Ontology-based data access is a powerful form of extending database technology, where a classical extensional database (EDB) is enhanced by an ontology that generates new intensional knowledge which may contribute to answer a query. The ontological integrity constraints for generating this intensional knowledge can be specified in description logics such as DL-Lite. It was recently shown that these formalisms allow for very efficient query-answering. They are, however, too weak to express simple and useful integrity constraints that involve joins. In this paper we introduce a more expressive formalism that takes joins into account, while still enjoying the same low query-answering complexity. In our framework, ontological constraints are expressed by sets of rules that are so-called tuple-generating dependencies (TGDs) . We propose the language of sticky sets of TGDs, which are sets of TGDs with a restriction on multiple occurrences of variables (including joins) in the rule bodies. We establish complexity results for answering conjunctive queries under sticky sets of TGDs, showing, in particular, that ontological conjunctive queries can be compiled into first-order and thus SQL queries over the given EDB instance. We also show how sticky sets of TGDs can be combined with functional dependencies. In summary, we obtain a highly expressive and effective ontological modeling language that unifies and generalizes both classical database constraints and important features of the most widespread tractable description logics.

Ontological queries are evaluated against an ontology rather than directly on a 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 query against the underlying relational database. The focus here is on soundness and completeness. We review previous results and present a new rewriting algorithm for rather general types of ontological constraints. In particular, we show how a conjunctive query against an ontology can be compiled into a union of conjunctive queries against the underlying database. Ontological query optimization, in this context, attempts to improve this process so to produce possibly small and cost-effective UCQ rewritings for an input query. We review existing optimization methods, and propose an effective new method that works for linear Datalog ± , a class of Datalog-based rules that encompasses well-known description logics of the DL-Lite family. * This is an extended and revised version of the paper [1].Description Logics. Description logics (DLs) are logical languages for expressing and modelling ontologies. The best known DLs are those underlying the OWL language 1 . The main ontological reasoning and query answering tasks in the complete OWL language, called OWL Full, are undecidable. For the most well-known decidable fragments of OWL, ontological reasoning and query answering is still computationally very hard, typically 2exptime-complete.In description logics, the ontological axioms are usually divided into two sets: The ABox (assertional box), which essentially contains factual knowledge such as "IBM is a company", denoted by company (ibm), or "IBM is listed on the NASDAQ", which could be represented as a fact of the form list comp(ibm, nasdaq ), and a TBox (terminological box) which contains axioms and constraints that allow us, on the one hand, to infer new facts from those given in the ABox, and, on the other hand, to express restrictions such as keys. For example, a TBox may contain an axiom stating that for each fact list comp(X, Y ), Y must be a financial index, which in DL is expressed as ∃list comp − ⊑ fin idx . If the fact fin idx (nasdaq ) is not already present in the ABox, it can be derived via the above axiom from list comp(ibm, nasdaq ). Thus, the atomic query "q(X) ← fin idx (X)" would return nasdaq as one of the answers. Note that the axiom ∃list comp − ⊑ fin idx , which corresponds to an inclusion dependency, is enforced by adding new tuples, rather than just being checked. This is one main difference between ontological constraints and classical database dependencies. In database terms, the above axiom is to be interpreted more like a trigger than a classical constraint.Ontology Based Data Access (OBDA). We are currently witnessing the marriage of ontological reasoning and database technology. In fact, this amalgamation consi...

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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.