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
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