The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and the ability to represent conceptual modeling formalisms, on the other. The main aim of this article is to carry out a thorough and systematic investigation of inference in extensions of the original DL-Lite logics along five axes: by (i) adding the Boolean connectives and (ii) number restrictions to concept constructs, (iii) allowing role hierarchies, (iv) allowing role disjointness, symmetry, asymmetry, reflexivity, irreflexivity and transitivity constraints, and (v) adopting or dropping the unique same assumption. We analyze the combined complexity of satisfiability for the resulting logics, as well as the data complexity of instance checking and answering positive existential queries. Our approach is based on embedding DL-Lite logics in suitable fragments of the one-variable first-order logic, which provides useful insights into their properties and, in particular, computational behavior

Abstract. We present Ontop, an open-source Ontology-Based Data Access (OBDA) system that allows for querying relational data sources through a conceptual representation of the domain of interest, provided in terms of an ontology, to which the data sources are mapped. Key features of Ontop are its solid theoretical foundations, a virtual approach to OBDA, which avoids materializing triples and is implemented through the query rewriting technique, extensive optimizations exploiting all elements of the OBDA architecture, its compliance to all relevant W3C recommendations (including SPARQL queries, R2RML mappings, and OWL 2 QL and RDFS ontologies), and its support for all major relational databases.

Abstract. We present the architecture and technologies underpinning the OBDA system Ontop and taking full advantage of storing data in relational databases. We discuss the theoretical foundations of Ontop: the tree-witness query rewriting, T -mappings and optimisations based on database integrity constraints and SQL features. We analyse the performance of Ontop in a series of experiments and demonstrate that, for standard ontologies, queries and data stored in relational databases, Ontop is fast, efficient and produces SQL rewritings of high quality.

We present the framework of ontology-based data access, a semantic paradigm for providing a convenient and user-friendly access to data repositories, which has been actively developed and studied in the past decade. Focusing on relational data sources, we discuss the main ingredients of ontology-based data access, key theoretical results, techniques, applications and future challenges.

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Abstract. We investigate the computational complexity of reasoning over various fragments of the Extended Entity-Relationship (EER) language, which includes a number of constructs: ISA between entities and relationships, disjointness and covering of entities and relationships, cardinality constraints for entities in relationships and their refinements as well as multiplicity constraints for attributes. We extend the known EXPTIME-completeness result for UML class diagrams [5] and show that reasoning over EER diagrams with ISA between relationships is EXPTIME-complete even without relationship covering. Surprisingly, reasoning becomes NP-complete when we drop ISA between relationships (while still allowing all types of constraints on entities). If we further omit disjointness and covering over entities, reasoning becomes polynomial. Our lower complexity bound results are proved by direct reductions, while the upper bounds follow from the correspondences with expressive variants of the description logic DL-Lite, which we establish in this paper. These correspondences also show the usefulness of DL-Lite as a language for reasoning over conceptual models and ontologies.

In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PT L, the spatial logics RCC-8, BRCC-8, S4 u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness and 'computational realisability' within the hierarchy. We demonstrate how different combining principles as well as spatial and temporal primitives can produce NP-, PSPACE-, EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out of components that are at most NP-or PSPACE-complete.

We design temporal description logics suitable for reasoning about temporal conceptual data models and investigate their computational complexity. Our formalisms are based on DL-Lite logics with three types of concept inclusions (ranging from atomic concept inclusions and disjointness to the full Booleans), as well as cardinality constraints and role inclusions. The logics are interpreted over the Cartesian products of object domains and the flow of time (Z, <), satisfying the constant domain assumption. Concept and role inclusions of the TBox hold at all moments of time (globally) and data assertions of the ABox hold at specified moments of time. To express temporal constraints of conceptual data models, the languages are equipped with flexible and rigid roles, standard future and past temporal operators on concepts and operators 'always' and 'sometime' on roles. The most expressive of our temporal description logics (which can capture lifespan cardinalities and either qualitative or quantitative evolution constraints) turns out to be undecidable. However, by omitting some of the temporal operators on concepts/roles or by restricting the form of concept inclusions we construct logics whose complexity ranges between NLOGSPACE and PSPACE. These positive results are obtained by reduction to various clausal fragments of propositional temporal logic, which opens a way to employ propositional or first-order temporal provers for reasoning about temporal data models.