Abstract. We propose a new family of Description Logics (DLs), called DL-Lite, 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. 1.

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, it was an open problem whether conjunctive query answering over DL knowledge bases is decidable if transitive roles are admitted in the query. In this paper, we consider conjunctive queries over knowledge bases formulated in the popular DL SHIQ and allow transitive roles in both the query and the knowledge base. We show that query answering is decidable and establish the following complexity bounds: regarding combined complexity, we devise a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query. Regarding data complexity, we prove co-NP-completeness. 1

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.

The use of ontologies in various application domains, such as Data Integration, the Semantic Web, or ontology-based data management, where ontologies provide the access to large amounts of data, is posing challenging requirements w.r.t. a trade-off between expressive power of a DL and efficiency of reasoning. The logics of the DL-Lite family were specifically designed to meet such requirements and optimized w.r.t. the data complexity of answering complex types of queries. In this paper we propose DL-Litebool, an extension of DL-Lite with full Booleans and number restrictions, and study the complexity of reasoning in DL-Litebool and its significant sub-logics. We obtain our results, together with useful insights into the properties of the studied logics, by a novel reduction to the one-variable fragment of first-order logic. We study the computational complexity of satisfiability and subsumption, and the data complexity of answering positive existential queries (which extend unions of conjunctive queries). Notably, we extend the LOGSPACE upper bound for the data complexity of answering unions of conjunctive queries in DL-Lite to positive queries and to the possibility of expressing also number restrictions, and hence local functionality in the TBox.

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

Abstract. Conjunctive query answering plays a prominent role in applications of description logics (DLs) that involve instance data, but its exact complexity was a long-standing open problem. We determine the complexity of conjunctive query answering in expressive DLs between ALC and SHIQ, and thus settle the problem. In a nutshell, we show that conjunctive query answering is 2ExpTime-complete in the presence of inverse roles, and only ExpTime-complete without them. 1

Abstract. We study query answering in Description Logics (DLs). In particular, we consider conjunctive queries, unions of conjunctive queries, and their extensions with safe negation or inequality, which correspond to well-known classes of relational algebra queries. We provide a set of decidability, undecidability and complexity results for answering queries of the above languages over various classes of Description Logics knowledge bases. In general, such results show that extending standard reasoning tasks in DLs to answering relational queries is unfeasible in many DLs, even in inexpressive ones. In particular: (i) answering even simple conjunctive queries is undecidable in some very expressive DLs in which standard DL reasoning is decidable; (ii) in DLs where answering (unions of) conjunctive queries is decidable, adding the possibility of expressing safe negation or inequality leads in general to undecidability of query answering, even in DLs of very limited expressiveness. We also highlight the negative consequences of these results for the integration of ontologies and rules. We believe that these results have important implications for ontology-based information access, in particular for the design of query languages for ontologies. 1

Abstract. An important reasoning task, in addition to the standard DL reasoning services, is conjunctive query answering. In this paper, we present a decision procedure for conjunctive query entailment in the expressive Description Logic SHOQ. This is, to the best of our knowledge, the first decision procedure for conjunctive query entailment in a logic that allows for nominals. We achieve this by combining the techniques used in the conjunctive query entailment procedure for SHIQ with the techniques proposed for a restricted class of conjunctive queries in SHOQ. 1

Syndication systems on the Web have attracted vast amounts of attention in recent years. As technologies have emerged and matured, there has been a transition to more expressive syndication approaches; that is, subscribers and publishers are provided with more expressive means of describing their interests and published content, enabling more accurate information filtering. In this paper, we formalize a syndication architecture that utilizes expressive Web ontologies and logic-based reasoning for selective content dissemination. This provides finer grained control for filtering and automated reasoning for discovering implicit subscription matches, both of which are not achievable in less expressive approaches. We then address one of the main limitations with such a syndication approach, namely matching newly published information with subscription requests in an efficient and practical manner. To this end, we investigate continuous query answering for a large subset of the Web Ontology Language (OWL); specifically, we formally define continuous queries for OWL knowledge bases and present a novel algorithm for continuous query answering in a large subset of this language. Lastly, an evaluation of the query approach is shown, demonstrating its effectiveness for syndication purposes. Categories and Subject Descriptors