The impact of disjunction on query answering under guarded-based existential rules

We study the complexity of conjunctive query answering under (weakly-)(frontier-)guarded disjunctive existential rules, i.e., existential rules extended with disjunction, and their main subclasses, linear rules and inclusion dependencies (IDs). Our main result states that conjunctive query answering under a fixed set of disjunctive IDs is 2EXPTIME-hard. This quite surprising result together with a 2EXPTIME upper bound for weakly-frontier- guarded disjunctive rules, obtained by exploiting recent results on guarded negation first-order logic, gives us a complete picture of the computational complexity of our problem. We also consider a natural subclass of disjunctive IDs, namely frontier-one (only one variable is propagated), for which the combined complexity decreases to EXPTIME. Finally, we show that frontier-guarded rules, combined with negative constraints, are strictly more expressive than DL-Lite_bool ^H, one of the most expressive languages of the DL-Lite family. We also show that query answering under DL-Lite_bool ^H is 2EXPTIMEcomplete in combined complexity.