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

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

Rule-based and object-oriented techniques are rapidly making their way into the infrastructure for representing and reasoning about the Semantic Web and combining these two paradigms emerges as an important objective. We present a new family of representation languages, which extents existing language families for the Semantic Web: namely Description Logic Programs (DLPs) and DLPs with uncertainty (µDLPs). The former combine the expressive power of description logics (which capture the meaning of the most popular features of structured representation of knowledge) and disjunctive logic programs (powerful rule-based representation languages). The latter are DLPs in which the management of uncertainty is considered as well. We show that µDLPs may be applied in the context of distributed information search in the Semantic Web, where the representation of the inherent uncertainty of the relationships among resource ontologies, to which an automated agent has access to, is required.

We extend Answer Set Programming with, possibly infinite, open domains.

Abstract. As applications of description logics proliferate, efficient reasoning with knowledge bases containing many assertions becomes ever more important. For such cases, we developed a novel reasoning algorithm that reduces a SHIQ knowledge base to a disjunctive datalog program while preserving the set of ground consequences. Queries can then be answered in the resulting program while reusing existing and practically proven optimization techniques of deductive databases, such as join-order optimizations or magic sets. Moreover, we use our algorithm to derive precise data complexity bounds: we show that SHIQ is data complete for NP, and we identify an expressive fragment of SHIQ with polynomial data complexity.

We integrate an expressive class of description logics (DLs) and answer set programming by extending the latter to support inverted predicates and infinite domains, features that are present in most DLs. The extended language, conceptual logic programming (CLP) proves to be a viable alternative for intuitively representing and reasoning nonmonotonically, in a decidable way, with possibly infinite knowledge. Not only can conceptual logic programs (CLPs) simulate finite answer set programming, they are also flexible enough to simulate reasoning in an expressive class of description logics, thus being able to play the role of ontology language, as well as rule language, on the Semantic Web.

We integrate an expressive class of description logics (DLs) and answer set programming by extending the latter to support inverted predicates and infinite domains, features that are present in most DLs. The extended language, conceptual logic programming (CLP) proves to be a viable alternative for intuitively representing and reasoning nonmonotonically, in a decidable way, with possibly infinite knowledge. Not only can conceptual logic programs (CLPs) simulate finite answer set programming, they are also flexible enough to simulate reasoning in an expressive class of description logics, thus being able to play the role of ontology language, as well as rule language, on the Semantic Web.

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We integrate ontology languages and logic programming (LP) by extending disjunctive logic programs (DLPs) and their semantics in order to support inverses and an infinite universe, without introducing function symbols. We show that this extension is still decidable, and can be used to simulate, on the one hand, answer set programming with a finite universe, and on the other hand, several expressive description logics (DLs), which can be seen as ontology languages. The integration leads to a "best of both worlds": from the LP side it inherits a flexible and intuitive representation of knowledge, whereas the DLs side provides the possibility to represent infinite knowledge.

We present the class FDNC of logic programs which allows for function symbols(F), disjunction (D), non-monotonic negation under the answer set semantics (N), and constraints (C), while still retaining the decidability of the standard reasoning tasks. Thanks to these features, FDNC programs are a powerful formalism for rule-based modeling of applications with potentially infinite processes and objects, and which allows also for common-sense reasoning in this context. This is evidenced, for instance, by tasks in reasoning about actions and planning: brave and open queries over FDNC programs capture the well-known problems of plan existence and secure (conformant) plan existence, respectively, in transition-based actions domains. As for reasoning from FDNC programs, we show that consistency checking and brave/cautious reasoning tasks are ExpTimecomplete in general, but have lower complexity under syntactic restrictions that give rise to a family of program classes. Furthermore, we also determine the complexity of open queries (i.e., with answer variables), for which deciding non-empty answers is shown to be ExpSpace-complete under cautious entailment. Furthermore, we present algorithms for all reasoning tasks that are worst-case optimal. The majority of them resorts to a finite representation of the stable models of an FDNC program that employs maximal founded sets of knots, which are labeled trees of depth at most 1 from which each stable model can be reconstructed. Due to this property, reasoning over FDNC programs can in many cases be reduced to reasoning from knots. Once the knotrepresentation for a program is derived (which can be done off-line), several reasoning tasks are not more expensive than in the function-free case, and some are even feasible in polynomial time. This knowledge compilation technique paves the way to potentially more efficient online reasoning methods not only for FDNC, but also for other formalisms.