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 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.

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

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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Vagueness and imprecision abound in multimedia information processing and retrieval. In this paper, towards dealing with vagueness and imprecision in the reasoning layers of the Semantic Web, we present an approach to fuzzy description logic programs under the answer set semantics. We generalize normal description logic programs (dl-programs) under the answer set semantics by fuzzy vagueness and imprecision. We define a canonical semantics of positive and stratified fuzzy dl-programs in terms of a unique least model and iterative least models, respectively. We then define the answer set semantics of general fuzzy dlprograms, and show in particular that all answer sets of a fuzzy dl-program are minimal models, and that the answer set semantics of positive and stratified fuzzy dl-programs coincides with their canonical least model and iterative least model semantics, respectively. Furthermore, we also provide a characterization of the canonical semantics of positive and stratified fuzzy dl-programs in terms of a fixpoint and an iterative fixpoint semantics, respectively. 1.

We present extended conceptual logic programs (ECLPs), for which reasoning is decidable and, moreover, can be reduced to finite answer set programming.

In this paper, we present a novel formalism of hybrid MKNF knowledge bases, which allows us to seamlessly integrate an arbitrary decidable description logic with logic programming rules. We thus obtain a powerful hybrid formalism that combines the best features of both description logics, such as the ability to model taxonomic knowledge, and logic programming, such as the ability to perform nonmonotonic reasoning. Extending DLs with unrestricted rules makes reasoning undecidable. To obtain decidability, we apply the well-known DL-safety restriction that makes the rules applicable only to explicitly named individuals, and thus trade some expressivity for decidability. We present several reasoning algorithms for different fragments of our logic, as well as the corresponding complexity results. Our results show that, in many cases, the data complexity of reasoning with hybrid MKNF knowledge bases is not higher than the data complexity of reasoning

Abstract. For realizing the Semantic Web vision, extensive work is underway for getting the layers of its conceived architecture ready. Given that the Ontology Layer has reached a certain level of maturity with W3C recommendations such as RDF and the OWL Web Ontology Language, current interest focuses on the Rules Layer and its integration with the Ontology Layer. Several proposals have been made for solving this problem, which does not have a straightforward solution due to various obstacles. One of them is the fact that evaluation principles like the closed-world assumption, which is common in rule languages, are usually not adopted in ontologies. Furthermore, naively adding rules to ontologies raises undecidability issues. In this paper, after giving a brief overview about the current state of the Semantic-Web stack and its components, we will discuss nonmonotonic logic programs under the answer-set semantics as a possible formalism of choice for realizing the Rules Layer. We will briefly discuss open issues in combining rules and ontologies, and survey some existing proposals to facilitate reasoning with rules and ontologies. We will then focus on description-logic programs (or dl-programs, for short), which realize a transparent integration of rules and ontologies supported by existing reasoning engines, based on the answer-set semantics. We will further discuss a generalization of dlprograms, viz. HEX-programs, which offer access to different ontologies as well as higher-order language constructs. 1

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).