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Both OWL-DL and function-free Horn rules are decidable fragments of first-order logic with interesting, yet orthogonal expressive power. A combination of OWL-DL and rules is desirable for the Semantic Web; however, it might easily lead to the undecidability of interesting reasoning problems. Here, we present a decidable such combination where rules are required to be DL-safe: each variable in the rule is required to occur in a non-DL-atom in the rule body. We discuss the expressive power of such a combination and present an algorithm for query answering in the related logic SHIQ extended with DL-safe rules, based on a reduction to disjunctive programs.

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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We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C 2 , the two variable fragment of predicate logic with counting quantiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI , as ALCQI with cardinality restrictions has the same complexity as C 2 (NExpTime-complete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals . Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTime-complete problem. Finally, we sharpen this result and show that pure concept satisability for A...

In the current "Syntactic Web", uninterpreted syntactic constructs are given meaning only by private off-line agreements that are inaccessible to computers. In the Semantic Web vision, this is replaced by a web where both data and its semantic definition are accessible and manipulable by computer software. DAML+OIL is an ontology language specifically designed for this use in the Web; it exploits existing Web standards (XML and RDF), adding the familiar ontological primitives of object oriented and frame based systems, and the formal rigor of a very expressive description logic. The definition of DAML+OIL is now over a year old, and the language has been in fairly widespread use. In this paper, we review DAML+OIL's relation with its key ingredients (XML, RDF, OIL, DAML-ONT, Description Logics), we discuss the design decisions and trade-offs that were the basis for the language definition, and identify a number of implementation challenges posed by the current language. These issues are important for designers of other representation languages for the Semantic Web, be they competitors or successors of DAML+OIL, such as the language currently under definition by W3C.

Although the OWL Web Ontology Language adds considerable expressive power to the Semantic Web it does have expressive limitations, particularly with respect to what can be said about properties. We present SWRL (the Semantic Web Rules Language), a Horn clause rules extension to OWL that overcomes many of these limitations. SWRL extends OWL in a syntactically and semantically coherent manner: the basic syntax for SWRL rules is an extension of the abstract syntax for OWL DL and OWL Lite; SWRL rules are given formal meaning via an extension of the OWL DL model-theoretic semantics; SWRL rules are given an XML syntax based on the OWL XML presentation syntax; and a mapping from SWRL rules to RDF graphs is given based on the OWL RDF/XML exchange syntax. We discuss the expressive power of SWRL, showing that the ontology consistency problem is undecidable, provide several examples of SWRL usage, and discuss a prototype implementation of reasoning support for SWRL. 1

Description logic (DL) ABoxes are a tool for describing the state of affairs in an application domain. In this paper, we consider the problem of updating ABoxes when the state changes. We assume that changes are described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs by investigating whether the updated ABox can be expressed in these DLs and, if so, whether it is computable and what is its size. It turns out that DLs have to include nominals and the “@” constructor of hybrid logic (or, equivalently, admit Boolean ABoxes) for updated ABoxes to be expressible. We devise algorithms to compute updated ABoxes in several expressive DLs and show that an exponential blowup in the size of the whole input (original ABox + update information) cannot be avoided unless every PTIME problem is LOGTIMEparallelizable. We also exhibit ways to avoid an exponential blowup in the size of the original ABox, which is usually large compared to the update information.

We consider the restriction of the guarded fragment to the two-variable case where, in addition, binary relations may be specified as transitive. We show that (i) this very restricted form of the guarded fragment without equality is undecidable and that (ii) when allowing non-unary relations to occur only in guards, the logic becomes decidable. The latter subclass of the guarded fragment is the one that occurs naturally when translating multi-modal logics of the type K4, S4 or S5 into rst-order logic. We also show that the loosely guarded fragment without equality and with a single transitive relation is undecidable.

Number restrictions are concept constructors that are available in almost all implemented Description Logic systems. However, they are mostly available only in a rather weak form, which considerably restricts their expressive power. On the one hand, the roles that may occur in number restrictions are usually of a very restricted type, namely atomic roles or complex roles built using either intersection or inversion. In the present paper, we increase the expressive power of Description Logics by allowing for more complex roles in number restrictions. As role constructors, we consider composition of roles (which will be present in all our logics) and intersection, union, and inversion of roles in different combinations. We will present two decidability results (for the basic logic that extends ALC by number restrictions on roles with composition, and for one extension of this logic), and three undecidability results for three other extensions of the basic logic. On the other hand, with t...