Miki Hermann

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We introduce and investigate a new type of reductions between counting problems, which we call subtractive reductions. We show that the main counting complexity classes #P, #NP, as well as all higher counting complexity classes # · kP, k 2, are closed under subtractive reductions. We then pursue problems that are complete for these classes via subtractive(More)
Innnite sets of terms appear frequently at diierent places in computer science. On the other hand, several practically oriented parts of logic and computer science require the manipulated objects to be nite or nitely representable. Schematizations present a suitable formalism to manipulate nitely innnite sets of terms. Since schematizations provide a(More)
Abduction is an important method of non-monotonic reasoning with many applications in AI and related topics. In this paper, we concentrate on propositional abduction, where the background knowledge is given by a propositional formula. Decision problems of great interest are the existence and the relevance problems. The complexity of these decision problems(More)
This article introduces a generalisation of the crossed rule approach to the detection of Knuth-Bendix completion procedure divergence. It introduces closure chains, which are special rule closures constructed by means of particular substitution operations and operators, as a suitable formalism for progress in this direction. Supporting substitution algebra(More)
  • M. HERMANN, F. STRATMANN, M. WILCK, A. WIEDENSOHLER
When sampling aerosol particles from aircraft, the inlet system is the most critical item because it can strongly modify the number concentration, size distribution, and chemical composition of the particles. In this investigation, the authors describe a new aircraft-borne aerosol inlet and its sampling characteristics for submicrometer particle(More)
Reiter’s default logic formalizes nonmonotonic reasoning using default assumptions. The semantics of a given instance of default logic is based on a fixpoint equation defining an extension. Three different reasoning problems arise in the context of default logic, namely the existence of an extension, the presence of a given formula in an extension, and the(More)
Abduction is an important method of non-monotonic reasoning with many applications in artificial intelligence and related topics. In this paper, we concentrate on propositional abduction, where the background knowledge is given by a propositional formula. We have recently started to study the counting complexity of propositional abduction. However, several(More)