The Price of Selfishness: Conjunctive Query Entailment for ALCSelf Is 2EXPTIME-Hard

In logic-based knowledge representation, query answering has essentially replaced mere satisfiability checking as the inferencing problem of primary interest. For bases in basic description logic ALC, computational complexity conjunctive (CQ) is well known to be EXPTIME-complete and hence not harder than satisfiability. This does change when extended by certain features (such counting or role hierarchies), whereas adding others (inverses, nominals transitivity together with role-hierarchies) turns CQ exponentially harder. We contribute this line results showing surprising fact that even extending ALC just Self operator – which proved innocuous many other contexts increases entailment 2EXPTIME. As common for type problem, our proof establishes a reduction from alternating Turing machines running exponential space, but several novel ideas encoding tricks are required make approach work specific, restricted setting.