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Can an object property be both functional and transitive?

From: Jie Bao <baojie@cs.rpi.edu>
Date: Mon, 26 Jan 2009 14:36:44 -0500
Message-ID: <b6b357670901261136o3544ca71w54e99c068615ca99@mail.gmail.com>
To: W3C OWL Working Group <public-owl-wg@w3.org>

I come across this issue when update the Quick Reference. This issue
may already have been discussed, as I was not in the WG from the very
beginning. I just need a confirmation.

In OWL 1 DL, This is not allowed, for decidability considerations.
http://www.w3.org/TR/owl-semantics/syntax.html#2.3.2.4

In OWL 2 DL, it is allowed, i.e., an object property CAN be both
functional and transitive
http://www.w3.org/2007/OWL/wiki/Syntax#Object_Property_Axioms (Figure 15)

As far as I can guess, this may reflect the recent progress on
undecidability results of DL with number restrictions.

Yevgeny Kazakov, Ulrike Sattler, and Evgeny Zolin. How many legs do I
have? Non-simple roles in number restrictions revisited. In Proc. of
the 14th Int. Conf. on Logic for Programming, Artificial Intelligence,
and Reasoning (LPAR'2007), Yerevan, Armenia October 15-19, 2007.
http://www.cs.man.ac.uk/~ezolin/pub/zolin_2007_RBox.pdf

However, I'm not sure this result sufficiently ensures that all OWL 2
ontologies that abide the abstract syntax will be decidable. Quote
from the paper

"We have shown that, in the absence of inverse roles, the restriction
imposed by SHQ to nonsimple roles in number restrictions can be
relaxed substantially and that, in the presence
of inverse roles, this restriction turns out to be crucial for decidability."

Since OWL 2 has  inverse properties (role), is there any restriction
on its use to ensure the decidability of OWL 2 DL?

Regards

Jie

--
Jie
http://www.cs.rpi.edu/~baojie
Received on Monday, 26 January 2009 19:37:24 GMT

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