[Om] OpenMath on the Semantic Web?

Paul Libbrecht paul at activemath.org
Tue Feb 3 15:58:37 CET 2009

Erm, allow me to ask before reading all these references:

- I believe we have an instance-of type of relationship, namely the  
relationship between OMS and symbol-declaration

- do we have any construct or FMP to say that a symbol-declaration is  
a generalization of another symbol-declaration? (i.e. that, in order  
to restrict the world, one could just consider the more general case) ?
I am not 100% sure that DEFMP satisfies this.

- properties? would be attributions?

And clearly, OWL or RDF is missing a notion of applications,  
variables, bound-variables.


Le 03-févr.-09 à 11:22, Christoph LANGE a écrit :
>  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
> OWL).
> @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.
> Cheers,
> Christoph
> -- 
> Christoph Lange, Jacobs Univ. Bremen, http://kwarc.info/clange,  
> Skype duke4701

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