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A most promising approach to answering queries in ontology-based data access (OBDA) is through query rewriting. In this paper we present novel rewriting approaches for several extensions of OBDA. The goal is to understand their relative expressiveness and to pave the way for efficient query answering algorithms.

In many scenarios, complete and incomplete information coexist. For this reason, the knowledge representation and database communities have long shown interest in simultaneously supporting the closed- and the open-world views when reasoning about logic theories. Here we consider the setting of querying possibly incomplete data using logic theories, formalized as the evaluation of an ontology-mediated query (OMQ) that pairs a query with a theory, sometimes called an ontology, expressing background knowledge. This can be further enriched by specifying a set of closed predicates from the theory that are to be interpreted under the closed-world assumption, while the rest are interpreted with the open-world view. In this way we can retrieve more precise answers to queries by leveraging the partial completeness of the data. The central goal of this paper is to understand the relative expressiveness of ontology-mediated query languages in which the ontology part is written in the expressive Description Logic (DL) ALCHOI and includes a set of closed predicates. We consider a restricted class of conjunctive queries. Our main result is to show that every query in this non-monotonic query language can be translated in polynomial time into Datalog with negation as failure under the stable model semantics. To overcome the challenge that Datalog has no direct means to express the existential quantification present in ALCHOI , we define a two-player game that characterizes the satisfaction of the ontology, and design a Datalog query that can decide the existence of a winning strategy for the game. If there are no closed predicates—in the case of querying an ALCHOI knowledge base—our translation yields a positive disjunctive Datalog program of polynomial size. To the best of our knowledge, unlike previous translations for related fragments with expressive (non-Horn) DLs, these are the first polynomial time translations.

In this article, we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from deciding whether a given sequence of actions preserves the satisfaction of a given set of integrity constraints, for every possible initial data instance, to deciding the (non)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. For describing states of the data instances and expressing integrity constraints on them, we use description logics (DLs) closely related to the two-variable fragment of first-order logic with counting quantifiers. The updates are defined as actions in a simple yet flexible language, as finite sequences of conditional insertions and deletions, which allow one to use complex DL formulas to select the (pairs of) nodes for which (node or arc) labels are added or deleted. We formalize the preceding data management problems as a static verification problem and several planning problems and show that, due to the adequate choice of formalisms for describing actions and states of the data, most of these data management problems can be effectively reduced to the (un)satisfiability of suitable formulas in decidable logical formalisms. Leveraging this, we provide algorithms and tight complexity bounds for the formalized problems, both for expressive DLs and for a variant of the popular DL-Lite, advocated for data management in recent years.