Embedding transitivity rules.

In recent years, many classes of existential rules have been exhibited for which CQ entailment is decidable. However, most of these classes cannot express transitivity of binary relations, a frequently used modelling construct. We began to investigate the issue of whether transitivity can be safely combined with decidable classes of existential rules. On the one hand, we obtained negative results, proving that transitivity is incompatible with many classes having finite chase, and with UCQ-reducible classes in general. Second, we showed that transitivity can be safely added to linear rules (a subclass of guarded rules, which generalizes the description logic DL-Lite${}_R$) in the case of atomic CQs, and also for general CQs if we place a minor syntactic restriction on the rule set (only needed when predicate arity is strictly greater than 2). Finally, we pinpointed the combined and data complexities of query entailment over linear rules + transitivity.

A generic algorithm for query reformulation.

We first designed and implemented a query reformulation algorithm that takes as input any set of existential rules and a UCQ $q$, and outputs a sound, minimal and complete UCQ-reformulation of $q$, whenever such a reformulation exists (i.e., when the set of existential rules is UCQ-reducible). The core operation, unification, relies on a special technique that we first developed for conceptual graphs (“piece-unification”). A noteworthy feature of the implemented unification is that it is able to process rules without decomposing their head into single atoms. Experiments showed that this feature has a very high impact on the efficiency of query reformulation in terms of running time.

This algorithm can be seen as an instantiation of a generic reformulation algorithm, parametrized by a reformulation operator. As a complementary work, we studied the properties that should be fulfilled by any reformulation operator to ensure the correctness and the termination of this generic algorithm and analyzed some known operators with respect to these properties.

Optimization of query reformulation algorithms

Query reformulation techniques have the advantage of being independent from the data. However, a main bottleneck is that the size of the obtained query can be exponential in the size of the original query, hence the produced reformulation maybe not usable in practice (and the corresponding SQL query may not even be accepted by the RDBMS). To overcome this combinatorial explosion in practice, we made two proposals, which have in common to consider other forms of reformulation, while staying equivalent to UCQs in terms of expressivity.

We defined semi-conjunctive queries (SCQs), which are a syntactical extension of conjunctive queries allowing for internal disjunctions. Briefly, a union of SCQs can be encoded in a more compact form than a UCQ. We designed and implemented an algorithm called Compact, which computes a sound and complete reformulation of a UCQ in the form of a union of SCQs (USCQ). First experiments showed that USCQs are both very efficiently computable and (often) more efficiently evaluable than their equivalent UCQs.

We developed another solution, which starts from a simple observation: in practice, combinatorial explosion is mainly due to some very simple rules, which form the core of any ontology. These rules typically express concept and relation hierarchies, concept properties and relation signatures. We proposed a technique that consists in compiling these rules into a preorder on atoms and embedding this preorder into the reformulation process. This allows us to compute compact reformulations that can be considered as “pivotal” representations, in the sense that they can be easily translated into different kinds of queries that can be evaluated by different kinds of database systems (e.g., unfolded into a classical UCQ or a USCQ, processed as such on data saturated by the compilable rules, or transformed into a Datalog program). Experiments show that this technique leads to substantial gains in the query reformulation process, in terms of size and runtime, it scales on very large ontologies (several ten thousands of rules), and it is competitive w.r.t. other existing tools, including those tailored for more specific rules corresponding to DL-Lite ontologies. This technique has been implemented in the sofware platform Graal.

Ontology-based query answering with Semantic Web languages