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

[Christoph LANGE]

2010-07-18 16:17 Professor James Davenport <jhd at cs.bath.ac.uk>:
> > I am slowly loosing the overview of the discussion, I need a summary.
> OK let me try.
> <OMS name="sin" cd="transc1"/> is an object defined by OpenMath (as is
> every symbol), except that this one has a complete definition (what we
> ought to call a DeFMP), which I will call transc1#sin#FMP1.

That reminds me of a separate problem: We don't have proper identifiers for
FMPs.  I will start a separate thread about that.

> DLMF does not, de jure, DEFINE functions - it states properties of them
> (de facto, one might think it did, but when one comes to drill down and
> ask "exactly what is the definition" it gets messier).
> 4.14 mentions lots of functions.
> 4.14.E1 (which is informally the same as, and I believe is owl:sameas,
> transc1#sin#FMP1) is an equation which the human reading 4.14 MIGHT choose
> to read as a definition).

I agree that it is owl:sameAs, and as soon as you are done with your DLMF
review, I will start to create such links in separate RDF files.

> Therefore the questions are:
> (a) can we say that transc1#sin#FMP1 relates to 4.14.E1?
> (b) should be try to say so in OM syntax in a CD (which probably means no
> other tool will process it),

Here it wouldn't be a problem that other tools out there on the "web of data"
can't process the OCD format, because we have an OCD→RDF translator, which
would just need a few little fixes.

> or in RDF/OWL in some associatedfile, or in RDF/OWL in some derived file?

In my envisaged scenario these are not two alternatives, but two complementary
parts of the big picture.  The links to external datasets, which we either
can't or don't want to express inside the OCD, will be maintained in an
associated RDF file.  But, secondly, there is a _derived_ RDF file (by the
OCD→RDF translation), which contains RDF representations of the metadata in
the CDs, and RDF representations of the structural relations in the CD (e.g.
that for a symbol some FMPs have been given).

> (c) How does OpenMath convert transc1#sin#FMP1 into a DEFINITION

You mean how OpenMath applications know that this FMP is not just any
equation, but that it indeed happens to define the sin function?  I think that
(and a possible DeFMP) has to be discussed for OpenMath first, and is
independent from any RDF considerations in the first place.

> (d) What will DLMF do to move more towards the Semantic Web and having a
> definitive url 'defining' sin

Even if DLMF doesn't mathematically _define_ sin, it would be good if there
were a URL for sin, so that we could more densely cross-link OpenMath and
DLMF.  Suppose we only had "descriptive" FMPs in OpenMath, and descriptive
equations in DLMF, then we could still say:

              OpenMath                       DLMF

Symbols       transc1#sin <-- owl:sameAs --> (DLMF's ID for sin)
                   |                                  |
   is described by |                                  | is described by
                   |                                  |
                   v                                  v
Equations      sin#FMP1   <-- owl:sameAs -->       4.14.E1

(later, "is described by" could be promoted into "is (mathematically) defined
by", where appropriate)

> (e) [ALL] how can (c) and (d) be synchronised, or at least done compatibly.
> 
> Anyone care to object to/clarify this summary?

I hope I did – rather clarify than object :-)

Cheers,

Christoph

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