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

[Christoph LANGE]

Hi Urs,

2010-07-18 14:48 Urs Holzer <urs at andonyar.com>:
> 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.

Yes, but that information would be associated with a concrete materialization
of the equation, not with the abstract equation.  Linked data practice
distinguishes those two things.  Let http://dlfm.nist.gov/4.14.E1 be the
equation, and let http://dlmf.nist.gov/4.14.html#E1 be the materialization
(called "information resource" in the WWW jargon) of that equation in HTML.
Then we can assert certain mathematical properties about the equation as RDF
triples having 4.14.E1 as their subject, whereas administrative information
about the document could be asserted as RDF triples having 4.14.html#E1 as
their subject.

This paper may be helpful as background information:
http://www.stlab.istc.cnr.it/documents/papers/IRW@eswc2009.pdf

> I believe that two documents are only owl:sameAs if they are exactly the
> same, byte by byte.

You are confusing syntax and semantics here.  See
http://www.w3.org/TR/2009/REC-owl2-syntax-20091027/#Individual_Equality (and
select "show RDF examples" below the ToC to see that this is owl:sameAs).

> 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 
> <smybol4.14.E1>. (Where <smybol4.14.E1> is not a document that can be 
> retrieved, but just an identifier.)

Exactly, just that I chose different URIs above.  Your document 4.14.E1 is my
4.14.html#E1.  And your symbol4.14.E1 is yet something different – if I get it
correctly, it is "the sin function", i.e. what Bruce called
http://dlmf.nist.gov/#sin in previous mails, and it would be related to "the
equation" that I'm talking about above by some "is defined by" relation.

> 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>.

I agree with these.

> 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> .

Yes, except that for DLMF it might be more appropriate to use OpenMath's
relation1#eq.

> 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?)

Right, that's what I want.  It's just that we cannot currently do this, as
DLMF doesn't have identifiers for symbols (yet).

> I am slowly loosing the overview of the discussion, I need a summary.

Michael's mail may already serve as a very high-level summary.  I agree with
his observations and will reply more specifically (by mail or Trac ticket).

Cheers,

Christoph

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