Abstract. We present a novel combination of disjunctive logic programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a well-balanced interface between disjunctive logic programs and description logics, which guarantees the decidability of the resulting formalism without assuming syntactic restrictions. We show that the new formalism has very nice semantic properties. In particular, it faithfully extends both disjunctive programs and description logics. Furthermore, we describe algorithms for reasoning in the new formalism, and we give a precise picture of its computational complexity. We also provide a special case with polynomial data complexity. 1

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

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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)

Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DL-Lite family of tractable description logics (DLs) [11, 19]. An important result of these works is that the main

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Managing uncertainty and/or vagueness is starting to play an important role in Semantic Web representation languages. Our aim is to overview basic concepts on representing uncertain and vague knowledge in current Semantic Web ontology and rule languages (and their combination).

Applications of semantic technologies often require the representation of and reasoning with structured objects—that is, objects composed of parts connected in complex ways. Although OWL is a general and powerful language, its class descriptions and axioms cannot be used to describe arbitrarily connected structures. OWL representation of structured objects can thus be underconstrained, which reduces the inferences that can be drawn and causes performance problems in reasoning. To address these problems, we extend OWL with description graphs, which provide for the description of structured objects in a simple and precise way. To represent conditional aspects of the domain, we also allow for SWRL-like rules over description graphs. Based on a novel observation about the nature of structured objects, we ensure decidability of our formalism. We also present a hypertableau-based decision procedure, which we implemented in the HermiT reasoner. To evaluate its performance, we extracted description graphs from the GALEN and FMA ontologies, classified them successfully, and even detected a modeling error in GALEN. 1

Abstract. With the advent of the Semantic Web, the question becomes important how to best combine open-world based ontology languages, like OWL, with closed-world rules paradigms. One of the most mature proposals for this combination is known as Hybrid MKNF knowledge bases [11], which is based on an adaptation of the stable model semantics to knowledge bases consisting of ontology axioms and rules. In this paper, we propose a well-founded semantics for such knowledge bases which promises to provide better efficiency of reasoning, which is compatible both with the OWL-based semantics and the traditional well-founded semantics for logic programs, and which surpasses previous proposals for such a well-founded semantics by avoiding some issues related to inconsistency handling. 1

Abstract. In the ongoing discussion about combining rules and Ontologies on the Semantic Web a recurring issue is how to combine first-order classical logic with nonmonotonic rule languages. Whereas several modular approaches to define a combined semantics for such hybrid knowledge bases focus mainly on decidability issues, we tackle the matter from a more general point of view. In this paper we show how Quantified Equilibrium Logic (QEL) can function as a unified framework which embraces classical logic as well as disjunctive logic programs under the (open) answer set semantics. In the proposed variant of QEL we relax the unique names assumption, which was present in earlier versions of QEL. Moreover, we show that this framework elegantly captures the existing modular approaches for hybrid knowledge bases in a unified way. 1