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

[Christoph LANGE]

Hi David,

  let me turn this topic into a new thread and answer the rest separately.

2010-07-16 11:30 David Carlisle <davidc at nag.co.uk>:
> On 15/07/2010 23:07, Professor James Davenport wrote:
>  > Q. Why was DefinitionURL deprecated in MathML (by declaring it to be
>  > pragmatic-only).
> 
> the notes don't record who asked the question,

that was me, …

> but it's not deprecated (you can't deprecate something that was never there)
> the attribute isn't in Strict MathML because it isn't in OpenMath.

… and I interpreted it as a de facto "deprecation" because from a
content-oriented point of view my impression is that new tools will rather use
strict CMML, whereas pragmatic CMML was rather kept for historical and
political reasons.  So from that point of view anything that is not
expressible in strict CMML seems deprecated to me.  But that objection was
based on the wrong assumption that definitionURLs that don't fit into the
CDBase/CD/Name schema wouldn't be expressible at all in strict CMML.

Note that I was not concerned about the @definitionURL _attribute_.  It is
perfectly clear to me that strict CMML has the CD/name syntax to express the
same, but my point was that CD/name cannot express the same as @definitionURL.

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.  

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, but I think we _could_
introduce arbitrary links into OpenMath via a relaxed interpretation of FMPs,
or probably via attributions.  I.e. we wouldn't be forced to enhance the
syntax of OpenMath CDs by something RDF-like.

<FMP>
  <OMOBJ>
    <OMA>
      <OMS cd="relation1" name="eq"/>
        <!-- or take e.g. <OMS cd="owl" name="sameAs"/>, which is more
             common in the Linked Data world -->
      <OMS cd="transc1" name="sin"/>
      <OMS cdbase="http://dlmf.nist.gov" cd="..." name="sin"/>
    </OMA>
  </OMOBJ>
</FMP>

<FMP>
  <OMOBJ>
    <OMA>
      <OMS cd="..." name="has-notation-census-entry"/>
        <!-- or take e.g. <OMS cd="rdfs" name="seeAlso"/>, which is more
             common in the Linked Data world but has a very weak semantics -->
      <OMS cd="transc1" name="sin"/>
      <OMS cdbase="http://wiki.math-bridge.org" cd="..." name="sin"/>
    </OMA>
  </OMOBJ>
</FMP>
    

> MathML DefinitionURL in general (if it doesn't point to a CD) 
> corresponds to an OpenMath annotation using a symbol "definitionurl" in 
> some CD and a OMstring to hold the URI.

Aha!  I wasn't aware of that.  But this is specified nowere in the MathML 3
spec, is it?  My understanding was that pragmatic CMML is not more expressive
than strict CMML, i.e. that for everything you can express in pragmatic CMML
there is a well-defined translation to strict CMML somewhere in the spec.
Otherwise human guesswork would be involved, and that would kill
machine-understandability.

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"?

<csymbol definitionURL="http://cdbase/cd#name"/> translates to
<OMS cdbase="http://cdbase" cd="cd" name="name"/>

but what does <csymbol definitionURL="http://example.org/foo/bar"/> translate
to?  (Note again that a lot of such #-less URIs exist out there, for good
reasons)

<OMATTR>
  <OMATP>
    <OMS cd="..." name="definitionurl"/>
    <OMSTR>http://example.org/foo/bar</OMSTR>
  </OMATP>
  <!-- WHAT GOES HERE?  A dummy OMS, an OMV, ...? -->
</OMATTR>

> In the case that the definitionurl is of the form uri-of-cd#symbolname then
> it just corresponds to the usual OMS cd=... name=... attrbutes.

Always?  Suppose we have a "see-also" link to
http://en.wikipedia.org/wiki/Exponential_function#Formal_definition.  That
fits into the schema and could be linked to using
<OMS cdbase="http://en.wikipedia.org/wiki" cd="Exponential_function"
name="Formal_definition"/>, but that might give a system the false impression
that http://en.wikipedia.org/wiki/Exponential_function has the semantics of an
OpenMath CD, which it has not.  So we might express such links differently,
e.g. using the above-mentioned attribution.

But then, if we treat some a/b#c URIs as links to OpenMath CD symbols, and
others not, then we'd need some way to decide whether a given a/b#c URI is a
CD symbol or not.

Cheers,

Christoph

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