[Om] Identifiers for FMPs

[Christoph LANGE]

Dear all,

  a preliminary consensus of the discussion about linking OpenMath CDs to DLMF
is that the entries for which DLMF currently has permanent URIs are best
conceived as counterparts to our FMPs.

When we link from our FMPs to somewhere, but, more importantly, when others
(such as DLMF) link to our FMPs, they need identifiers.  What I'm currently
doing in my OCD→RDF translation is simply counting, i.e. the first FMP of the
sin function would get the URI http://www.openmath.org/cd/transc1#sin-FMP1,
the second one FMP2.  (Actually the counting is slightly more complex, but
I'll keep it simple in this mail.)  That will get us into trouble if e.g.

 * wrong or redundant FMPs should ever be deleted
 * additional important FMPs should be added

Also, I see a lot of potential danger in having the "naming of FMPs" done by
some algorithm that is external to the CDs, which takes away control from the
CD authors.  (Imagine a CD author who created some FMPs and then wants to
contribute some RDF links to e.g. DLMF – that author would have to know how
that external algorithm counts.)

Therefore, I'd strongly suggest to introduce at least some optional mechanism
for naming FMPs.  This can be a <Name> child element in the OpenMath XML
"tradition", but we could also borrow @xml:id.

So far we've been talking about FMPs, but isn't the actual counterpart to a
DLMF equation a _pair_ of CMP (if existing) and FMP?  The OpenMath 2 way of
pairing CMPs and FMPs is hard to process (although possible, of course, I have
also done it), especially in cases where either the CMP or the FMP is missing.
The actual objects we are interested in are not XML-encoded OMOBJs in an <FMP>
container, but "mathematical properties" of symbols.  In the "OpenMath 3 draft
CDs" this was elegantly solved as

<Property>
  <CMP/>
  <FMP/>
</Property>

That would probably be something worth to adopt.

Besides the obvious technical advantage, such an enhancement would give us the
opportunity to assign meaningful short names to mathematical properties, such
as "NAME's identity", "NAME's theorem", "implicit definition of ...", which
would IMHO facilitate maintenance and understanding.

What do you think?

Cheers,

Christoph

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