text: Description Logic Programs (dl-programs) proposed by constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.
  @cite_18: In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic, and rule bases have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalismwhich allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present several embeddings of normal and disjunctive non-ground logic programs under the stable-model semantics into first-order AEL, and compare them in combination with classical theories, with respect to stable expansions and autoepistemic consequences. Our results reveal differences and correspondences of the embeddings and provide a useful guidance in the choice of a particular embedding for knowledge combination.
  @cite_9: 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.
  @cite_21: Description logics (DLs) and rules are formalisms that emphasize different aspects of knowledge representation: whereas DLs are focused on specifying and reasoning about conceptual knowledge, rules are focused on nonmonotonic inference. Many applications, however, require features of both DLs and rules. Developing a formalism that integrates DLs and rules would be a natural outcome of a large body of research in knowledge representation and reasoning of the last two decades; however, achieving this goal is very challenging and the approaches proposed thus far have not fully reached it. In this paper, we present a hybrid formalism of MKNFp knowledge bases, which integrates DLs and rules in a coherent semantic framework. Achieving seamless integration is nontrivial, since DLs use an open-world assumption, while the rules are based on a closed-world assumption. We overcome this discrepancy by basing the semantics of our formalism on the logic of minimal knowledge and negation as failure (MKNF) by Lifschitz. We present several algorithms for reasoning with MKNFp knowledge bases, each suitable to different kinds of rules, and establish tight complexity bounds.
  @cite_5: 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.
  @cite_13: We propose a combination of logic programming under the answer set semantics with the description logics SHIF(D) and SHOIN(D), which underly the Web ontology languages OWL Lite and OWL DL, respectively. To this end, we introduce description logic programs (or dl-programs), which consist of a description logic knowledge base L and a finite set P of description logic rules (or dl-rules). Such rules are similar to usual rules in nonmonotonic logic programs, but they may also contain queries to L, possibly under default negation, in their bodies. They allow for building rules on top of ontologies but also, to a limited extent, building ontologies on top of rules. We define a suite of semantics for various classes of dl-programs, which conservatively extend the standard semantics of the respective classes and coincide with it in absence of a description logic knowledge base. More concretely, we generalize positive, stratified, and arbitrary normal logic programs to dl-programs, and define a Herbrand model semantics for them. We show that they have similar properties as ordinary logic programs, and also provide fixpoint characterizations in terms of (iterated) consequence operators. For arbitrary dl-programs, we define answer sets by generalizing Gelfond and Lifschitz's notion of a transform, leading to a strong and a weak answer set semantics, which are based on reductions to the semantics of positive dl-programs and ordinary positive logic programs, respectively. We also show how the weak answer sets can be computed utilizing answer sets of ordinary normal logic programs. Furthermore, we show how some advanced reasoning tasks for the Semantic Web, including different forms of closed-world reasoning and default reasoning, as well as DL-safe rules, can be realized on top of dl-programs. Finally, we give a precise picture of the computational complexity of dl-programs, and we describe efficient algorithms and a prototype implementation of dl-programs which is available on the Web.
  @cite_12: 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.
summary: Integrating ASP with description logics has attracted a great deal of attention recently. The existing approaches can be roughly classified into three categories. The first is to adopt a nonmonotonic formalism that covers both ASP and first-order logic (if not for the latter, then extend it to the first-order case) @cite_21 @cite_18 , where ontologies and rules are written in the same language, resulting in a tight coupling. The second is a loose approach: An ontology knowledge base and the rules share the same constants but not the same predicates, and the communication is via a well-defined interface, such as dl-atoms @cite_13 . The third is to combine ontologies with hybrid rules @cite_5 @cite_9 @cite_12 , where predicates in the language of ontologies are interpreted classically, whereas those in the language of rules are interpreted nonmonotonically.