Abstract not found

We describe an extension of the description logic underlying OWL-DL, SHOIN, with a number of expressive means that we believe will make it more useful in practise. Roughly speaking, we extend SHOIN with all expressive means that were suggested to us by ontology developers as useful additions to OWL-DL, and which, additionally, do not affect its decidability. We consider complex role inclusion axioms of the form R ◦ S ˙ ⊑ R or S ◦ R ˙ ⊑ R to express propagation of one property along another one, which have proven useful in medical terminologies. Furthermore, we extend SHOIN with reflexive, symmetric, transitive, and irreflexive roles, disjoint roles, a universal role, and constructs ∃R.Self, allowing, for instance, the definition of concepts such as a “narcist”. Finally, we consider negated role assertions in Aboxes and qualified number restrictions. The resulting logic is called SROIQ. We present a rather elegant tableau-based reasoning algorithm: it combines the use of automata to keep track of universal value restrictions with the techniques developed for SHOIQ. We believe that SROIQ could serve as a logical basis for possible future extensions of OWL-DL.

Abstract. This is a system description of the Description Logic reasoner FaCT++. The reasoner implements a tableaux decision procedure for the well known SHOIQ description logic, with additional support for datatypes, including strings and integers. The system employs a wide range of performance enhancing optimisations, including both standard techniques (such as absorption and model merging) and newly developed ones (such as ordering heuristics and taxonomic classification). FaCT++ can, via the standard DIG interface, be used to provide reasoning services for ontology engineering tools supporting the OWL DL ontology language. 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

In this paper, we propose a set of tasks that are relevant for the modular reuse of ontologies. In order to formalize these tasks as reasoning problems, we introduce the notions of conservative extension, safety and module for a very general class of logic-based ontology languages. We investigate the general properties of and relationships between these notions and study the relationships between the relevant reasoning problems we have previously identified. To study the computability of these problems, we consider, in particular, Description Logics (DLs), which provide the formal underpinning of the W3C Web Ontology Language (OWL), and show that all the problems we consider are undecidable or algorithmically unsolvable for the description logic underlying OWL DL. In order to achieve a practical solution, we identify conditions sufficient for an ontology to reuse a set of symbols “safely”—that is, without changing their meaning. We provide the notion of a safety class, which characterizes any sufficient condition for safety, and identify a family of safety classes–called locality—which enjoys a collection of desirable properties. We use the notion of a safety class to extract modules from ontologies, and we provide various modularization algorithms that are appropriate to the properties of the particular safety class in use. Finally, we show practical benefits of our safety checking and module extraction algorithms. 1.

Modularity is a key requirement for collaborative ontology engineering and for distributed ontology reuse on the Web. Modern ontology languages, such as OWL, are logic-based, and thus a useful notion of modularity needs to take the semantics of ontologies and their implications into account. We propose a logic-based notion of modularity that allows the modeler to specify the external signature of their ontology, whose symbols are assumed to be defined in some other ontology. We define two restrictions on the usage of the external signature, a syntactic and a slightly less restrictive, semantic one, each of which is decidable and guarantees a certain kind of “black-box ” behavior, which enables the controlled merging of ontologies. Analysis of real-world ontologies suggests that these restrictions are not too onerous. 1

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).

In the Semantic Web context information would be retrieved, processed, shared, reused and aligned in the maximum automatic way possible. Our experience with such applications in the Semantic Web has shown that these are rarely a matter of true or false but rather procedures that require degrees of relatedness, similarity, or ranking. Apart from the wealth of applications that are inherently imprecise, information itself is many times imprecise or vague. For example, the concepts of a “hot” place, an “expensive” item, a “fast” car, a “near” city, are examples of such concepts. Dealing with such type of information would yield more realistic, intelligent and effective applications. In the current paper we extend the OWL web ontology language, with fuzzy set theory, in order to be able to capture, represent and reason with such type of information.

It is widely recognized today that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are a family of knowledge representation languages that have gained considerable attention the last decade, mainly due to their decidability and the existence of empirically high performance of reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms (S), inverse roles (I), role hierarchies (H) and number restrictions (N). We illustrate why transitive role axioms are difficult to handle in the presence of fuzzy interpretations and how to handle them properly. Then we extend these results by adding role hierarchies and finally number restrictions. The main contributions of the paper are the decidability proof of the fuzzy DL languages fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base satisfiability problem of the fuzzy-SI and fuzzy-SHIN. 1.

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,