Convergence Classes And Spaces Of Partial Functions, Anthony K. Seda, Roland Heinze, Pascal Hitzler

Computer Science and Engineering Faculty Publications

We study the relationship between convergence spaces and convergence classes given by means of both nets and filters, we consider the duality between them and we identify in convergence terms when a convergence space coincides with a convergence class. We examine the basic operators in the Vienna Development Method of formal systems development, namely, extension, glueing, restriction, removal and override, from the perspective of the Logic for Computable Functions. Thus, we examine in detail the Scott continuity, or otherwise, of these operators when viewed as operators on the domain (X → Y) of partial functions mapping X into …

Semantic Operators And Fixed-Point Theory In Logic Programming, Anthony K. Seda, Pascal Hitzler

Computer Science and Engineering Faculty Publications

We consider rather general operators mapping valuations to (sets of) valuations in the context of the semantics of logic programming languages. This notion generalizes several of the standard operators encountered in this subject and is inspired by earlier work of M.C. Fitting. The fixed points of such operators play a fundamental role in logic programming semantics by providing standard models of logic programs and also in determining the computability properties of these standard models. We discuss some of our recent work employing topological ideas, in conjunction with order theory, to establish methods by which one can find the fixed points …

A "Converse" Of The Banach Contraction Mapping Theorem, Pascal Hitzler, Anthony K. Seda

Computer Science and Engineering Faculty Publications

We prove a type of converse of the Banach contraction mapping theorem for metric spaces: if X is a T₁ topological space and f: X -> X is a function with the unique fixed point a such that fⁿ(x) converges to a for each x is a member of X, then there exists a distance function d on X such that f is a contraction on the complete ultrametric space (X,d) with contractivity factor 1/2. We explore properties of the resulting space (X,d).

Generalized Metrics And Topology In Logic Programming Semantics, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Many fixed-point theorems are essentially topological in nature. Among them are the Banach contraction mapping theorem on metric spaces and the fixed-point theorem for Scott-continuous mappings on complete partial orders. The latter theorem is fundamental in denotational semantics since semantic operators in most programming language paradigms satisfy its requirements. The use of negation in logic programming and non-monotonic reasoning, however, renders some semantic operators to be non-monotonic, hence discontinuous with respect to the Scott topology, and therefore invalidates the standard approach, so that alternative methods have to be sought. In this thesis, we investigate topological methods, including generalized metric fixed-point …

Evolution Of Topology In Axi-Symmetric And 3-D Viscous Flows, Gerik Scheuermann, W. Kollmann, Xavier Tricoche, Thomas Wischgoll

Computer Science and Engineering Faculty Publications

No abstract provided.

Parallel Detection Of Closed Streamlines In Planar Flows, Thomas Wischgoll, Gerik Scheuermann, Hans Hagen

Computer Science and Engineering Faculty Publications

No abstract provided.

Unique Supported-Model Classes Of Logic Programs, Pascal Hitzler, Anthony K. Seda

Computer Science and Engineering Faculty Publications

We study classes of programs, herein called unique supported-model classes, with the property that each program in the class has a unique supported model. Elsewhere, the authors examined these classes from the point of view of operators defined relative to certain three-valued logics. In this paper, we complement our earlier results by considering how unique supported-model classes fit into the framework given by various classes of programs in several well-known approaches to semantics.

Kontraktionssatze Auf Verallgemeinerten Metrischen Raumen, Pascal Hitzler

Computer Science and Engineering Faculty Publications