Revisiting Conjunctive Query Entailment for $\mathcal S$
For knowledge representation researchers, this clarifies the exact computational complexity of a fundamental reasoning problem, correcting previous misconceptions.
The paper resolves the complexity of conjunctive query entailment for the description logic S, showing it is 2ExpTime-complete, contrary to prior partial results suggesting lower complexity. It also establishes coNExpTime bounds for rooted queries or queries with at most one transitive role.
We clarify the complexity of answering unions of conjunctive queries over knowledge bases formulated in the description logic $\mathcal S$, the extension of $\mathcal{ALC}$ with transitive roles. Contrary to what existing partial results suggested, we show that the problem is in fact 2ExpTime-complete; hardness already holds in the presence of two transitive roles and for Boolean conjunctive queries. We complement this result by showing that the problem remains in coNExpTime when the input query is rooted or is restricted to use at most one transitive role (but may use arbitrarily many non-transitive roles).