We present a novel combination of disjunctive programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a well-balanced interface between disjunctive 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 define the well-founded semantics for the normal case, where normal programs are combined with tractable description logics, and we explore its semantic and computational properties. In particular, we show that the well-founded semantics approximates the answer set semantics. We also describe algorithms for the problems of consistency checking and literal entailment under the well-founded semantics, and we give a precise picture of their computational complexity. As a crucial property, in the normal case, consistency checking and literal entailment under the well-founded semantics are both tractable in the data complexity, and even first-order rewritable (and thus can be done in LOGSPACE in the data complexity) in a special case that is especially useful for representing mappings between ontologies.The Semantic Web [7,28] aims at an extension of the current World Wide Web by standards and technologies that help machines to understand the information on the Web so that they can support richer discovery, data integration, navigation, and automation of tasks. The main ideas behind it are to add a machine-readable meaning to Web pages, to use ontologies for a precise definition of shared terms in Web resources, to use knowledge representation technology for automated reasoning from Web resources, and to apply cooperative agent technology for processing the information of the Web.The Semantic Web consists of several hierarchical layers, where the Ontology layer, in form of the OWL Web Ontology Language [63,35,5], is currently the highest layer of sufficient maturity. OWL consists of three increasingly expressive sublanguages, namely OWL Lite, OWL DL, and OWL Full. OWL Lite and OWL DL are essentially very expressive description logics with an RDF syntax [35]. As shown in [33], ontology entailment in OWL Lite (resp., OWL DL) reduces to knowledge base (un)satisfiability in the description logic SHIF(D) (resp., SHOIN (D)). As a next important step in the development of the Semantic Web, one aims at sophisticated representation and reasoning capabilities for the Rules, Logic, and Proof layers of the Semantic Web.In particular, there is a large body of work on integrating rules and ontologies, which is a key requirement of the layered architecture of the Semantic Web. Significant research efforts focus on hybrid integrations of rules and ontologies, called description logic programs (or dl-programs)...

Standardization of solver input languages has been a main driver for the growth of several areas within knowledge representation and reasoning, fostering the exploitation in actual applications. In this document we present the ASP-Core-2 standard input language for Answer Set Programming, which has been adopted in ASP Competition events since 2013.

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Abstract. Towards providing a suitable tool for building the Rule Layer of the Semantic Web, hex-programs have been introduced as a special kind of logic programs featuring capabilities for higher-order reasoning, interfacing with external sources of computation, and default negation. Their semantics is based on the notion of answer sets, providing a transparent interoperability with the Ontology Layer of the Semantic Web and full declarativity. In this paper, we identify classes of hex-programs feasible for implementation yet keeping the desirable advantages of the full language. A general method for combining and evaluating sub-programs belonging to arbitrary classes is introduced, thus enlarging the variety of programs whose execution is practicable. Implementation activity on the current prototype is also reported.