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

[Bruce Miller]

On 07/17/2010 02:15 PM, Christoph LANGE wrote:
> Hi Urs, hi Bruce (there's an important question to you in this mail),

Urs is right on targt; I just responded to a
post earlier in the thread making exactly that
point.

>    you raise a valid point.  In fact, from a strict "RDF Linked Data" point of
> view, DLMF is not (yet) the most suitable target to link to, as it does not
> properly distinguish "the sine function" from "the page describing the sine
> function".  Or does it?  We should ask Bruce.
>
> My motivation for pushing links from the OpenMath CDs to DLMF is mainly that
> this use case makes a lot of sense, as we already have that information (as
> natural language reference to the A&S book) in the CDs, so why not expose it
> to machines?  We wanted to provide some links from the (HTML-rendered) CDs to
> relevant related resources anyway, and I'd rather like to do this by putting
> the links into the CDs instead of e.g. putting them into a proprietary file
> that only our OCD→XHTML XSLTs understand.
>
> I consider it more of a temporary problem that the DLMF does not yet expose
> its content as machine-readable linked data.  (If we get this properly started
> on openmath.org, which is not too hard, that might convince DLMF of following
> us.)
>
> 2010-07-17 19:04 Urs Holzer<urs at andonyar.com>:
>> One other thing that strikes me here: in linked data practice one often
>> makes a distinction between a resuource and its description. (Is this
>> correct, Christoph?) So, It hink that<http://dlmf.nist.gov/4.14.E1>  is
>> a description of a resource 'sin', not the 'sin' itself. (Or does DLMF
>> say that<http://dlmf.nist.gov/4.14.E1>  is the resource and
>> <http://dlmf.nist.gov/4.14#E1>  is the description?) If I am right, using
>> owl:sameAs might cause trouble. For example,
>> <http://dlmf.nist.gov/4.14.E1>  might have an author:
>>
>>    <http://dlmf.nist.gov/4.14.E1>  dc:author "Levinson" .
>
> @Bruce, direct question to you:  There seem to be two ways to address a
> definition in the DLMF: 4.14#E1 (@David, this would BTW give us a nice OMS,
> but I'm afraid this is not the URL/URI that we want) and 4.14.E1.  It this
> difference intended?  And if so, what do those two URLs/URIs mean?
>
> To me, 4.14#E1 seems to be a paragraph on a page, whereas the (i) popup calls
> 4.14.E1 a "permalink", which suggests to me that this might be a persistent
> identifier for an object, and we might call that object "the definition of the
> sin function", or probably "the sin function".

http://dlmf.nist.gov/4.14.E1 is the permalink to,
and identifies, Equation 1 in Section 14 of Chapter 4.
It corresponds to equation 4.14.1 in the (print) handbook.

In the future, that url may end up pointing to a page
devoted to that specific equation (think wiki/fora/
web too-point-oh stuff), but at present there's no need;
So currently, the system redirects the above url to:
http://dlmf.nist.gov/4.14#E1
which refers to the fragment identifying equation 1 within
http://dlmf.nist.gov/4.14
which is the permalink to Section 14 of Chapter 4.

As such, there is no "deep" significance to a
url like .../4.14#E1.  However, all other permalinks are
links to "document objects" (chapters, sections,
figures, tables,...) some of which are _also_
"mathematical objects" (equations).  These objects
all have (or can have) things like creation dates,
authors, etc.

Other than that, http://dlmf.nist.gov/4.14.E1 is
certainly not "sin", but might be taken as the definition
of it.  That does raise another interesting question.

Currently, we've established "definitions" for
all the important functions in an informal way;
the primary purpose is to have a main entry point
where a reader can find clarification about what "xyz" is.
As such, there is currently no real permanence as to
which object (which may be an equation and/or text!)
defines a function; in the future, with edits, a
different location may server as a better (informal)
definition.

Does a formal and/or permanent "defining equation or
passage" really need to be established by & within DLMF?
I suspect that could be both tricky and controversial
in many cases!  Sometimes there are several reasonable
choices for the "definition" (eg. DE's vs explicit
expansions vs...).  I suppose that an issue here
is that these different definitions potentially define
different functions, although the goal of a work
like DLMF is to hammer on them until they _are_ the same!

Short of specific document objects being taken as
"definitions" it is certainly safe to say that
sin must "satisfy" ../4.14.E1 or a variety of other
things.  I'd find "see also" as deeply unsatisfying :>

bruce