# Boolean expressions for n-ary dataranges

From: Michael Schneider <schneid@fzi.de>
Date: Sun, 14 Dec 2008 12:04:06 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A0EA6CB9@judith.fzi.de>
To: <public-owl-wg@w3.org>
```Hi!

While trying to align the formulae in the RDF-Based Semantics with those in
the Direct Semantics, a few questions arose about n-ary dataranges (the
"n-ary stub"), where I am not sure whether OWL 2 Full is currently in line
with OWL 2 DL.

The Direct Semantics states in Section 2.2.2 [1]:

"Data ranges, however, can be n-ary,
[...]
An n-ary data range DR is interpreted as
an n-ary relation (DR)DT over ?D."

Now, in the following Table 3, I can see that complements are really defined
for n-ary dataranges, not just for unary ones:

ComplementOf( DR )  |  (?D)^n \ (DR)^DT where n is the arity of DR

* My first question is: Is this really intended?
Do we want/need complements of n-ary dataranges?

* Second, I don't know what is the situation for
intersections and unions of dataranges (also Table 3).
Are they supposed to be defined for n-ary dataranges, too?
I don't remember any discussion on this, when we talked about
the addition of these features (before and at F2F4).
But it would look odd, IMHO, if only complements are allowed
for n-aries, but not the other boolean constructs.
I would expect that either all or none of the boolean constructs
can be used together with n-ary dataranges.

* Third: Dataranges (marked by "DR") are also mentioned at other places
of the spec. For example, data-QCRs [2] and domain/range axioms [3]
are defined for data ranges, not for data types.
Now I wonder: From the definitions of these language constructs,
it doesn't appear that they can be used with n-ary dataranges,
because the instances of the dataranges mentioned there
are values of data properties, hence ordinary datatype values.
But this should then be made a bit more clear, because it seems
to be in odd with Section 2.2.2 [1], which says that dataranges
can be n-ary.

Cheers,
Michael

[1] http://www.w3.org/2007/OWL/wiki/Direct_Semantics#Data_Ranges
[2] http://www.w3.org/2007/OWL/wiki/Direct_Semantics#Class_Expressions
[3]
http://www.w3.org/2007/OWL/wiki/Direct_Semantics#Data_Property_Expression_Ax
ioms

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: Michael.Schneider@fzi.de
Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555

FZI Forschungszentrum Informatik an der Universität Karlsruhe
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```
Received on Sunday, 14 December 2008 11:04:48 UTC

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