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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows one to express <i>every</i> property of finite structures that is decidable in the complexity class &#931;<sup><i>P</i></sup><sub>2</sub> (NP<sup>NP</sup>). Thus, under widely believed(More)
This article surveys various complexity and expressiveness results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn(More)
Towards the integration of rules and ontologies in the Semantic Web, 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. This combination allows for building rules on top of ontologies but also, to a limited(More)
This paper addresses complexity issues for important problems arising with disjunctive logic programming. In particular, the complexity of deciding whether a disjunctive logic program is consistent is investigated for a variety of well-known semantics, as well as the complexity of deciding whether a propositional formula is satisfied by all models according(More)
Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about <italic>logic-based abduction</italic>. Candidates for abductive explanations are usually subjected to minimality criteria such as subset-minimality,(More)
In this paper, we extend Gelfond and Lifschitz’s answer set semantics to prioritized extended logic programs. In such programs, an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion(More)
We study the complexity of several recently proposed methods for updating or revising propositional knowledge bases. In particular, we derive complexity results for the following problem: given a knowledge base <italic>T</italic>, an update <italic>p</italic>, and a formula <italic>q</italic>, decide whether <italic>q</italic> is derivable from(More)
The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to(More)
The Fréchet distance between two curves in a metric space is a measure of the similarity between the curves. We present a discrete variation of this measure. It provides good approximations of the continuous measure and can be efficiently computed using a simple algorithm. We also consider variants of discrete Fréchet distance, and find an interesting(More)