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

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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Abstract. Lightweight ontologies in the form of RDF vocabularies such as SIOC, FOAF, vCard, etc. are increasingly being used and exported by “serious ” applications recently. Such vocabularies, together with query languages like SPARQL also allow to syndicate resulting RDF data from arbitrary Web sources and open the path to finally bringing the Semantic Web to operation mode. Considering, however, that many of the promoted lightweight ontologies overlap, the lack of suitable standards to describe these overlaps in a declarative fashion becomes evident. In this paper we argue that one does not necessarily need to delve into the huge body of research on ontology mapping for a solution, but SPARQL itself might — with extensions such as external functions and aggregates — serve as a basis for declaratively describing ontology mappings. We provide the semantic foundations and a path towards implementation for such a mapping language by means of a translation to Datalog with external predicates.

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

The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.

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).

The language of HEX-programs under the answer-set semantics is designed for interoperating with heterogeneous sources via external atoms and for meta-reasoning via higher-order literals in the context of the Semantic Web. As an important technique in managing knowledge bases, the notion of forgetting has received increasing interest in the knowledge-representation area. In this paper, we introduce a semantics-based theory of forgetting for HEX-programs and, in turn, for a class of OWL/RDF ontologies which allows to fully employ semantic information in managing ontologies like editing, merging, aligning, and redundancy removal. 1

We present a principled framework for modular web rule bases, called MWeb. According to this framework, each predicate defined in a rule base is characterized by its defining reasoning mode, scope, and exporting rule base list. Each predicate used in a rule base is characterized by its requesting reasoning mode and importing rule base list. For valid MWeb modular rule bases S, theMWebAS andMWebWFS semantics of each rule base s ∈ S w.r.t. S are defined, model-theoretically. These semantics extend the answer set semantics (AS) and the well-founded semantics with explicit negation (WFSX) on ELPs, respectively, keeping all of their semantical and computational characteristics. Our framework supports: (i) local semantics and different points of view, (ii) local closed-world and open-world assumptions, (iii) scoped negation-as-failure, and (iv) restricted propagation of local inconsistencies. Additionally, it guarantees monotonicity of reasoning, in the case that new rule bases are added to the modular rule base, while the importing rule base list of the predicates of the old rule bases remains the same.