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Describing Trees in OWL?

From: Stephan Opfer <stephan.opfer@gmx.net>
Date: Thu, 31 May 2012 10:40:32 +0200
Message-ID: <4FC72E80.8000809@gmx.net>
To: public-owl-dev@w3.org
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 12:13:55 GMT

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