[Om] How to translate csymbol/@definitionURL [Re: OpenMath 2010]

[Christoph LANGE]

Hi David,

  thanks for explaining the background about "P".  It seems to be a bad
practice in our group (or a good practice that doesn't happen to conform with
MathML? – not sure how Michael would put it).

2010-07-16 13:04 David Carlisle <davidc at nag.co.uk>:
> > Once you start thinking about linking OpenMath CDs to other datasets using
> > URIs (e.g. the DLMF, Paul's notation census, DBpedia, etc.), see my OM
> > workshop talk on Linked Data, there will be URIs that don't fit into the
> > CDBase/CD#name schema.
> 
> Openmath already has a rich annotation mechanism though, which ought to 
> be able to handle that.

Indeed it does.  We might just have to figure out the details of how to do it.
Once we got that settled, I'd suggest adding some relevant links to the CDs.
First of all, we might want to replace (or complement) the natural language
references to "Abramowitz/Stegun chapter X.X" by links to DLMF.

The question remains how to associate such links with symbol definitions in a
CD, i.e. how to say that the transc1#sin symbol links to some external
resources.  As said before, I would do it via FMPs:

<CDDefinition>
  <Name>sin</Name>
  <FMP>
    <OMOBJ>
      <OMA>
        <OMS cd="..." name="the-type-of-link"/>
        <!-- link target goes here, either OMS or
             something attributed with mathmlattr#definitionURL -->
      </OMA>
    </OMOBJ>
  </FMP>
</CDDefinition>

I think that would be legal, because the "compliance" section of OpenMath does
not require a phrasebook that would not be interested in those RDF-like FMPs
(e.g. a phrasebook for a CAS) to respect those FMPs, as they are not relevant
to the application domain.

Or could it be done with attributions?  That would have the advantage of a
shorter syntax for multiple links (simply a sequence of OMATPs).  But then,
what would be the thing to be attributed with such a link?  We would again
need an FMP as a container, and something to carry the attributions, but what
would that be?

> > Suppose we want to say: transc1#sin is the same as
> > http://dlmf.nist.gov/...#sin, and suppose we want to say: the notation
> > census entries for transc1#sin are at http://wiki.math-bridge.org/...#sin.
> > OpenMath does not really have a way of "linking" to things,
> 
> You can specify the URI in openmath attributions. Of course it would be 
> up the the relevant phrasebook that to encode that the attributions are 
> URIs to be used in certain ways.

Considering my existing OpenMath CD → RDF translation as a phrasebook, this is
something I would be most happy to add to the phrasebook.

Indeed the phrasebook would have to do some work, because RDF distinguishes
literal values (e.g. strings) from URIs, whereas OpenMath/MathML doesn't.  But
that is feasible.

> > And how would it work?  You can only attribute something that is
> > an OpenMath object, so how would you say "this is something that has a
> > definitionURL"?
> 
> http://monet.nag.co.uk/~dpc/draft-spec/chapter4.html#contm.p2s
> 
> step 9b or 9c depending on whether the definitionurl is pointing at an 
> OM CD symbol.

Could we please do it on a concrete example?  I don't completely get it from
the rewrite rules.  Suppose we have

<csymbol definitionURL="http://example.org/foo/bar">bar</csymbol>

then by rule 9c this would turn into 

<semantics>
  <csymbol>bar</csymbol>
  <annotation cd="mathmlattr" name="definitionURL">
    http://example.org/foo/bar</annotation>
</semantics>

But <csymbol>bar</csymbol> is not valid strict markup (and thus not
translatable to OpenMath), as it doesn't have a CD.  So would it be rewritten
to <ci>bar</ci> instead?

Cheers, and thanks in advance,

Christoph

-- 
Christoph Lange, Jacobs Univ. Bremen, http://kwarc.info/clange, Skype duke4701