Polynomial combined first-order rewritings for linear and guarded existential rules

Abstract

We consider the problem of ontological query answering, that is, the problem of answering a database query (typically a conjunctive query) in the presence of an ontology. This means that during the query answering process we also need to take into account the knowledge that can be inferred from the given database and ontology. Building, however, ontology-aware database systems from scratch, with sophisticated optimization techniques, is a highly non-trivial task that requires a great engineering effort. Therefore, exploiting conventional database systems is an important route towards efficient ontological query answering. Nevertheless, standard database systems are unaware of ontologies. An approach to ontological query answering that enables the use of standard database systems is the so-called polynomial combined query rewriting, originally introduced in the context of description logics: the conjunctive query q and the ontology Σ are rewritten in polynomial time into a first-order query qΣ (in a database-independent way), while the database D and the ontology Σ are rewritten in polynomial time into a new database DΣ (in a query-independent way), such that the answer to q in the presence of Σ over D coincides with the answer to qΣ over DΣ. The latter can then be computed by exploiting a conventional database system.In this work, we focus on linear and guarded existential rules, which form robust rule-based languages for modeling ontologies, and investigate the limits of polynomial combined query rewriting. In particular, we show that this type of rewriting can be successfully applied to (i) linear existential rules when the rewritten query can use the full power of first-order queries, (ii) linear existential rules when the arity of the underlying schema is fixed and the rewritten query is positive existential, namely it uses only existential quantification, conjunction, and disjunction, and (iii) guarded existential rules when the underlying schema is fixed and the rewritten query is positive existential. We can show that the above results reach the limits (under standard complexity-theoretic assumptions such as ▪) of polynomial combined query rewriting in the case of linear and guarded existential rules.