Physical Sciences and Mathematics Commons^™

Nichtmonotone, Neuro-Symbolische Und Begriffliche Wissensverarbeitung, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Diese Schrift dient dem Bericht uber die Hauptaspekte meiner Forschertatigkeit an der TU Dresden seit der Promotion. In diesen dreieinhalb Jahren war es mein Bestreben, selbststandig aktuelle, theoretisch fundierte und anwendungsbezogene Fragestellungen zu entwickeln und zu verfolgen.

Naturgemaß war meine Forschung in dieser Zeit vor allem zu Anfang sehr explorativ. Meine Suche konzentrierte sich dabei auf das Herausarbeiten theoretischer Zusammenhange. Ob ich einen Ansatz dann weiterverfolgte entschied sich anschließend aufgrund einer Evaluation aus angewandter Sicht.

Die in dieser Schrift dargestellten Forschungsansatze gedenke ich in Zukunft fortzufuhren. Sie bilden die Keimzellen fur langfristig angelegte angewandte und theoretische Untersuchungen. Ich werde in …

Default Reasoning Over Domains And Concept Hierarchies, Pascal Hitzler

Computer Science and Engineering Faculty Publications

W.C. Rounds and G.-Q. Zhang have proposed to study a form of disjunctive logic programming generalized to algebraic domains [1]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with default negation, giving rise to a new nonmonotonic reasoning framework on hierarchical knowledge which encompasses answer set programming with extended disjunctive logic programs. We also show that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis. Together, we obtain a default reasoning paradigm for conceptual …

Logic Programs And Connectionist Networks, Pascal Hitzler, Steffen Holldobler, Anthony K. Seda

Computer Science and Engineering Faculty Publications

Graphs of the single-step operator for first-order logic programs—displayed in the real plane—exhibit self-similar structures known from topological dynamics, i.e., they appear to be fractals, or more precisely, attractors of iterated function systems. We show that this observation can be made mathematically precise. In particular, we give conditions which ensure that those graphs coincide with attractors of suitably chosen iterated function systems, and conditions which allow the approximation of such graphs by iterated function systems or by fractal interpolation. Since iterated function systems can easily be encoded using recurrent radial basis function networks, we eventually obtain connectionist systems which …

Detection Of Closed Hyperstreamlines, Thomas Wischgoll

Computer Science and Engineering Faculty Publications

No abstract provided.

Corollaries On The Fixpoint Completion: Studying The Stable Semantics By Means Of The Clark Completion, Pascal Hitzler

Computer Science and Engineering Faculty Publications

The fixpoint completion fix (P) of a normal logic program P is a program transformation such that the stable models of P are exactly the models of the Clark completion of fix (P). This is well-known and was studied by Dung and Kanchanasut [15]. The correspondence, however, goes much further: The Gelfond-Lifschitz operator of P coincides with the immediate consequence operator of fix (P), as shown by Wendt [51], and even carries over to standard operators used for characterizing the well-founded and the Kripke-Kleene semantics. We will apply this knowledge to the study of …

Approximating First-Order Logic Programs By Feedforward Networks, Pascal Hitzler

Computer Science and Engineering Faculty Publications

We want to apply Funahashi's theorem in order to approximate the T_P operator for first-order (normal) logic programs P via 3-layer feedforward networks. I.e. we need to understand T_P as a continuous function on the reals.

We will need to study some preliminaries from set-theoretic topology first result from [HS00, HHS0_x], which extends results from [HKS99]. We close with some further considerations about the methods and results.

Virtual Exploration Of A Cardiovascular System, Elke Moritz, Thomas Wischgoll, Joerg Meyer

Computer Science and Engineering Faculty Publications

No abstract provided.

Operator-Based Semantics For Logic Programs, Pascal Hitzler

Computer Science and Engineering Faculty Publications

The question how knowledge can be represented by means of logic programs with negation has been a driving force for the field of non-monotonic reasoning. Implemented systems, known as answer set programming systems, have emerged recently and are currently being used in various application domains like the semantic web.

Intuitively, logic programs are being used for encoding commonsense reasoning, in particular the phenomenon that human reasoning tends to ”jump to conclusions” under incomplete knowledge. Formally, this kind of reasoning is described by interpreting the first-order syntax of logic programs in a more sophisticated way. This, in turn, is most easily …