[Om] OpenMath on the Semantic Web?

Christoph LANGE ch.lange at jacobs-university.de
Tue Feb 3 11:22:58 CET 2009

Hi Paul, dear all,

  let me reply to your blog post and your mails at once.  First about your
blog post: A good statement!  The semantic web community is sometimes a bit
self-centered.  For example, I was once asked by a semantic web expert why we
used OMDoc for semantic markup and not just the "standard" RDFa.  Replace
OMDoc by OpenMath for the purpose of this discussion.  Well, we have reasons
for using our "non-standard" markup (if interested, see
https://svn.omdoc.org/repos/omdoc/trunk/doc/blue/foaf/note.pdf), but actually
the good thing about this criticism was that it made us _think_ _why_ there
are benefits in using OMDoc/OpenMath.

I suppose that nothing was wrong about your WWW submission, but that you
failed to speak "their" language, i.e. to explain to them _why_ OpenMath is a
bit more semantic than "ordinary XML" and indeed has more than "implicit
semantics".  I usually compare OpenMath CDs to RDFS ontologies, which have a
similar expressivity -- you define collections of symbols (or classes, or
properties) with unique identifiers, a few formal interrelations, plus
informal descriptions and explanations.  Thus, OpenMath can be considered an
ontology language, but it's not obvious in the first place.

@Jürgen: I think that OpenMath indeed doesn't compare that well to more formal
ontology languages like OWL.

@James: I agree that DefMPs would make OpenMath a bit more formal (more like

@David: I think the OpenMath symbols ontology you mentioned is not too
"semantic" in the sense that was asked for here.  IMHO there is not too much
value in knowing that, e.g., every transc1#sin is a #transc1_Symbols and this
an #OpenMathSymbol -- a fact that we can obtain from the respective
rdfs:subClassOf relationship.  I think there's a lot more of "CD structure"
that could be expressed in terms of semantic web ontologies -- imagine a
combination of your "symbol ontology" and my "document ontology", which
doesn't talk too much about symbols, but about the other structural aspects of
CDs.  (See
http://kwarc.info/projects/swim/pubs/semwiki08-notation-semantics.pdf for
details.)  The value of the MONET OpenMath ontology only comes from its
integration with the other MONET ontologies
(http://monet.nag.co.uk/monet/publicdocs/monet_ontologies.html), which are
indeed useful for CAS web services, if I understand correctly.  But the
OpenMath symbols ontology hardly does more than giving URIs to OpenMath
symbols and grouping them by CD -- and thereby giving the queries, problems,
and services something they can talk about.



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

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