[Om] Content Dictionary for Linked Data with RDF

Christoph LANGE ch.lange at jacobs-university.de
Fri Mar 2 22:22:30 CET 2012

Hi Ken,

2012-03-02 18:07 Wenzel, Ken:
> Our main idea is to use OpenMath expression in the same way for reasoning as
> owl:Restrictions or spin:constraints/spin:rules (http://spinrdf.org/spin.html).


> We're currently building a prototype reasoner based on Symja (http://code.google.com/p/symja/)
> and later on Maxima (embedded with ABCL) that is able to use OpenMath expressions
> which are linked to owl:Class descriptions for computing numeric properties of instances
> (e.g. the mass of a fluid depending on its volume and density).

Once more: Cool!

In July we will have an OpenMath workshop in Bremen (as a part of CICM =
Conference on Intelligent Computer Mathematics; see
http://www.informatik.uni-bremen.de/cicm2012/cicm.php).  I should really
get the call for papers and an initial homepage posted soon.  But a
submission on your work would be most welcome.

> We're currently using Manchester OWL for three reasons:
>> One of their drawbacks is, that they don't allow free variables for querying.
> (But we're working on this...)
> SPARQL on the other hand is much more powerful but not as well aligned
> with set theory as Manchester OWL descriptions.

Sounds very good to me.

>> But let's talk about URIs of single resources.  In the past I have
>> always advocated the approach of treating them as OpenMath
>> symbols, as, in fact, both are identified by URIs.
> I'm also thinking that it would be possible to map RDF resource URIs to OM symbols.
> (We've also used this approach in our first prototypical implementations.)
> The problem is that OM symbols should really be treated as math operators or
> math constants and not as arbitrary RDF resources (classes, properties, individuals) which
> can be math symbols but they don't have to.

I can understand your view and I think it is widely accepted in the OM 
community.  But, as I said in my reply to Arnold, _I_ don't share it, 
for the following reasons:

* It should be possible to develop mathematical models for any concept 
of the real world.  Therefore I consider any such concept worth to be 
treated as a "mathematical symbol", if necessary.

* RDF and OWL provide, in fact, also mathematical formalizations of the 
world.  Just that they do it in a fixed, specific logic, whereas OM is 
not committed to a specific logic and easily allows for writing down 
higher-order constructs, if you wish.  In the logics of RDF and OWL it 
is possible to provide mathematical formalizations of "arbitrary 
resources", so why shouldn't it be possible in OM?

> In the end the use of strings is more aligned with the current usage of OM symbols
> and does not require an implementor to decide if an OM symbol is used as
> math symbol or as reference to an RDF resource.

I wouldn't speak of "deciding" – unifying the space of RDF resources and 
the space of OM symbols is, at least semantically, not a problem (at 
least not for me, see above).  There is just a little technical barrier 
(the URI syntax).

> But I am also sharing your opinion that it may be useful to introduce a
> new concept like<OMIRIREF>  to OpenMath.

This is indeed an alternative.  For this it would even suffice to 
introduce a symbol such as <OMS cd="www1" name="uri"/>, which would be 
applied to a string argument and turn it into a URI.  But the result of 
this would be that we have an OpenMath object representing a URI, and 
this is no longer _so_ different from directly representing URIs via OMS.

Example: <OMA><OMS cd="www1" name="uri"/><OMSTR>http://www...</OMSTR></OMA>

I think this issue has been discussed before on this list, and that at 
least Paul Libbrecht also participated, but I don't find the mail.

>> And another final question is whether (and if so, how) your CD allows
>> for representing complete RDF triples as OM objects - of
>> maybe this is not intended after all.
> Yes, it is intended.
> For example:
> set1.in("This is a comment.", rdf.valueset("rdfs:comment", rdf.resource("foaf:Person")))
> relation1.eq(rdf.value("rdfs:comment", rdf.resource("foaf:Person")), "This is the only comment.")

OK, thanks, I understand.



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

→ SePublica Workshop @ ESWC 2012.  Crete, Greece, 27/28 May 2012.
    Deadline 29 Feb.  http://sepublica.mywikipaper.org
→ I-SEMANTICS 2012.  Graz, Austria, 5-7 September 2012
    Abstract Deadline 2 April.  http://www.i-semantics.at

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