Abstract not found

Ontologies are set to play a key role in the "Semantic Web" by providing a source of shared and precisely defined terms that can be used in descriptions of web resources. Reasoning over such descriptions will be essential if web resources are to be more accessible to automated processes. SHOQ(D) is an expressive description logic equipped with named individuals and concrete datatypes which has almost exactly the same expressive power as the latest web ontology languages (e.g., OIL and DAML). We present sound and complete reasoning services for this logic. 1

The vision of a Semantic Web has recently drawn considerable attention, both from academia and industry. Description logics are often named as one of the tools that can support the Semantic Web and thus help to make this vision reality.

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UML is the de-facto standard formalism for software design and analysis. To support the design of large-scale industrial applications, sophisticated CASE tools are available on the market, that provide a user-friendly environment for editing, storing, and accessing multiple UML diagrams. It would be highly desirable to equip such CASE tools with automated reasoning capabilities in order to detect relevant formal properties of UML diagrams, such as inconsistencies or redundancies. With regard to this issue, we consider UML class diagrams, which are one of the most important components of UML, and we address the problem of reasoning on such diagrams. We resort to several results developed in the eld of Description Logics (DLs), a family of logics that admit decidable reasoning procedures.

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Description Logics (DLs) are the formal foundations of the standard web ontology languages OWL-DL and OWL-Lite. 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 modeling constructs; (ii) well established and flexible query mechanisms such as Conjunctive Queries (CQs); (iii) optimization 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, data complexity has been characterized only for answering atomic queries, and was still open for answering CQs in expressive DLs. We tackle this issue and prove a tight CONP upper bound for the problem in SHIQ, as long as no transitive roles occur in the query. We thus establish that for a whole range of DLs from AL to SHIQ, answering CQs with no transitive roles has CONP-complete data complexity. We obtain our result by a novel tableaux-based algorithm for checking query entailment, inspired by the one in [19], but which manages the technical challenges of simultaneous inverse roles and number restrictions (which leads to a DL lacking the finite model property).

With the advent of Semantic Web languages such as OWL (Web Ontology Language), the expressive Description Logic SHOIN is exposed to a wider audience of ontology users and developers. As an increasingly large number of OWL ontologies become available on the Semantic Web and the descriptions in the ontologies become more complicated, finding the cause of errors becomes an extremely hard task even for experts. The problem is worse for newcomers to OWL who have little or no experience with DL-based knowledge representation. Existing ontology development environments, in conjunction with a reasoner, provide some limited debugging support, however this is restricted to merely reporting errors in the ontology, whereas bug diagnosis and resolution is usually left to the user. In this thesis, I present a complete end-to-end framework for explaining, pinpointing and repairing semantic defects in OWL-DL ontologies (or in other words, a SHOIN knowledge base). Semantic defects are logical contradictions that manifest as either inconsistent ontologies or unsatisfiable concepts. Where possible, I show extensions to handle related defects such as unsatisfiable roles, unintended entailments and nonentailments,

Abstract. It is generally acknowledged that any Knowledge Base (KB) should be able to adapt itself to new information received. This problem has been extensively studied in the field of belief change, the dominating approach being the AGM theory. This theory set the standard for determining the rationality of a given belief change mechanism but was placed in a certain context which makes it inapplicable to logics used in the Semantic Web, such as Description Logics (DLs) and OWL. We believe the Semantic Web community would benefit from the application of the AGM theory to such logics. This paper is a preliminary study towards the feasibility of this application. Our approach raises interesting theoretical challenges and has an important practical impact too, given the central role that DLs and OWL play in the Semantic Web. 1

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