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Re: datatype test case (value spaces, rdfs:subClassOf)

From: pat hayes <phayes@ai.uwf.edu>
Date: Sat, 30 Nov 2002 20:04:01 -0600
Message-Id: <p05111b0dba0f1546d692@[10.0.100.247]>
To: Jeremy Carroll <jjc@hplb.hpl.hp.com>
Cc: w3c-rdfcore-wg@w3.org

>Brian wrote:
>>This point seems to be
>>  subtle enough to have misled DanC.
>
>I am sorry Dan, I've got another one.
>
>Dan wrote:
>
>>   xsd:float rdfs:subClassOf xsd:double.
>>
>>That is *not* datatype(xsd:float, xsd:double) entailed
>>by the empty graph; the value space of float is *not*
>>specified to be a subset of the value space of double.
>>So there's no justification ala step 2 above.
>>
>>For details, see
>>		Floating-point datatypes are not real datatypes
>>			Mark Reinhold <mr@eng.sun.com>
>>				5 October 1999
>>http://lists.w3.org/Archives/Public/www-xml-schema-comments/2000JanMar/0130.html
>
>
>
>Unfortunately the details describe descrepancies between the 
>*mappings* of the two datatypes not their *value spaces*.
>
>A proof of (with appropriate knowledge of datatypes).
>
>xsd:float rdfs:subClassOf xsd:double .
>
>xsd:float value space defn:
>http://www.w3.org/TR/xmlschema-2/#float
>[[
>The basic ˇvalue spaceˇ of float consists of the values m × 2^e, 
>where m is an integer whose absolute value is less than 2^24, and e 
>is an integer between -149 and 104, inclusive. In addition to the 
>basic ˇvalue spaceˇ described above, the ˇvalue spaceˇ of float also 
>contains the following special values: positive and negative zero, 
>positive and negative infinity and not-a-number.
>]]
>
>xsd:double value space defn:
>http://www.w3.org/TR/xmlschema-2/#double
>[[
>The basic ˇvalue spaceˇ of double consists of the values m × 2^e, 
>where m is an integer whose absolute value is less than 2^53, and e 
>is an integer between -1075 and 970, inclusive. In addition to the 
>basic ˇvalue spaceˇ described above, the ˇvalue spaceˇ of double 
>also contains the following special values: positive and negative 
>zero, positive and negative infinity and not-a-number.
>]]
>
>The special values are the same, and each of the basic values of 
>xsd:float is an xsd:double because if |m| < 2^24 then |m|<2^53 and
>if -149 <= e <= 104 then -1075 <= e <= 970.
>
>QED.

Not QED. It might be QED if one were justified in reading these 
English descriptions as mathematically definitive and written in 
set-theoretic terms, but one is not. They are English, not 
mathematics, and they can be understood in different ways.

The XSD term 'value space' can be understood in various ways. I am 
not convinced that value spaces are sets in the usual mathematical 
sense, given what the XSD spec says about them. It is possible to 
read those paragraphs as saying that the value spaces are something 
like algebras or categories (or OOP classes) which are isomorphic to 
those sets of integers, but are themselves both distinct and 
disjunct, by definition of 'category' or 'algebra' (or 'class' in 
OOP, ie a set of methods, and subclass means inheritance.) . And I 
bet that many readers of the XML Schema docs, and probably some of 
the *authors* of those specs, do read them that way, at least 
intuitively. Anyone used to thinking in a strongly typed world (Java 
classes, eg.) would think that way naturally. They would respond to 
your proof: but of course saying that they are both numbers in a 
certain range does not mean they are literally *the same*, because 
things in distinct categories can never be literally *the same*. They 
are different *kinds* of number: these are floats, and those others 
are doubles. Some of them might add: numbers themselves don't 
*really* exist at all; there are only distinct kinds of numbers. Two 
different kinds of number might have the same  numerical value - 
which is all that those words mean that misled you - but that doesn't 
make them literally the same thing. Reals and integers are different 
classes of thing, and things in distinct classes are essentially 
different from one another. (That last argument has been made by some 
writers to RDF-logic, by the way, and they were extremely stubborn 
about it, citing OOP practice as their authority.)

In case this seems insane, bear in mind that most people, even 
theoretical physicists, distinguish the *complex* number zero from 
the real number zero, and write the former as a pair 0+0i . This is 
just as natural or unnatural as distinguishing the real zero from the 
integer zero, however, or the floating-point zero from the 
fixed-point zero. (It's no good saying that complex zero is 
two-dimensional: think of the complex plane with the real line as it 
x-axis, then zero is the origin, and it is the same *point* on the 
line and on the plane.)

BTW, the fact that even 'mathematical' English prose can be read in 
various ways is a good illustration for why a spec needs to have a 
genuinely mathematical version somewhere, if only in an appendix. XML 
Schema spec is seriously flawed by its lack of an exact semantics, 
IMO. The spec kind of plays at being mathematical, but it isn't 
really. If it were, there would be no room for alternative 
interpretations.

>
>Moreover we see that
>
>xsd:int rdfs:subClassOf xsd:double .
>
>but not
>
>xsd:int rdfs:subClassOf xsd:float .
>
>by similar reading of the recommendation.
>
>(I am sorry Brian, I know you hate this. I tend to side with Dan in 
>principle, but also wonder about why we should want to do this.
>I am not sure anyone would implement this).
>
>Frankly worrying about these relationships is implicit in our charter.

I disagree. Our charter requires us to track XSD as closely as 
possible, not to rewrite or disambiguate it. If it (XSD) is unclear 
or ambiguous, then tracking it may be impossible. I think we have 
come to that point here. We will not go wrong by simply not 
committing ourselves on some of these topics.

Pat
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Received on Saturday, 30 November 2002 23:52:51 EST

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