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RE: "Transitive over" properties

From: Ian Horrocks <horrocks@cs.man.ac.uk>
Date: Sat, 10 Jan 2004 17:48:39 +0000
Message-ID: <16384.15095.516891.477366@merlin.horrocks.net>
To: "Peter Crowther" <Peter.Crowther@melandra.com>
Cc: "Jos De_Roo" <jos.deroo@agfa.com>, "Mikhail Khlopotov" <mik@chel.com.ru>, "www-rdf-logic" <www-rdf-logic@w3.org>

You can't represent "Transitive over" in OWL or RDF - it requires
property inclusion (subProperty) axioms w.r.t. complex roles, in
particular role compositions. In general, this leads to
undecidability, but in a restricted form provides most of what is
required and is still decidable. You will find the details in [1] (a
paper published at IJCAI-03).

Sorry for late response to thread and for self publicising :-)


[1] http://www.cs.man.ac.uk/~horrocks/Publications/download/2003/HoSa03a.pdf

On January 4, Peter Crowther writes:
> > From: Mikhail Khlopotov
> > I found no direct way to express "transitive over"
> > properties, I mean properties, which are not transitive by 
> > themselves, but are transitive over another property.
> I seem to recall a proof that such relations plus inverses, possibly
> plus cardinality, is undecidable --- I'm out of that area at the moment,
> so would have to check the literature for precise details.  I suspect a
> number of the other people on the list could provide a reference from
> memory.  It was for this reason of undecidability that the feature was
> not included in OWL-DL.
> Some other KR formalisms have them, notably GRAIL
> (http://www.opengalen.org/ is probably a good place to start for GRAIL).
> An alternative approach to part-whole relations that may fit with OWL-DL
> uses SEP triples.  This uses three classes rather than one, to denote
> (i) the thing as a whole, (ii) the thing and its parts, and (iii) the
> parts.  Apparently it is then possible to represent part-whole
> relationships, moderately sensibly, without needing transitive-over
> relationships.  I know Professor Alan Rector at University of Manchester
> has been working on using this approach with OWL; I don't know how far
> he's got, as it's over a year since I last spoke to him about this.
> Sorry not to have more information to hand; I hope what little I can
> provide is of some use!
> 		- Peter
> --
> Peter Crowther, Director, Melandra Limited
Received on Saturday, 10 January 2004 12:52:10 UTC

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