How to Tell Easy from Hard: Complexity of Conjunctive Query Entailment in Extensions of ALC

It is commonly known that the conjunctive query entailment problem for certain ex-tensions of (the well-known ontology language) ALC is computationally harder than their knowledge base satisfiability problem while for others the complexities coincide, both under the standard and the finite-model semantics. We expose a uniform principle behind this divide by identifying a wide class of (finitely) locally-forward description logics, for which we prove that (finite) query entailment problem can be solved by a reduction to exponentially many calls of the (finite) knowledge base satisfiability problem. Consequently, our algorithm yields tight ExPTIME upper bounds for locally-forward logics with ExPTIME-complete knowledge base satisfiability problem, including logics between ALC and mu ALCHbregQ (and more), as well as ALCSCC with global cardinality constraints, for which the complexity of querying remained open. Moreover, to make our technique applicable in future research, we provide easy-to-check sufficient conditions for a logic to be locally-forward based on several novel versions of the model-theoretic notion of unravellings.Together with existing results, this provides a nearly complete classification of the "benign" vs. "malign" primitive modelling features extending ALC, missing out only the Self operator. We then show a rather surprising result, namely that the conjunctive entailment problem for ALCSelf is exponentially harder than for ALC. This places the seemingly in-nocuous Self operator among the "malign" modelling features, like inverses, transitivity or nominals.