Elena Botoeva

Expressive approximations in DL-lite ontologies

Ontology based data access (OBDA) is concerned with providing access to typically very large data sources through a mediating conceptual layer that allows one to improve answers to user queries by taking into account domain knowledge. In the context of OBDA applications, an important issue is that of reusing existing domain ontologies. However, such ontologies are often formulated in expressive languages, which are incompatible with the requirements of efficiently accessing large amounts of data. Approximation of such ontologies by means of less expressive ones has been proposed as a possible solution to this problem. In this work we present our approach to semantic (as opposed to syntactic) approximation of OWL 2 TBoxes by means of TBoxes in DL-LiteA. The point of interest in DL-LiteA approximations is capturing entailments involving chains of existential role restrictions, which can play an essential role in query answering. The presence of TBox assertions involving existential chains affects query answering by enriching the number of obtained rewritings, and hence allows us to cope better with incomplete information about object and data properties. We provide an approximation algorithm and show its soundness and completeness. We also discuss the implementation of the algorithm.

Knowledge base exchange

In this article, we define and study the problem of exchanging knowledge between a source and a target knowledge base (KB), connected through mappings. Differently from the traditional database exchange setting, which considers only the exchange of data, we are interested in exchanging implicit knowledge. As representation formalism we use Description Logics (DLs), thus assuming that the source and target KBs are given as a DL TBox+ABox, while the mappings have the form of DL TBox assertions. We define a general framework of KB exchange, and study the problem of translating the knowledge in the source KB according to the mappings expressed in OWLź2źQL, the profile of the standard Web Ontology Language OWL 2 based on the description logic DL-Lite R . We develop novel game- and automata-theoretic techniques, and we provide complexity results that range from NLogSpace to ExpTime.

Inseparability and conservative extensions of description logic ontologies: A survey

The question whether an ontology can safely be replaced by another, possibly simpler, one is fundamental for many ontology engineering and maintenance tasks. It underpins, for example, ontology versioning, ontology modularization, forgetting, and knowledge exchange. What ‘safe replacement’ means depends on the intended application of the ontology. If, for example, it is used to query data, then the answers to any relevant ontology-mediated query should be the same over any relevant data set; if, in contrast, the ontology is used for conceptual reasoning, then the entailed subsumptions between concept expressions should coincide. This gives rise to different notions of ontology inseparability such as query inseparability and concept inseparability, which generalize corresponding notions of conservative extensions. In this chapter, we survey results on various notions of inseparability in the context of description logic ontologies, discussing their applications, useful model-theoretic characterizations, algorithms for determining whether two ontologies are inseparable (and, sometimes, for computing the difference between them if they are not), and the computational complexity of this problem.

Games for query inseparability of description logic knowledge bases

We consider conjunctive query inseparability of description logic knowledge bases with respect to a given signature-a fundamental problem in knowledge base versioning, module extraction, forgetting and knowledge exchange. We give a uniform game-theoretic characterisation of knowledge base conjunctive query inseparability and develop worst-case optimal decision algorithms for fragments of Horn- ALCHI , including the description logics underpinning OWL?2?QL and OWL?2?EL. We also determine the data and combined complexity of deciding query inseparability. While query inseparability for all of these logics is P-complete for data complexity, the combined complexity ranges from P- to ExpTime- to 2ExpTime-completeness. We use these results to resolve two major open problems for OWL?2?QL by showing that TBox query inseparability and the membership problem for universal conjunctive query solutions in knowledge exchange are both ExpTime-complete for combined complexity. Finally, we introduce a more flexible notion of inseparability which compares answers to conjunctive queries in a given signature over a given set of individuals. In this case, checking query inseparability becomes NP-complete for data complexity, but the ExpTime- and 2ExpTime-completeness combined complexity results are preserved.

Description logic knowledge base exchange

Data exchange is a field of database theory that deals with transferring data between differently structured databases, with motivation coming from industry [21,17]. The starting point of intensive investigation of the problem of data exchange was given in [14] where it was defined as, given data structured under a source schema and a mapping specifying how it should be translated to a target schema, to transform the source data into data structured under the target schema such that it accurately reflects the source data w.r.t. the mapping. This problem has been studied for different combinations of languages used to specify the source and target schema, and the mappings [8]. Most of the results in the literature consider tuple generating dependencies (tgds) as the language to specify mappings. Tgds allow one to express containment of conjunctive queries, and have been widely employed in other areas of database theory. Furthermore, once a target instance is materialized, one mightwant to perform query answering over it.

Efficient Handling of SPARQL OPTIONAL for OBDA

OPTIONAL is a key feature in SPARQL for dealing with missing information. While this operator is used extensively, it is also known for its complexity, which can make efficient evaluation of queries with OPTIONAL challenging. We tackle this problem in the Ontology-Based Data Access (OBDA) setting, where the data is stored in a SQL relational database and exposed as a virtual RDF graph by means of an R2RML mapping. We start with a succinct translation of a SPARQL fragment into SQL. It fully respects bag semantics and three-valued logic and relies on the extensive use of the LEFT JOIN operator and COALESCE function. We then propose optimisation techniques for reducing the size and improving the structure of generated SQL queries. Our optimisations capture interactions between JOIN, LEFT JOIN, COALESCE and integrity constraints such as attribute nullability, uniqueness and foreign key constraints. Finally, we empirically verify effectiveness of our techniques on the BSBM OBDA benchmark.

Expressivity and Complexity of MongoDB Queries

In this paper, we consider MongoDB, a widely adopted but not formally understood database system managing JSON documents and equipped with a powerful query mechanism, called the aggregation framework. We provide a clean formal abstraction of this query language, which we call MQuery. We study the expressivity of MQuery, showing the equivalence of its well-typed fragment with nested relational algebra. We further investigate the computational complexity of significant fragments of it, obtaining several (tight) bounds in combined complexity, which range from LogSpace to alternating exponential-time with a polynomial number of alternations.