On the k-Boundedness for Existential Rules

The chase is a fundamental tool for existential rules. Several chase variants are known, which differ on how they handle redundancies possibly caused by the introduction of nulls. Given a chase variant, the halting problem takes as input a set of existential rules and asks if this set of rules ensures the termination of the chase for any factbase. It is well-known that this problem is undecidable for all known chase variants. The related problem of boundedness asks if a given set of existential rules is bounded, i.e., whether there is a predefined upper bound on the number of (breadth-first) steps of the chase, independently from any factbase. This problem is already undecidable in the specific case of datalog rules. However, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound is unknown. Hence, in this paper, we investigate the decidability of the k-boundedness problem, which asks whether a given set of rules is bounded by an integer k. We prove that k-boundedness is decidable for three chase variants, namely the oblivious, semi-oblivious and restricted chase.Comment: 20 pages, revised version of the paper published at RuleML+RR 201

Ontology-Based Query Answering with Existential Rules

International audienceIt is widely acknowledged that modern information sytems require an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit the semantics encoded in ontologies. We focus here on ontology-based data access (OBDA), a new paradigm that seeks to take ontological knowledge into account when querying data. This paradigm is currently the subject of intense research in the database, knowledge representation and reasoning, and Semantic Web communities. Indeed, it is expected to have a major impact in many application domains, however some foundational issues need first to be adressed. In this context, we consider an emerging logical framework based on existential rules, also known as Datalog+/-. This framework can also be defined in graph terms. Compared to the lighweight description logics currently developed for OBDA, it is more powerful and flexible; an important feature is that predicate arity is not restricted, which allows for a natural coupling with database schemas and facilitates the integration of additional information, such as contextual knowledge. On the other hand, the existential rule framework extends the deductive database language Datalog by enabling to infer the existence of entities that do not necessarily occur in the database (hence the name existential rules), a feature that has been recognized as crucial in the context of incomplete information. In this talk, we will provide an introduction to this framework in the context of OBDA, then present the main decidability and complexity results as well as algorithmic techniques, and discuss some challenging research issues

An Introduction to Ontology-Based Query Answering with Existential Rules

International audienceThe need for an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit ontological knowl-edge, has been acknowledged in the database, knowledge representation and Semantic Web communities. We focus here on the ontology-based data querying problem, which consists in querying data while taking on-tological knowledge into account. To tackle this problem, we consider a logical framework based on existential rules, also called Datalog ± . In this course, we introduce fundamental notions on ontology-based query answering with existential rules. We present basic reasoning techniques, explain the relationships with other formalisms such as lightweight de-scription logics, and review decidability results as well as associated al-gorithms. We end with ongoing research and some challenging issues

Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence Ontology Based Query Answering with Existential Rules

Ontology-Based Query Answering (OBQA) is currently a problem that receives a lot of attention both from knowledge representation and databases communities. The aim is to answer queries that are at least as expressive as conjunctive queries while taking an ontology into account. This is important in order to improve the quality of query answering and interoperability between different sources of data. The mainstream formalism to deal with ontologies is description logics (DLs) ([Baader et al., 2007]). While historical DLs are very expressive, most of the OBQA research focus on recently introduced lightweight DLs (EL [Baader, 2003] and DL-Lite [Calvanese et al., 2007]). Real-world ontologies expressed in these DLs already exist, such as the medical ontology SNOMED-CT (based on EL). During my Ph.D, I am considering an alternative, rulebase