PDF e-Pub

## Section: New Results

### Semantic Query Answering

This is a core topic for the team, in which the year has been particularly fruitful.

First, we investigated efficient query answering techniques in knowledge bases. A large and useful set of ontologies enjoys FOL (first-order logic) reducibility of query answering, that is: answering a query $q$ can be reduced to evaluating a certain first-order logic (FOL) formula (obtained from the query and ontology) against only the explicit facts. We devised a novel query optimization framework for ontology-based data access settings enjoying FOL reducibility. Our framework is based on searching within a set of alternative equivalent FOL queries, that is, FOL reformulations, one with minimal evaluation cost when evaluated through a relational database system. We applied this framework to the DL-Lite${}_{ℛ}$ Description Logic underpinning the W3C's OWL2 QL ontology language, and demonstrated through experiments its performance benefits when two leading SQL systems, one open-source and one commercial, are used for evaluating the FOL query reformulations. This work has lead to a major publication in the PVLDB journal [13], and a demonstration at the Semantic Web conference [4], while the complete details appear in [16] and the PhD thesis of the student author.  [2].

Second, we initiated a study of extensions of conjunctive queries to conjunctive regular path queries. The first step has been to study regular path queries under linear existential rules, generalizing previous work on DL-Lite${}_{ℛ}$, which is at the core of the Semantic Web OWL 2 QL profile. Regular path queries are queries that check for a path between two individuals, which is labeled by a word belonging to a given regular language. Such navigational languages are very popular for graph-based data representation, such as RDF. We have studied the complexity for this query language, and shown that it is NL-complete in data complexity, and EXPTIME-complete in combined complexity (and PTIME complete with bounded arity). This work has received the best paper award at RR'16 , and is currently being extented to conjunctive regular path queries.

Last, we studied the expressivity of several variants of Datalog, the classical language for deductive databases. In particular, we have studied its expressivity when given access (or not) to input negation (the ability to check if an extensional atoms hold or not) and to a linear order. We provided a complete Venn diagram regarding the expressivity of all the variants when considering homomorphism-closed query. The trickiest (and most surprising) points is the existence of polynomial-time computable homomorphism closed queries that are not expressible within Datalog with linear order but without input negation. These results have been published at IJCAI'16  [7].