From SPARQL Working Group
Draft reply to: MS-2
Thank you for your comment about the SPARQL Entailment Regimes document.
Although the Direct Semantics Entailment Regime seems to allow for higher order queries, the restriction that variables can only bind to a finite set of names (such as class, property, or individual names) means that even queries that seem to be higher order (as the subclass query in the example in Sec. 6.4) can still be reduced to standard first-order queries. In particular, one can answer such a query by checking whether each of the finitely many instantiations of the query (where class variables are replaced by class names from the queried ontology, etc) are entailed by the queried ontology under OWL's Direct Semantics.
We tried to make it clearer in Sec. 6.4 that no higher order reasoning is required to answer SPARQL queries with the Direct Semantics entailment regime. We do not think that discussing optimized implementation techniques that go beyond entailment checking can be discussed in the specification.
We hope that this answer addresses your comment and would be grateful if you would acknowledge this by sending a reply to this mailing list.
Birte, on behalf of the SPARQL-WG