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Re: Universal Property

From: Carsten Lutz <clu@tcs.inf.tu-dresden.de>
Date: Wed, 16 Jan 2008 18:43:27 +0100 (CET)
To: Uli Sattler <sattler@cs.man.ac.uk>
Cc: "Web Ontology Language ((OWL)) Working Group WG" <public-owl-wg@w3.org>
Message-id: <Pine.LNX.4.64.0801161834530.6794@frege.inf.tu-dresden.de>

On Wed, 16 Jan 2008, Uli Sattler wrote:
>
> Hi,
>
> below is a brief explanation of the "universal property" as mentioned in 
> earlier discussions and emails:
>
> - let's assume we had an object property, owl:universal, that comes with the 
> following restriction to its interpretation: it is symmetric, transitive (and 
> thereby reflexive), and a super-property of all other properties (or those 
> found in the ontology that  owl:universal is used in)

Just to be sure:

It is actually a tiny bit more than that: it connects every two
objects that exist.  This implies that it has the above properties,
but the converse is not true. You can also think of it as an analogue
of owl:Thing, only for properties. Its semantics is simple: it is 
always interpreted as the cross-product of owl:Thing.

[...]
> - it is computationally unproblematically and basically syntactic sugar 
> because we can express it in OWL11....but

In a strict logical sense, it cannot be expressed (you need to extend
the signature). But we can "simulate" it along the lines described by
Uli above.  So it is really not much more than syntactic sugar. In
particular, it will not lead to problems for implementers: the
existence of the "simulation" shows that all problems introduced by
the universal role are already there.

greetings,
 		Carsten

--
*      Carsten Lutz, Institut f"ur Theoretische Informatik, TU Dresden       *
*     Office phone:++49 351 46339171   mailto:lutz@tcs.inf.tu-dresden.de     *
Received on Wednesday, 16 January 2008 17:43:54 GMT

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