Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the resulting set of facts. The chase, however, does not terminate necessarily, and checking whether the chase terminates on a given set of rules and facts is undecidable. Numerous acyclicity notions were proposed as sufficient conditions for chase termination. In this paper, we present two new acyclicity notions called model-faithful acyclicity (MFA) and model-summarising acyclicity (MSA). Furthermore, we investigate the landscape of the known acyclicity notions and establish a complete taxonomy of all notions known to us. Finally, we show that MFA and MSA generalise most of these notions. Existential rules are closely related to the Horn fragments of the OWL 2 ontology language; furthermore, several prominent OWL 2 reasoners implement CQ answering by using the chase to materialise all relevant facts. In order to avoid termination problems, many of these systems handle only the OWL 2 RL profile of OWL 2; furthermore, some systems go beyond OWL 2 RL, but without any termination guarantees. In this paper we also investigate whether various acyclicity notions can provide a principled and practical solution to these problems. On the theoretical side, we show that query answering for acyclic ontologies is of lower complexity than for general ontologies. On the practical side, we show that many of the commonly used OWL 2 ontologies are MSA, and that the number of facts obtained by materialisation is not too large. Our results thus suggest that principled development of materialisation-based OWL 2 reasoners is practically feasible.

This is a Ph.D summary focusing on ontology based query answering with existential rules.

Recently, large amounts of data are being published using Semantic Web standards. Simultaneously, there has been a steady rise in links between objects from multiple sources. However, the ontologies behind these sources have remained largely disconnected, thereby challenging the interoperability goal of the Semantic Web. We address this problem by automatically finding alignments between concepts from multiple linked data sources. Instead of only considering the existing concepts in each ontology, we hypothesize new composite concepts, defined using conjunctions and disjunctions of (RDF) types and value restrictions, and generate alignments between them. In addition, our techniques provide a novel method for curating the linked data web by pointing to likely incorrect or missing assertions. Our approach provides a deeper understanding of the relationships between linked data sources and increases the interoperability among previously disconnected ontologies.

The Distributed Ontology Language DOL, currently being standardized as ISO WD 17347 within the OntoIOp (Ontology Integration and Interoperability) activity of ISO/TC 37, provides a unified framework for (1) ontologies formalized in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) ontology annotation. A DOL ontology consists of modules formalized in languages such as OWL or Common Logic, serialized in the existing syntaxes of these languages. On top, DOL’s meta level allows for expressing heterogeneous ontologies and links between ontologies, including (heterogeneous) imports and alignments, conservative extensions, and theory interpretations. We present the abstract syntax of these meta-level constructs, with three alternative semantics: direct, translational, and collapsed semantics.

We address the issue of Ontology-Based Data Access which consists of exploiting the semantics expressed in ontologies while querying data. Ontologies are represented in the framework of existential rules, also known as Datalog+/-. We focus on the backward chaining paradigm, which involves rewriting the query (assumed to be a conjunctive query, CQ) into a set of CQs (seen as a union of CQs). The proposed algorithm accepts any set of existential rules as input and stops for so-called finite unification sets of rules (fus). The rewriting step relies on a graph notion, called a piece, which allows to identify subsets of atoms from the query that must be processed together. We first show that our rewriting method computes a minimal set of CQs when this set is finite, i.e., the set of rules is a fus. We then focus on optimizing the rewriting step. First experiments are reported in the associated technical report.

Recently, ontology stream reasoning has been introduced as a multidisciplinary approach, merging synergies from Artificial Intelligence, Database, World-Wide-Web to reason on semantic augmented data streams. Although knowledge evolution and real-time reasoning have been largely addressed in ontology streams, the challenge of predicting its future (or missing) knowledge remains open and yet unexplored. We tackle predictive reasoning as a correlation and interpretation of past semantics-augmented data over exogenous ontology streams. Consistent predictions are constructed as Description Logics entailments by selecting and applying relevant cross-streams association rules. The experiments have shown accurate prediction with real and live stream data from Dublin City in Ireland.

When answering queries in the presence of ontologies, adopting the closed world assumption for some predicates easily results in intractability. We analyze this situation on the level of individual ontologies formulated in the description logics DL-Lite and EL and show that in all cases where answering CQs with (open and) closed predicates is tractable, it coincides with answering CQs with all predicates assumed open. In this sense, CQ answering with closed predicates in inherently intractable. Our analysis also yields a dichotomy between AC0 and coNP for CQ answering in DL-Lite and a dichotomy between PTime and coNP for EL. Interestingly, the situation is less dramatic in the more expressive description logic ELI, where we find ontologies for which CQ answering is in PTime, but does not coincide with CQ answering where all predicates are open.

The study of preferences has a long tradition in many disciplines, but it has only relatively recently entered the realm of data management through their application in answering queries to relational databases. The current revolution in data availability through the Web and, perhaps most importantly in the last few years, social media sites and applications, puts ontology languages at the forefront of data and information management technologies. In this paper, we propose the first (to our knowledge) integration of ontology languages with preferences as in relational databases by developing PrefDatalog+/-, an extension of the Datalog+/- family of languages with preference management formalisms closely related to those previously studied for relational databases. We focus on two kinds of answers to queries that are relevant to this setting, skyline and k-rank (a generalization of top-k queries), and develop algorithms for computing these answers to both DAQs (disjunctions of atomic queries) and CQs (conjunctive queries). We show that DAQ answering in PrefDatalog+/- can be done in polynomial time in the data complexity, as in relational databases, as long as query answering can also be done in polynomial time (in the data complexity) in the underlying classical ontology.

Rewriting-based approaches for answering queries over an OWL 2 DL ontology have so far been developed mainly for Horn fragments of OWL 2 DL. In this paper, we study the possibilities of answering queries over non-Horn ontologies using datalog rewritings. We prove that this is impossible in general even for very simple ontology languages, and even if PTIME = NP. Furthermore, we present a resolution-based procedure for SHI ontologies that, in case it terminates, produces a datalog rewriting of the ontology. We also show that our procedure necessarily terminates on DL-Lite Bool H,+ ontologies — an extension of OWL 2 QL with transitive roles and Boolean connectives.

A robust system for ontology-based data access should provide meaningful answers to queries even when the data conflicts with the ontology. This can be accomplished by adopting an inconsistency-tolerant semantics, with the consistent query answering (CQA) semantics being the most prominent example. Unfortunately, query answering under the CQA semantics has been shown to be computationally intractable, even when extremely simple ontology languages are considered. In this paper, we address this problem by proposing two new families of inconsistency-tolerant semantics which approximate the CQA semantics from above and from below and converge to it in the limit. We study the data complexity of conjunctive query answering under these new semantics, and show a general tractability result for all known first-order rewritable ontology languages. We also analyze the combined complexity of query answering for ontology languages of the DL-Lite family.