RE: RDF-Based Semantics and n-ary dataranges

>-----Original Message-----
>From: public-owl-wg-request@w3.org [mailto:public-owl-wg-request@w3.org]
>On Behalf Of Ian Horrocks
>Sent: Wednesday, April 01, 2009 8:47 PM
>To: W3C OWL Working Group
>Subject: RDF-Based Semantics and n-ary dataranges
>
>We didn't manage to conclude this discussion.
>
>Summary of (my understanding of) the discussion so far:
>
>* we all believe that OWL 2 *should* only support unary datatypes/
>ranges, and that ontology documents including n-ary *should* be non-
>conformant

Hm, I thought that if C&P extends Pellet by support for certain n-ary
datatypes, then C&P should still be allowed to call Pellet a conformant OWL
2 DL reasoner?
 
>* some of us believe that the existing spec actually says this (but
>some additional explication may be useful)

I haven't seen this stated anywhere, but I might have overlooked it. That's
why I asked.

>* the structure of n-ary restrictions is defined in SS&FS, but
>(hopefully) only the unary case can occur in conforming ontologies
>(as above)
>* Michael believes that as a result the RDF-Based semantics is broken

Yes, it is _syntactically_ broken. It essentially contains an expression of
the form

  "<x1,...,xn> in S"

where "S" is defined to denote a subset of the object domain. 

If something like this would be written in the Direct Semantics, you would
certainly be horrified. And so you should be for the RDF-Based Semantics as
well. Because this has nothing to do with the distinction between the Direct
Semantics and the RDF-Based Semantics. It only has to do with what can be
written syntactically in the set theory that underlies both our semantics.
(There are other problems as well, but I think this is the simplest one to
acknowledge.) 

The problem is: Interpretation function under the semantics of RDF are
restricted to interpret names by individuals (instances of the domain IR).
In addition (in RDFS), there are two functions that allow me to /indirectly/
talk about subsets of the domain IR (the class extension function
"ICEXT()"), and subsets of the product IRxIR (the property extension
function "IEXT()"). But there is not yet such a function (or a collection of
functions) that allow me to talk about subsets of the products IR^n for
arbitrary n. 

So the underlying logic may allow me to write statements as above, at least
for an "S" representing a set of n-ary tuples. The problem is that I do not
reach this functionality of the underlying logic from within the current
framework of the RDFS semantics. So I need to extend this framework. This is
what I suggest to do (before April 15th...).

>* Peter doesn't agree.
>
>Comments?
>
>Ian
>

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
Research Scientist, Dept. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: michael.schneider@fzi.de
WWW  : http://www.fzi.de/michael.schneider
=======================================================================
FZI Forschungszentrum Informatik an der Universität Karlsruhe
Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe
Tel.: +49-721-9654-0, Fax: +49-721-9654-959
Stiftung des bürgerlichen Rechts, Az 14-0563.1, RP Karlsruhe
Vorstand: Prof. Dr.-Ing. Rüdiger Dillmann, Dipl. Wi.-Ing. Michael Flor,
Prof. Dr. Dr. h.c. Wolffried Stucky, Prof. Dr. Rudi Studer
Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus
=======================================================================