Query Rewriting and Optimization for Ontological Databases

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 that 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 article, 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 that 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 soas to produce possibly small and cost-effective UCQ rewritings for an input query.