[Om] Adding DLMF links to CDs [Re: How to translate csymbol/@definitionURL]

[Professor James Davenport]

On Sun, July 18, 2010 2:09 am, Bruce Miller wrote:
> On 07/17/2010 08:11 AM, Christoph LANGE wrote:
>> That means,<http://dlmf.nist.gov/4.14.E1>  _is_ transc1#sin, with all of
>> its properties.  The representation of transc1#sin at the URI
>> <http://dlmf.nist.gov/4.14.E1>  just happens to be encoded differently,
>> i.e. not in the OCD format, and it needs not explicitly declare the same
>> properties
>> as we do in the CD (i.e. on the DLMF site there don't have to be the
>> same examples as in the CD), but still it means the same.
>
> [Finding the right place to jump in...
>   but possibly missing the point...]
>
> I don't think this is the assertion of equivalence
> that you want to be making.  The mathematical object
> associated with http://dlmf.nist.gov/4.14.E1 is an
> equation or relation; Someday, with the right content
> negotiation or type extension (eg. appending .om
> to the url), this may fetch an OM object, but that
> object would also be a relation, not a CD.
> It can certainly be considered as a "definition"
> of sin, but it isn't "equivalent to" sin, nor is
> it a CD defining sin.
That's a fair comment. Indeed, if I were being negative, I could say that
DLMF DOESN'T define 'sin', it "merely" states a set of properties about
it. Of course, in some cases the definition is difficult (consider log).
In fact, OpenMath doesn't do as good a job as it could here. This is the
old DeFMP proposal, which in modern parlance would, I think, take the
first FMP for sin (which is in fact 4.14.1) and write it as
<FMP type="defining"> ...
At this point, OpenMath WOULD be definiting sin, by stating that this
equation can be regarded as a definition of sin (so not all FMPs CAN be
definitions), and the head <OMS cd="relation1" name="eq"/> could be read
as ':=' or $=_{def}$ or whatever.
> I understand that the goal is to formalize the
> mention of dlmf urls within CDs;
> is there a relation type more like "defines"
> that could be used? (or "satisfies", or...)
> Can that not have a status such that if two resources
> employ a "sin" that is "defined by" http://dlmf.nist.gov/4.14.E1
> that they can be considered to be using the same "sin"?
> (this is what you're after, isn't it?)
I don't know enough RDF/OWL to comment, but I do think that is a key
question.
> *
> Incidentally2, yes, the reference-number-based URL's
You mean 4.14.E1 rather than 4.14#E1 I assume?
> are intended to be permanent, but the reference
> numbers are different from A&S (a different book).
That's what I understood: thanks for making it definitive.
Then a more modest goal would be to state that

"The FMP for sin is owl:sameas dlmf.nist.gov/4.14.E1" and here I think we
really DO mean owl:sameas, since I think they both have the same deep
author (Gauss, I believe), and who the shallow author is doesn't reallly
concern me - I imagine both JHD and DLMF looked at A+S before writing
their components.

If/When (and I sincerely hope it's 'when') OpenMath adopts DeFMP, then we
would be able to say that OpenMath DOES define sin, by privileging [OED
sense 2: "The action of according high status, validity, or importance to
a concept, viewpoint, etc., in comparison to others"] this FMP, and saying
that all properties of sin can, in principle, be deduced from this
definition and the OpenMath properties of the definiens.

James Davenport
Lecturer on XX10190, CM30070, CM30078/50123, CM50209
Hebron & Medlock Professor of Information Technology, University of Bath
OpenMath Content Dictionary Editor and Programme Chair, OpenMath 2009
IMU Committee on Electronic Information and Communication
Council of the British Computer Society
Federal Council, International Foundation for Computational Logic