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Nichtmonotone, Neuro-Symbolische Und Begriffliche Wissensverarbeitung, Pascal Hitzler
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 …
Logic Programs, Iterated Function Systems, And Recurrent Radial Basis Function Networks, Sebastian Bader, Pascal Hitzler
Logic Programs, Iterated Function Systems, And Recurrent Radial Basis Function Networks, Sebastian Bader, Pascal Hitzler
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 …
Logic Programs And Connectionist Networks, Pascal Hitzler, Steffen Holldobler, Anthony K. Seda
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 …
Default Reasoning Over Domains And Concept Hierarchies, Pascal Hitzler
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 …
Detection Of Closed Hyperstreamlines, Thomas Wischgoll
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
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
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 TP operator for first-order (normal) logic programs P via 3-layer feedforward networks. I.e. we need to understand TP as a continuous function on the reals.
We will need to study some preliminaries from set-theoretic topology first result from [HS00, HHS0x], 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
Virtual Exploration Of A Cardiovascular System, Elke Moritz, Thomas Wischgoll, Joerg Meyer
Computer Science and Engineering Faculty Publications
No abstract provided.
The Integration Of Connectionism And First-Order Knowledge Representation And Reasoning As A Challenge For Artificial Intelligence, Sebastian Bader, Steffen Holldobler, Pascal Hitzler
The Integration Of Connectionism And First-Order Knowledge Representation And Reasoning As A Challenge For Artificial Intelligence, Sebastian Bader, Steffen Holldobler, Pascal Hitzler
Computer Science and Engineering Faculty Publications
Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way that the strengths of either paradigm will be retained. Current state-of-the-art research, however, fails by far to achieve this ultimate goal. As one of the main obstacles to be overcome we perceive the question how symbolic knowledge can be encoded by means of connectionist systems: Satisfactory answers to this will …
Operator-Based Semantics For Logic Programs, Pascal Hitzler
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 …