RE: Datatype disjointness implemented

Hello,

I deliberately omitted any explicit mention of the definition of the value
spaces and pointed to XML Schema for that. The additional statement that the
value spaces are disjoint is somewhat redundant (it is not completely so because
we ate talking about owl:real instead of xsd:decimal), but I included it in
order to highlight an important consequence of XML Schema's definitions.

Furthermore, while I agree with Bijan that there is no one set of numbers, I
don't really think that this is all that relevant to OWL: what matters to us is
that we enable our readers to interpret XML Schema's definition in the correct
way. To that end, I included a bunch of examples that demonstrate various
consequences of these definitions. I believe that this will be sufficient for
people to interpret the definitions appropriately; furthermore, I am willing to
add further examples should anyone think we need further clarification.

Thus, even if someone might thing that the definitions from XML Schema are odd
or broken, the brokenness is not in our court, and we have undertaken measures
to fix it (via examples). Should anyone think that this brokenness absolutely
must be corrected, probably the best course of action would be to submit a LC
comment to the XML Schema WG.

Regards,

	Boris

> -----Original Message-----
> From: public-owl-wg-request@w3.org [mailto:public-owl-wg-request@w3.org] On
> Behalf Of Bijan Parsia
> Sent: 12 March 2009 22:14
> To: W3C OWL Working Group
> Subject: Re: Datatype disjointness implemented
> 
> We had a version of this discussion before wherein I pointed to
> several standard papers on issues with the ontology of mathematics.
> It's very sad that you did not bother to read or even glance at them.
> 
> On 12 Mar 2009, at 19:55, Alan Ruttenberg wrote:
> 
> > The change includes:
> >
> > xsd:double
> > xsd:float
> > Value Spaces. The value spaces of xsd:double and xsd:float are
> > specified in XML Schema Datatypes [XML Schema Datatypes]. Furthermore,
> > the value spaces of owl:real, xsd:double, and xsd:float are pairwise
> > disjoint.
> >
> > This is inconsistent, as it is inconsistent in XML Schema.
> 
> Nope.
> 
> > The value
> > spaces of both decimal and float and doubles are all "numbers" in XML
> > Schema, notwithstanding their later protestation that the sets are
> > disjoint.
> 
> The value spaces of both negative integer and positive integer are all
> "numbers" in XML Schema, notwithstanding their actual disjointness.
> (IOWs, it takes a lot more than what you provided to get an
> inconsistency.)
> 
> There is no univocal set of "numbers". For example, one can interpret
> the integers (all of them) into the positive integers into the even
> integers into the odd integers. You can use various, non identical set
> theoretic constructs (e.g, (), (()), ((()))... vs. (), (()), ((),
> (())), i.e., Zermelo vs. von Neumann reductions)  for the integers,
> and they will answer to all the purposes of arithmetic (i.e., meet the
> Peano Axioms) and yet, trivially and obviously) they are mostly non-
> disjoint (0 and 1 are the same in each, but we could fix that easily).
> 
> So, in principle, we cannot rely on the denotation of "numbers" to be
> determinate, thus we cannot reason from the use of "numbers" in a
> document which is *not* being particularly precise about various
> things to *anything*. We *can* reason from the formal constraints they
> put in, i.e., the axiomitization they use. There, what's central is
> precisely what you dismiss, the "further protestations".
> 
> > Specifically, it says, for floats:
> >
> > "Its value space is a subset of the rational numbers."
> >
> > This is inconsistent with floats being disjoint with owl:real, which
> > has as a subset, owl:rational.
> 
> Not at all. There's no presumption that owl:rational has to map into
> "the" rationals (since there is no such set). xsd:float can be a
> subset of pairs of Zermelo natural numbers and owl:rational can be the
> von Neumann ratios. Both have both mathematical and historical claim
> to being "the rationals" and yet, ontologically (and set
> theoretically) they are disjoint (pace 0 and 1).
> 
> Further more, we can, without any change in anything, map xsd:float
> into a subset of the rationals between 0 and 1 and owl:rational into
> all the others. This exactly models everything (including the
> disjointness).
> 
> > We can't repeat this inconsistency in OWL.
> 
> Since it isn't inconsistent by any standard, we can repeat it.
> Furthermore, there are simpler readings (e.g., "the floats are a
> subset of a identity-distinct copy of the rationals") which also
> perfectly makes things work out..
> 
> > If the value spaces are to
> > be disjoint, it needs to be explicitly stated how this comes about.
> 
> No, we don't. There are many ways that it could come about and they're
> all perfectly fine. We just need the axiom...the models can take care
> of themselves.
> 
> If we map them into anything it should be bit patterns and point out
> that there is an associated axiomization over that bit patterns which
> yields the same entailments as if you mapped them into the rationals.
> 
> > However I see no such theory other than the informal:
> >
> > "Thus, the value spaces of xsd:double and xsd:float can be understood
> > as containing "fresh copies" of the appropriate subsets of the value
> > space of owl:real."
> 
> This isn't informal at all. Or at least, it's as formal as the use of
> "numbers" was. We don't *need* to formalize it further by reducing it
> to some other "more primitive" notion, as the axiomization more than
> sufficiently characterizes it, i.e., floats are a set of entities
> disjoint with owl:real but with an axiomization which makes them
> indiscernable wrt facet axioms from a certain subset of owl:real.
> 
> That's absolutely formal.
> 
> You confuse formalization with reduction, that is, with a *preferred*
> formalization.
> 
> > An appropriate way to do this would be to have the value spaces of OWL
> > numbers not be numbers, but instead be pairs of numbers and tag.
> 
> Since this way furthers your agenda against disjointness, I don't
> think it's a very appropriate way.
> 
> > I
> > interpret this to mean that we are *not* adopting the value spaces as
> > specified by XML Schema,
> 
> Straw man arguments are not especially compelling.
> 
> > somewhat nullifying the motivation for the
> > change.
> 
> This is why it's inappropriate.
> 
> > Note that I do not, in pointing this out, consider such a repair as
> > removing our overruled objection to the overall change.
> 
>   I hope it is now clear that this is just a blind ally. Oppose
> disjointness if you want against history, implementor wishes, and
> (arguably) usability. There's no accounting for taste and there's no
> *technical* incoherence, per se, in adopting disjointness or non-
> disjointness. It is, truly, a judgement call. However wrongheaded I
> might think your judgement is in this case, it is yours and that's
> fair enough. But please cease these specious arguments.
> 
> > However, if
> > the change is to be adopted, it needs to done in a careful and
> > consistent manner.
> 
> As it has been.
> 
> Cheers,
> Bijan.

Received on Friday, 13 March 2009 09:03:11 UTC