The price of query rewriting in ontology-based data access

We give a solution to the succinctness problem for the size of first-order rewritings of conjunctive queries in ontologybased data access with ontology languages such as OWL 2 QL , linear Datalog± and sticky Datalog±. We show that positive existential and nonrecursive datalog rewritings, which do not use extra non-logical symbols (except for intensional predicates in the case of datalog rewritings), suffer an exponential blowup in the worst case, while first-order rewritings can grow superpolynomially unless NP ⊆ P/poly. We also prove that nonrecursive datalog rewritings are in general exponentially more succinct than positive existential rewritings, while first-order rewritings can be superpolynomially more succinct than positive existential rewritings. On the other hand, we construct polynomial-size positive existential and nonrecursive datalog rewritings under the assumption that any data instance contains two fixed constants.