In OWL, is it possible to assert that a class is not "empty"?

Question

Given the different types of axioms available in OWL, is it possible to assert that a class is not "empty"? Or in other words, can we assert that there exists at least one individual that is part of the specified class?

So, basically I am looking for an equivalence of:

ObjectAssertNotEmpty(a:SomeClass)

Answer 1

That is exactly what the model theoretic underpinning of Description Logics aim to do is to assume that all concepts (or OWL classes) are not empty. That is the basis of satisfiability checking and consistency checking.

Answer 2

In an RDF serialization, all it takes is to identify such an individual:

[] a a:SomeClass .

I presume the OWL syntax should be able to specify it this way:

ClassAssertion( a:SomeIndividual a:SomeClass )

It doesn't matter that you call the individual a:SomeIndividual here, it could very well be owl:sameAs any other individual. Once you state that something is in the class, it follows that the class is not empty.