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

Bruce Miller bruce.miller at nist.gov
Sun Jul 18 03:09:45 CEST 2010

On 07/17/2010 08:11 AM, Christoph LANGE wrote:

> Suppose the OWL reasoner already knows some facts about the source of the link
> (here: transc1#sin), such as (in terms of my ontology for OpenMath CDs,
> prefixed "om" here):
> <transc1#sin>  rdf:type om:SymbolDefinition .
> <transc1#sin>  dc:description "This symbol represents ..." .
> <transc1#sin>  om:hasProperty<id-of-some-FMP>  .
> ...
> Then,<transc1#sin>  owl:sameAs<http://dlmf.nist.gov/4.14.E1>  would imply:
> <http://dlmf.nist.gov/4.14.E1>  rdf:type om:SymbolDefinition .
> <http://dlmf.nist.gov/4.14.E1>  dc:description ...
> That means,<http://dlmf.nist.gov/4.14.E1>  _is_ transc1#sin, with all of its
> properties.  The representation of transc1#sin at the URI
> <http://dlmf.nist.gov/4.14.E1>  just happens to be encoded differently, i.e.
> not in the OCD format, and it needs not explicitly declare the same properties
> as we do in the CD (i.e. on the DLMF site there don't have to be the same
> examples as in the CD), but still it means the same.

[Finding the right place to jump in...
  but possibly missing the point...]

I don't think this is the assertion of equivalence
that you want to be making.  The mathematical object
associated with http://dlmf.nist.gov/4.14.E1 is an
equation or relation; Someday, with the right content
negotiation or type extension (eg. appending .om
to the url), this may fetch an OM object, but that
object would also be a relation, not a CD.
It can certainly be considered as a "definition"
of sin, but it isn't "equivalent to" sin, nor is
it a CD defining sin.

I understand that the goal is to formalize the
mention of dlmf urls within CDs;
is there a relation type more like "defines"
that could be used? (or "satisfies", or...)
Can that not have a status such that if two resources
employ a "sin" that is "defined by" http://dlmf.nist.gov/4.14.E1
that they can be considered to be using the same "sin"?
(this is what you're after, isn't it?)

Incidentally, it was always the intent to develop
(or support the development of) DLMF CD's,
(once the set and actual properties became clearer)
but these urls aren't really the definitionURLs that
would correspond.

Perhaps, ultimately there should end up urls of the form
http://dlmf.nist.gov/#sin, but what they actually
signify is another potential area of discussion.

Incidentally2, yes, the reference-number-based URL's
are intended to be permanent, but the reference
numbers are different from A&S (a different book).


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