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 integration of Description Logics and Datalog rules presents many semantic and computational problems. In particular, reasoning in a system fully integrating Description Logics knowledge bases (DL-KBs) and Datalog programs is undecidable. Many proposals have overcomed this problem through a “safeness ” condition that limits the interaction between the DL-KB and the Datalog rules. Such a safe integration of Description Logics and Datalog provides for systems with decidable reasoning, at the price of a strong limitation in terms of expressive power. In this paper we define DL+log, a general framework for the integration of Description Logics and disjunctive Datalog. From the knowledge representation viewpoint, DL+log extends previous proposals, since it allows for a tighter form of integration between DL-KBs and Datalog rules which overcomes the main representational limits of the approaches based on the safeness condition. From the reasoning viewpoint, we present algorithms for reasoning in DL+log, and prove decidability and complexity of reasoning in DL+log for several Description Logics. To the best of our knowledge, DL+log constitutes the most powerful decidable combination of Description Logics and disjunctive Datalog rules proposed so far.

The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms, into a framework that is more useful for describing semantic content. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Non-monotonic description logic programs (or dl-programs) were introduced for such a combination, in which a pair (L,P) of a description logic knowledge base L and a set of rules P with negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this paper, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties: our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic

Integrating description logics (DL) and logic programming (LP) would produce a very powerful and useful formalism. However, DLs and LP are based on quite different principles, so achieving a seamless integration is not trivial. In this paper, we introduce hybrid MKNF knowledge bases that faithfully integrate DLs with LP using the logic of Minimal Knowledge and Negation as Failure (MKNF) [Lifschitz, 1991]. We also give reasoning algorithms and tight data complexity bounds for several interesting fragments of our logic. 1

We introduce HEX programs, which are nonmonotonic logic programs admitting higher-order atoms as well as external atoms, and we extend the wellknown answer-set semantics to this class of programs. Higher-order features are widely acknowledged as useful for performing meta-reasoning, among other tasks. Furthermore, the possibility to exchange knowledge with external sources in a fully declarative framework such as Answer-Set Programming (ASP) is nowadays important, in particular in view of applications in the Semantic Web area. Through external atoms, HEX programs can model some important extensions to ASP, and are a useful KR tool for expressing various applications. Finally, complexity and implementation issues for a preliminary prototype are discussed. 1

Abstract. Logic programming (LP) is often seen as a way to overcome several shortcomings of the Web Ontology Language (OWL), such as the inability to model integrity constraints or perform closed-world querying. However, the open-world semantics of OWL seems to be fundamentally incompatible with the closed-world semantics of LP. This has sparked a heated debate in the Semantic Web community, resulting in proposals for alternative ontology languages based entirely on logic programming. To help resolving this debate, we investigate the practical use cases which seem to be addressed by logic programming. In fact, many of these requirements have already been addressed outside the Semantic Web. By drawing inspiration from these existing formalisms, we present a novel logic of hybrid MKNF knowledge bases, which seamlessly integrates OWL with LP. We are thus capable of addressing the identified use cases without a radical change in the architecture of the Semantic Web. 1

The Semantic Web languages RDFS and OWL have been around for some time now. However, the presence of these languages has not brought the breakthrough of the Semantic Web the creators of the languages had hoped for. OWL has a number of problems in the area of interoperability and usability in the context of many practical application scenarios which impede the connection to the Software Engineering and Database communities. In this paper we present OWL Flight, which is loosely based on OWL, but the semantics is grounded in Logic Programming rather than Description Logics, and it borrows the constraint-based modeling style common in databases. This results in di#erent types of modeling primitives and enforces a di#erent style of ontology modeling. We analyze the modeling paradigms of OWL DL and OWL Flight, as well as reasoning tasks supported by both languages. We argue that di#erent applications on the Semantic Web require di#erent styles of modeling and thus both types of languages are required for the Semantic Web.

Abstract. In previous work, we have introduced probabilistic description logic programs (or pdl-programs), which are a combination of description logic programs (or dl-programs) under the answer set and well-founded semantics with Poole’s independent choice logic. Such programs are directed towards sophisticated representation and reasoning techniques that allow for probabilistic uncertainty in the Rules, Logic, and Proof layers of the Semantic Web. In this paper, we continue this line of research. We concentrate on the special case of stratified probabilistic description logic programs (or spdl-programs). In particular, we present an algorithm for query processing in such pdl-programs, which is based on a reduction to computing the canonical model of stratified dl-programs. 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

We propose a general framework for multi-context reasoning which allows us to combine arbitrary monotonic and nonmonotonic logics. Nonmonotonic bridge rules are used to specify the information flow among contexts. We investigate several notions of equilibrium representing acceptable belief states for our multi-context systems. The approach generalizes the heterogeneous monotonic multi-context systems developed by F. Giunchiglia and colleagues as well as the homogeneous nonmonotonic multi-context systems of Brewka, Serafini and Roelofsen. Background and Motivation Interest in formalizations of contextual information and inter-contextual information flow has steadily increased over the last years. Based on seminal papers by McCarthy (1987)