>>> 
>>> 
>> 
>> 
>> 
> 
> 
Received on Friday, 1 June 2012 08:43:10 GMT

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