Fast Query Answering over Existential Rules

Enhancing Datalog with existential quantification gives rise to Datalog(3), a powerful knowledge representation language widely used in ontology-based query answering. In this setting, a conjunctive query is evaluated over a Datalog(3) program consisting of extensional data paired with so-called "existential" rules. Owing to their high expressiveness, such rules make the evaluation of queries undecidable, even when the latter are atomic. Decidable generalizations of Datalog by existential rules have been proposed in the literature (such as weakly acyclic and weakly guarded); but they pay the price of higher computational complexity, hindering the implementation of effective systems. Conversely, the results in this article demonstrate that it is definitely possible to enable fast yet powerful query answering over existential rules that strictly generalize Datalog by ensuring decidability without any complexity overhead. On the theoretical side, we define the class of parsimonious programs that guarantees decidability of atomic queries. We then strengthen this class to strongly parsimonious programs ensuring decidability also for conjunctive queries. Since parsimony is an undecidable property, we single out Shy, an easily recognizable class of strongly parsimonious programs that generalizes Datalog while preserving its complexity even under conjunctive queries. Shy also generalizes the class of linear existential programs, while it is uncomparable to the other main classes ensuring decidability. On the practical side, we exploit our results to implement DLV3, an effective system for query answering over parsimonious existential rules. To assess its efficiency, we carry out an experimental analysis, evaluating DLV3 performances for ontology-based query answering on both real-world and synthetic ontologies.