The logical foundations of the standard web ontology languages are provided by expressive Description Logics (DLs), such as SHIQ and SHOIQ. In the Semantic Web and other domains, ontologies are increasingly seen also as a mechanism to access and query data repositories. This novel context poses an original combination of challenges that has not been addressed before: (i) sufficient expressive power of the DL to capture common data modelling constructs; (ii) well established and flexible query mechanisms such as those inspired by database technology; (iii) optimisation of inference techniques with respect to data size, which typically dominates the size of ontologies. This calls for investigating data complexity of query answering in expressive DLs. While the complexity of DLs has been studied extensively, few tight characterisations of data complexity were available, and the problem was still open for most DLs of the SH family and for standard query languages like conjunctive queries and their extensions. We tackle this issue and prove a tight coNP upper bound for positive existential queries without transitive roles in SHOQ, SHIQ,andSHOI. We thus establish that, for a whole range of sublogics of SHOIQ that contain AL, answering such queries has coNP-complete

We study the notion of update of an ontology expressed as a Description Logic knowledge base. Such a knowledge base is constituted by two components, called TBox and ABox. The former expresses general knowledge about the concepts and their relationships, whereas the latter describes the state of affairs regarding the instances of concepts. We investigate the case where the update affects only the instance level of the ontology, i.e., the ABox. Building on classical approaches on knowledge base update, our first contribution is to provide a general semantics for instance level update in Description Logics. We then focus on DL-Lite, a specific Description Logic where the basic reasoning tasks are computationally tractable. We show that DL-Lite is closed with respect to instance level update, in the sense that the result of an update is always expressible as a new DL-Lite ABox. Finally we provide an algorithm that computes the result of an update in DL-Lite, and we show that it runs in polynomial time with respect to the size of both the original knowledge base and the update formula.

Expressive Description Logics (DLs) have been advocated as formalisms for modeling the domain of interest in various application areas. An important requirement is the ability to answer complex queries beyond instance retrieval, taking into account constraints expressed in a knowledge base. We consider this task for positive existential path queries (which generalize conjunctive queries and unions thereof), whose atoms are regular expressions over the roles (and concepts) of a knowledge base in the expressive DL ALCQIbreg. Using techniques based on two-way tree-automata, we first provide an elegant characterization of TBox and ABox reasoning, which gives us also a tight EXPTIME bound. We then prove decidability (more precisely, a 2EXPTIME upper bound) of query answering, thus significantly pushing the decidability frontier, both with respect to the query language and the considered DL. We also show that query answering is EXP-SPACE-hard already in rather restricted settings.

Although description logic systems can adequately be used for representing and reasoning about incomplete information (e.g., for John we know he is French or Italian), in practical applications it can be assumed that (only) for some tasks the expressivity of description logics really comes into play whereas for building complete applications, it is often necessary to effectively solve instance retrieval problems with respect to largely deterministic knowledge. In this paper we present and analyze the main results we have found about how to contribute to this kind of scalability problem. We assume familiarity with description logics in general and tableau provers in particular.

Querying Description Logic knowledge bases has received great attention in the last years. In such a problem, the need of coping with incomplete information is the distinguishing feature with respect to querying databases. Due to this feature, we have to deal with two conflicting needs: on the one hand, we would like to query the knowledge base with sophisticated mechanisms provided by full first-order logic (FOL); on the other hand, the presence of incomplete information makes query answering a much more difficult task than in databases. In this paper we advocate the use of a nonmonotonic epistemic FOL query language as a means for expressing sophisticated queries over Description Logic knowledge bases. We show that through a controlled use of the epistemic operator, resulting in the language called EQL-Lite, we are able to formulate full FOL queries over Description Logic knowledge bases, while keeping computational complexity of query answering under control. In particular, we show that EQL-Lite queries over DL-Lite knowledge bases are FOL reducible (i.e., compilable into SQL) and hence can be answered in LOGSPACE through standard database technologies. 1

We develop a formal framework for comparing different versions of DL-Lite ontologies. Four notions of difference and entailment between ontologies are introduced and their applications in ontology development and maintenance discussed. These notions are obtained by distinguishing between differences that can be observed among concept inclusions, answers to queries over ABoxes, and by taking into account additional context ontologies. We compare these notions, study their meta-properties, and determine the computational complexity of the corresponding reasoning tasks. Moreover, we show that checking difference and entailment can be automated by means of encoding into QBF satisfiability and using off-the-shelf QBF solvers. Finally, we explore the relationship between the notion of forgetting (or uniform interpolation) and our notions of difference between ontologies.

Conjunctive queries (CQ) are fundamental for accessing description logic (DL) knowledge bases. We study CQ answering in (extensions of) the DL EL, which is popular for large-scale ontologies and underlies the designated OWL2-EL profile of OWL2. Our main contribution is a novel approach to CQ answering that enables the use of standard relational database systems as the basis for query execution. We evaluate our approach using the IBM DB2 system, with encouraging results. 1

The novel context of accessing and querying large data repositories through ontologies that are formalized in terms of expressive DLs requires on the one hand to consider query answering as the primary inference technique, and on the other hand to optimize it with respect to the size of the data, which dominates the size of ontologies. While the complexity of DLs has been studied extensively, data complexity in expressive DLs has been characterized only for answering atomic queries, and was still open for more expressive query languages, such as unions of conjunctive queries (UCQs). In this paper we advocate the need for studying this problem, and provide a significant technical contribution in this direction. Specifically, we prove a tight coNP upper bound for answering UCQs over SHIQ knowledge bases, for the case where the queries do not contain transitive roles. We thus establish that for a whole range of DLs from AL to SHIQ, answering such UCQs has coNP-complete data complexity. We obtain our result by a novel tableaux-based algorithm for checking query entailment, inspired by the one in [20], but which manages the technical challenges of simultaneous inverse roles and number restrictions (which leads to a DL lacking the finite model property). 1

Abstract. One of the most interesting usages of shared conceptualizations is ontology-based data access. That is, to the usual data layer of an information system we superimpose a conceptual layer to be exported to the client. Such a layer allows the client to have a conceptual view of the information in the system, which abstracts away from how such information is maintained in the data layer of the system itself. While ontologies are the best candidates for realizing the conceptual layer, relational DBMSs are natural candidates for the management of the data layer. The need of efficiently processing large amounts of data requires ontologies to be expressed in a suitable fragment of OWL: the fragment should allow, on the one hand, for modeling the kind of intensional knowledge needed in real-world applications, and, on the other hand, for delegating to a relational DBMS the part of reasoning (in particular query answering) that deals with the data. In this paper, we propose one such a fragment, in fact the largest In several areas (e.g., Enterprise Application Integration, Data Integration [10], and the

Abstract. Despite the success of the Web Ontology Language OWL, the development of expressive means for querying OWL knowledge bases is still an open issue. In this paper, we investigate how a very natural and desirable form of queries—namely conjunctive ones—can be used in conjunction with OWL such that one of the major design criteria of the latter—namely decidability—can be retained. More precisely, we show that querying the tractable fragmentEL ++ of OWL 1.1 is decidable. We also provide a complexity analysis and show that querying unrestrictedEL ++ is undecidable. 1