Abstract. We propose a new family of Description Logics (DLs), called DLLite, specifically tailored to capture basic ontology languages, while keeping low complexity of reasoning. Reasoning here means not only computing subsumption between concepts, and checking satisfiability of the whole knowledge base, but also answering complex queries (in particular, unions of conjunctive queries) over the instance level (ABox) of the DL knowledge base. We show that, for the DLs of the DL-Lite family, the usual DL reasoning tasks are polynomial in the size of the TBox, and query answering is LogSpace in the size of the ABox (i.e., in data complexity). To the best of our knowledge, this is the first result of polynomial time data complexity for query answering over DL knowledge bases. Notably our logics allow for a separation between TBox and ABox reasoning during query evaluation: the part of the process requiring TBox reasoning is independent of the ABox, and the part of the process requiring access to the ABox can be carried out by an SQL engine, thus taking advantage of the query optimization strategies provided by current Data Base Management Systems. Since it can be shown that even slight extensions to the logics of the DL-Lite family make query answering at least NLogSpace in data complexity, thus ruling out the possibility of using on-the-shelf relational technology for query processing, we can conclude that the logics of the DL-Lite family are the maximal DLs supporting efficient query answering over large amounts of instances.

Abstract. Many organizations nowadays face the problem of accessing existing data sources by means of flexible mechanisms that are both powerful and efficient. Ontologies are widely considered as a suitable formal tool for sophisticated data access. The ontology expresses the domain of interest of the information system at a high level of abstraction, and the relationship between data at the sources and instances of concepts and roles in the ontology is expressed by means of mappings. In this paper we present a solution to the problem of designing effective systems for ontology-based data access. Our solution is based on three main ingredients. First, we present a new ontology language, based on Description Logics, that is particularly suited to reason with large amounts of instances. The second ingredient is a novel mapping language that is able to deal with the so-called impedance mismatch problem, i.e., the problem arising from the difference between the basic elements managed by the sources, namely data, and the elements managed by the ontology, namely objects. The third ingredient is the query answering method, that combines reasoning at the level of the ontology with specific mechanisms for both taking into account the mappings and efficiently accessing the data at the sources.

In databases with integrity constraints, data may not satisfy the constraints. In this paper, we address the problem of obtaining consistent answers in such a setting, when key and inclusion dependencies are expressed on the database schema. We establish decidability and complexity results for query answering under different assumptions on data (soundness and/or completeness). In particular, after showing that the problem is in general undecidable, we identify the maximal class of inclusion dependencies under which query answering is decidable in the presence of key dependencies. Although obtained in a single database context, such results are directly applicable to data integration, where multiple information sources may provide data that are inconsistent with respect to the global view of the sources.

Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and rules. Developing a formalism that integrates DLs and rules would be a natural outcome of a large body of research in knowledge representation and reasoning of the last two decades; however, achieving this goal is very challenging and the approaches proposed thus far have not fully reached it. In this paper, we present a hybrid formalism of MKNF + knowledge bases, which integrates DLs and rules in a coherent semantic framework. Achieving seamless integration is nontrivial, since DLs use an open-world assumption, while the rules are based on a closed-world assumption. We overcome this discrepancy by basing the semantics of our formalism on the logic of minimal knowledge and negation as failure (MKNF) by Lifschitz. We present several algorithms for reasoning with MKNF + knowledge bases, each suitable to different kinds of rules, and establish tight complexity bounds.

No abstract

In this paper we study data complexity of answering conjunctive queries over description logic (DL) knowledge bases constituted by a TBox and an ABox. In particular, we are interested in characterizing the FOL-rewritability and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the DL used to express the knowledge base. FOL-rewritability means that query answering can be reduced to evaluating queries over the database corresponding to the ABox. Since first-order queries can be expressed in SQL, the importance of FOL-rewritability is that, when query answering enjoys this property, we can take advantage of Relational Data Base Management System (RDBMS) techniques for both representing data, i.e., ABox assertions, and answering queries via reformulation into SQL. What emerges from our complexity analysis is that the description logics of the DL-Lite family are essentially the maximal logics allowing for conjunctive query answering through standard database technology. In this sense, they are the first description logics specifically tailored for effective query answering over very large ABoxes. (C) 2012 Elsevier B.V. All rights reserved

We present description logics of minimal knowledge and negation as failure (MKNF-DLs), which augment description logics with modal operators interpreted according to Lifschitz's nonmonotonic logic MKNF. We show the usefulness of MKNF-DLs for a formal characterization of a wide variety of nonmonotonic features that are both commonly available inframe-based systems, and needed in the development of practical knowledge-based applications: defaults, integrity constraints, role, and concept closure. In addition, we provide a correct and terminating calculus for query answering in a very expressive MKNF-DL.

Abstract. Ontologies provide a conceptualization of a domain of interest. Nowadays, they are typically represented in terms of Description Logics (DLs), and are seen as the key technology used to describe the semantics of information at various sites. The idea of using ontologies as a conceptual view over data repositories is becoming more and more popular, but for it to become widespread in standard applications, it is fundamental that the conceptual layer through which the underlying data layer is accessed does not introduce a significant overhead in dealing with the data. Based on these observations, in recent years a family of DLs, called DL-Lite, has been proposed, which is specifically tailored to capture basic ontology and conceptual data modeling languages, while keeping low complexity of reasoning and of answering complex queries, in particular when the complexity is measured w.r.t. the size of the data. In this article, we present a detailed account of the major results that have been achieved for the DL-Lite family. Specifically, we concentrate on DL-LiteA,id, an expressive member of this family, present algorithms for reasoning and query answering over DL-LiteA,id ontologies, and analyze their computational complexity. Such algorithms exploit the distinguishing feature of the logics in the DL-Lite family, namely that ontology reasoning and answering unions of conjunctive queries is first-order rewritable, i.e., it can be delegated to a relational database management system. We analyze also the effect of extending the logic with typical DL constructs, and show that for most such extensions, the nice computational properties of the DL-Lite family are lost. We address then the problem of accessing relational data sources through an ontology, and present a solution to the notorious impedance mismatch between the abstract objects in the ontology and the values appearing in data sources. The solution exploits suitable mappings that create the objects in the ontology from the appropriate values extracted from the data sources. Finally, we discuss the QUONTO system that implements all the above mentioned solutions and is wrapped by the DIG-QUONTO server, thus providing a standard DL reasoner for DL-LiteA,id with extended functionality to access external data sources.