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

[Professor James Davenport]

On Sun, July 18, 2010 1:48 pm, Urs Holzer wrote:
> Professor James Davenport wrote:
>> Then a more modest goal would be to state that
>>
>> "The FMP for sin is owl:sameas dlmf.nist.gov/4.14.E1" and here I
>> think we really DO mean owl:sameas, since I think they both have the
>> same deep author (Gauss, I believe), and who the shallow author is
>> doesn't reallly concern me - I imagine both JHD and DLMF looked at
>> A+S before writing their components.
>
> I am not sure that we mean owl:sameas. There are other things that one
> wants to describe than only the author, say who is responsible, who can
> update it, how it is encoded and so on. I believe that two documents are
> only owl:sameAs if they are exactly the same, byte by byte.
Ok - but that's not my understanding. If you're right, then we can never
use owl:sameas in this are, which is at least a resolution.
I beleive that if you apply OM->MML->TeX, you actuallly do get the same
bits as 4.14.E1.
> In my opinion, the only right thing is to do the following:
>
> DMLF:
> We have a document <4.14.E1> that describes something we call
According to Bruce, 4.14.E1 is an equation, not a definition.
> <smybol4.14.E1>. (Where <smybol4.14.E1> is not a document that can be
> retrieved, but just an identifier.)
> Our document <4.14.E1> is based on the work of Gauss.
>
> OpenMath:
> Our FMP describes a symbol transc1#sin.
> Our FMP is based on the work of Gauss.
> Our symbol transc1#sin is the same as <smybol4.14.E1>.
>
> Note that if DMLF suddenly finds out that their <smybol4.14.E1> and
> <smybol6.23.E3> are the same, they can simply add a
> <smybol4.14.E1> owl:sameAs <smybol6.23.E3> .
True.
> I guess this is what Christoph had in mind from the beginning. What he
> wants to do is to encode the statement
>     Our symbol transc1#sin is the same as <smybol4.14.E1>.
> in OpenMath. How to do this has already been discussed (with no final
> result, right?)
>
> 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.
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).

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), or in RDF/OWL in some associatedfile, or in
RDF/OWL in some derived file?
(c) How does OpenMath convert transc1#sin#FMP1 into a DEFINITION
(d) What will DLMF do to move more towards the Semantic Web and having a
definitive url 'defining' sin
(e) [ALL] how can (c) and (d) be synchronised, or at least done compatibly.

Anyone care to object to/clarify this summary?

James Davenport
Lecturer on XX10190, CM30070, CM30078/50123, CM50209
Hebron & Medlock Professor of Information Technology, University of Bath
OpenMath Content Dictionary Editor and Programme Chair, OpenMath 2009
IMU Committee on Electronic Information and Communication
Council of the British Computer Society
Federal Council, International Foundation for Computational Logic