Is it possible to write a SPARQL query (or use some API) to retrieve the concept definitions from any ontology?

I don't know if you can do that with Sparql, i think it's not designed for such a task. But if you are not restricted to Sparql then you could give a try to the owlapi.

http://owlapi.sourceforge.net/

hth josh

By "necessary and sufficient conditions", I expect you mean the owl:equivalentClass definitions? I.e. local class restrictions applied to owl:equivalentClass, This can easily be done in SPARQL. Start with:

SELECT *
WHERE
{  ?s owl:equivalentClass ?o
}

SELECT *
WHERE
{  ?cls owl:equivalentClass ?restriction .
   ?restriction owl:onProperty ?prop .
   ?restriction ?restrictType ?value
}

Getting to intersections and other OWL statements is admittedly more complex, but entirely possible. Note the same can be done for rdfs:subClassOf restrictions (sometimes known as necessary conditions).

Do you ask for a single SPARQL query to get them all, and only those?

I guess that even for the "restricted" case, where you only allow for valid OWL DL ontologies as input graphs, this would essentially require to implement a major part of the matching algorithm that underlies the reverse OWL 2 RDF Mapping... as a SPARQL query! The matching of the many different forms of class expressions is among the most complex aspects of this algorithm, and that algorithm is complex!

So even if it would be technically feasible, I could not imagine anyone on earth who would want to execute such an insane exercise. But I don't really believe that it is possible at all, unless SPARQL would turn out to be Turing-complete. And for input beyond OWL 2 DL (i.e. for arbitrary RDF / OWL Full input), it is not even entirely well-defined what counts as a proper class expression or class axiom /syntactically/, and what not. But without such a definition, your question cannot even be answered in a meaningful and precise way with "yes" or "no" in such a scenario...

If you use Jena, or Jena+Pellet, retrieving the class hierarchy of an RDFS/OWL ontology is not too difficult. You can use listHierarchyRootClasses(), listSubClasses(), and listDeclaredProperties(). (Google is your friend for more info about these methods).

Getting this data from a remote SPARQL endpoint which provides no additional ontology of its concepts requires a quite complicated SPARQL query (that will probably timeout before you get any answer).