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Re: disjointness of numerics

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Wed, 28 Jan 2009 12:05:11 -0500 (EST)
Message-Id: <20090128.120511.237946118.pfps@research.bell-labs.com>
To: bparsia@cs.man.ac.uk
Cc: ian.horrocks@comlab.ox.ac.uk, schneid@fzi.de, sandro@w3.org, public-owl-wg@w3.org

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Subject: Re: disjointness of numerics
Date: Wed, 28 Jan 2009 16:11:06 +0000

> On 28 Jan 2009, at 15:58, Ian Horrocks wrote:
> > The semantics of OWL 1 says that values of unsupported datatypes
> > are interpreted as some element of a set that is at least as large as
> > the union of the interpretations of all the known datatypes and is
> > disjoint from the abstract domain. A reasoner implementing Vanilla OWL
> > would therefore not find this entailment, but nor would it conclude that
> > the two values are necessarily different.
> This is true, but isn't the question "What would a reasoner supporting
> the built-in (but optional) datatypes float and integer do?"
> Many (Cerebra, KAON2 I think) did not treat them as disjoint. Pellet,
> afacr, did. Arguably the (weakly) speced semantics defers to the XML
> Schema doc which says that they are.
> Cheers,
> Bijan.

Actually the XML Schema Datatypes REC document from 2004
http://www.w3.org/TR/2001/REC-xmlschema-2-20041028/ doesn't really solve
this issue.

It nails down the value spaces of the various datatypes, so that the
value for "2E0^^xsd:float" is 2 x 2^0 or the integer 2, and similarly
the value for "2^^xsd:integer" is the integer 2.  These two values are
the one and the same.

The strangeness of the document is that it also defines equality on each
value space, as identity, and then goes on to say that as a consequence,
values from two types that are not related (e.g., xsd:float and
xsd:integer) are not equal.  This consequence is *not* true.

This was all finessed after the fact to say that XSD equality also took
into account the primitive type, so that "2^^xsd:integer" would be
XSD equal to "2^^xsd:int" but not to "2E0^^xsd:float".  

The draft from 2006 http://www.w3.org/TR/xmlschema11-2/ clarifies this a
bit.  Within a primitive data type XSD equality need not be identity and
need not even be an equivalence relation.  Primitive data types are
artificially made disjoint with respect to XSD equality.  Wording has
been included to note that applications (like OWL) may choose to use a
different notion of equality.

Received on Wednesday, 28 January 2009 17:02:59 UTC

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