Query Rewriting and Optimization for Ontological Databases

Abstract

Ontological queries are evaluated against a knowledge base consisting of an extensional database and an ontology (i.e., a set of logical assertions and constraints which derive new intensional knowledge from the extensional database), rather than directly on the extensional database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper, we discuss two important aspects of this problem: query rewriting and query optimization. Query rewriting consists of the compilation of an ontological query into an equivalent first-order query against the underlying extensional database. We present a novel query rewriting algorithm for rather general types of ontological constraints which is well-suited for practical implementations. In particular, we show how a conjunctive query against a knowledge base, expressed using linear and sticky existential rules, that is, members of the recently introduced Datalog ± family of ontology languages, can be compiled into a union of conjunctive queries (UCQ) against the underlying database. Ontological query optimization, in this context, attempts to improve this rewriting process so to produce possibly small and cost-effective UCQ rewritings for an input query.

The price of query rewriting in ontology-based data access

“…Theorem 5 ( [16,11,25,13,24]). For any set Σ of tgds, let K Σ be the number of predicates in Σ and let L Σ be the maximum arity of the predicates in Σ.…”

“…. , A n (x j ), for each 1 ≤ j ≤ k. For (ii) and (iii), we only briefly comment on the UCQ-rewritings constructed in [16,11,25,13,24] using backward chaining. (ii) Since the tgds have a single atom in the body, the number of atoms in each of the CQs of the resulting UCQ-rewriting cannot be larger than the number of atoms in q.…”

Logic, Languages, and Rules for Web Data Extraction and Reasoning over Data

“…the data complexity, we need a more refined approach. This is done by unfolding the given set of TGDs (using a resolution-based procedure [28]) in order to construct a (finite) union of conjunctive queries, which is then evaluated over the input database. This allows us to conclude the AC 0 upper bound stated in the above theorem.…”

The pragmatic proof: Hypermedia API composition and execution

“…Several recent approaches support reasoning with existential rules on top of ontologies as for example Graal (Baget et al 2015) or IRIS ± (Gottlob et al 2014). These implementations are very promising, but still under development.…”