The price of query rewriting in ontology-based data access

Abstract

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.

Ontology-Mediated Queries

“…The only previously known result in Fig. 2a is indicated by the white dotted line; for details, see [34,54].…”

“…Kikot et al [57] and Thomazo [84] identified common structures in UCQ-rewritings and compactified them into unions of semiconjunctive queries (USCQs)-positive-existential (PE) formulas with matrices of the form ∨∧∨-of size |T | · 2 O ( |q | 2 ) . The first lower bounds on the size of FO-, PE-and NDL-rewritings 4 were obtained 1:4 M. Bienvenu, S. Kikot, R. Kontchakov, V. V. Podolskii, and M. Zakharyaschev by Gottlob et al [34] who constructed a sequence of OMQs (with tree-shaped CQs) whose PEand NDL-rewritings can only be of exponential size, while FO-rewritings are superpolynomial unless NP ⊆ P/poly.…”

“…ϱ n with n ≤ p(|Q |) [20,48]. (In general, the bounded derivation depth property of an ontology language is a necessary and sufficient condition of FO-rewritability [34]. ) We call a set Ω Q of words of the form w = ϱ 1 .…”

“…In the combined approach to OMQ answering, the infinite set of labelled nulls of the chase is encoded by a small number of their representatives and the CQ q is rewritten in order to eliminate spurious answers [60,68] or a special filtering procedure is used to get rid of them [67]. Gottlob and Schwentick [39] and Gottlob et al [34] showed that every Q has a polynomial-size PE-rewriting over any given data extended with two special constants, which are used by extra existential quantifiers in the rewriting to 'guess' a derivation of q in the chase (cf. also [8] for a succinctness trick in the same vein).…”

An Introduction to Description Logics and Query Rewriting

“…It is to be noted that there exist CQs q and QL TBoxes T any PE-rewritings of which are of exponential size in |q| provided that the rewritings use the same symbols as in q and T (Kikot et al, 2012a). One can always reduce the size of PE-rewritings to polynomial by employing two new constants that do not occur in q; for details and further references, consult (Gottlob et al, 2014).…”