[Om] Content Dictionary for Linked Data with RDF

[Wenzel, Ken]

Dear Christoph,
dear Paul,

> [...] can you describe your expected usage of this CD or 
> expressions built with it?
> Are you expecting to use OpenMath-aware tools in their 
> mathematical glory on rdf-graphs?
> ...
> Then my question is the same as Paul's - what kind of 
> OM-aware software 
> you are going to apply to these OM representations of LD, and what 
> benefits these give you over, e.g., SPARQL queries or OWL 
> reasoning over RDF.
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).

> I agree that it may be useful to apply the rdf.resourceset 
> operator to more complex descriptions of RDF resources, and now that I see how it 
> works, I agree that OWL Manchester syntax is a reasonable approach, that 
> my initial Turtle suggestion is nonsense - but then maybe SPARQL might 
> be more appropriate, as it is pure RDF and doesn't require 
> OWL.  
We're currently using Manchester OWL for three reasons:
- they are description logics based and hence are pretty scalable
- we can use existing OWL reasoners to evaluate them
- they are concise descriptions for sets of RDF resources
Besides these, they can also easily be translated to SPARQL without any use
of OWL.
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.

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

> 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.")
But I'm unsure how this could be implemented in a CAS.

I'm going to post further comments next week when I have hopefully more time
for this topic...


Best regards and have a nice weekend,

Ken