Towards Nonmonotonic Reasoning On Hierarchical Knowledge, Pascal Hitzler

Computer Science and Engineering Faculty Publications

W.C. Rounds and G.Q. Zhang have recently proposed to study a form of disjunctive logic programming generalized to algebraic domains [RZ01]. This system allows reasoning with information which is hierarchically structured and forms a (suitable) domain. We extend this framework to include reasoning with negative information, i.e. the implicit or explicit absence of bits of information. These investigations will naturally lead to a form of default reasoning which is strongly related to programming with answer sets to stable models, which has recently created much interest amongst artificial intelligence researchers concerned with knowledge representation and reasoning.

Ilp Operators For Propositional Connectionist Networks, Miguel Angel Gutierrez-Naranjo, Pascal Hitzler

Computer Science and Engineering Faculty Publications

No abstract provided.

Closed Streamlines In Flow Visualization, Thomas Wischgoll

Computer Science and Engineering Faculty Publications

Vector Fields occur in many of the problems in science and engineering. In combustion processes for instance, vector fields describe the flow of the gas. This process can be enhanced using vector field visualization techniques. Also wind tunnel experiments can be analyzed. An example is the design of an air wing. The wing can be optimized to crate a smoother flow around it. Vector field visualization methods help the engineer to detect critical features of the flow. Consequently, feature detection methods gained great importance during the last years.

Topological methods are often used to visualize vector fields because they clearly …

The Fixed-Point Theorems Of Priess-Crampe And Ribenboim In Logic Programming, Pascal Hitzler, Anthony K. Seda

Computer Science and Engineering Faculty Publications

Sibylla Priess-Crampe and Paulo Ribenboim recently established a general fixed-point theorem for multivalued mappings defined on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of this theorem and of its corollaries. In particular, we will relate these results to Scott-Ershov domains, familiar in programming language semantics, and to the generalized metrics of Khamsi, Kreinovich, and Misane which have been applied, by these latter authors, to logic programming. Amongst other things, we will also show that a unified treatment of the fixed-point theory …

Characterizing Logic Programming Semantics With Level Mappings, Pascal Hitzler, Matthias Wendt

Computer Science and Engineering Faculty Publications

Declarative semantics in logic programming and nonmonotonic reasoning are often defined via fixed points of semantic operators. While many relationships between different semantics known from the literature have been studied, a uniform treatment is still missing. In this paper, we provide uniform operator-free characterizations for some of the most important semantics, more precisely, for the stable, the well-founded, and the Fitting semantics, for the weakly-perfect model semantics, and for the least model semantics for negation-free programs.

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

Classes Of Logic Programs Which Possess Unique Supported Models, Anthony K. Seda, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Logic programming is concerned with the use of logic as a programming language. The main manifestation of this computing paradigm is in the various versions of Prolog which are now available, in which computation is viewed as deduction from sets of Horn clauses, although there is also growing interest in the related form known as answer set programming, see [10]. The reference [1] contains a good survey of the growth of logic programming over the last twenty-five years both as a stand-alone programming language and as a software component of large information systems. One advantage a logic program P has …

A New Fixed-Point Theorem For Logic Programming Semantics, Anthony K. Seda, Pascal Hitzler

Computer Science and Engineering Faculty Publications

We present a new fixed-point theorem akin to the Banach contraction mapping theorem, but in the context of a novel notion of generalized metric space, and show how it can be applied to analyse the denotational semantics of certain logic programs. The theorem is obtained by generalizing a theorem of Priess-Crampe and Ribenboim, which grew out of applications within valuation theory, but is also inspired by a theorem of S.G. Matthews which grew out of applications to conventional programming language semantics. The class of programs to which we apply our theorem was defined previously by us in terms of operators …

Der Kontraktionssatz Auf Metrischen Raumen Und Verallgemeinerungen, Pascal Hitzler

Computer Science and Engineering Faculty Publications

No abstract provided.

Characterizations Of Classes Of Programs By Three-Valued Operators, Anthony K. Seda, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Several important classes of normal logic programs, including the classes of acyclic, acceptable, and locally hierarchical programs, have the property that every program in the class has a unique two-valued supported model. In this paper, we call such classes unique supported model classes. We analyse and characterize these classes by means of operators on three-valued logics. Our studies will motivate the definition of a larger unique supported model class which we call the class of Phi-accessible programs. Finally, we show that the class of Phi -accessible programs is computationally adequate in that every partial recursive function can be implemented by …

Multivalued Mappings, Fixed-Point Theorems And Disjunctive Databases, Pascal Hitzler, Anthony K. Seda

Computer Science and Engineering Faculty Publications

In this paper, we discuss the semantics of disjunctive programs and databases and show how multivalued mappings and their fixed points arise naturally within this context. A number of fixed-point theorems for multivalued mappings are considered, some of which are already known and some of which are new. The notion of a normal derivative of a disjunctive program is introduced. Normal derivatives are normal logic programs which are determined by the disjunctive program. Thus, the well-known single-step operator associated with a normal derivative is single-valued, and its fixed points can be found by well-established means. It is shown how fixed …

Strictly Level-Decreasing Logic Programs, Pascal Hitzler, Anthony K. Seda

Computer Science and Engineering Faculty Publications

We study strictly level-decreasing logic programs (sld-programs) as defined earlier by the present authors. It will be seen that sld-programs, unlike most other classes of logic programs, have both a highly intuitive declarative semantics, given as a unique supported model, and are computationally adequate in the sense that every partial recursive function can be represented by some sld-program P. Allowing for a safe use of cuts, an interpreter based on SLDNF-resolution, as implemented for example in standard Prolog systems, is shown to be sound and complete with respect to this class of programs. Furthermore, we study connections between topological …

Generalized Ultrametrics, Domains And An Application To Computational Logic, Anthony K. Seda, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Fixed points of functions and operators are of fundamental importance in programming language semantics in giving meaning to recursive definitions and to constructs which involve self-reference. It follows therefore that fixed-point theorems are also of fundamental importance in theoretical computer science. Often, order-theoretic arguments are available in which case the well-known Knaster-Tarski theorem can be used to obtain fixed-points. Sometimes, however, analytical arguments are needed involving the Banach contraction mapping theorem as is the case for example in studying concurrency and communicating systems. Situations arise also in computational logic in the presence of negation which force non-monotonicity of the operators …

Architectural Power Estimation Based On Behavior Level Profiling, Srinivas Katkoori, Ranga Vemuri

Computer Science and Engineering Faculty Publications

High level synthesis is the process of generating register transfer (RT) level designs from behavioral specifications. High level synthesis systems have traditionally taken into account such constraints as area, clock period and throughput time. Many high level synthesis systems [1] permit generation of many alternative RT level designs meeting these constraints in a relatively short time. If it is possible to accurately estimate the power consumption of RT level designs, then a low power design from among these alternatives can be selected.In this paper, we present an accurate power estimation technique for register transfer level designs generated by high level …

Fixpunktsemantik Logischer Programme, Pascal Hitzler

Computer Science and Engineering Faculty Publications

No abstract provided.

Topology And Logic Programming Semantics, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Logic programming employs logic as a programming language. Thus a logic program consists of a set of clauses of a certain form most often a subset of the clauses of first order logic viewed as axioms. Computation in this paradigm is deduction from these axioms via some interpreter.

Logic programming semantics is concerned with background theory for logic programming. It tries to provide models for logic programs to give them their intended meaning and to connect them with practically implementable interpreters.

Spieltheorie, Alexander Chocholaty, Pascal Hitzler

Computer Science and Engineering Faculty Publications

No abstract provided.

Transformation Based Endorsement Systems, Thomas Sudkamp

Computer Science and Engineering Faculty Publications

Evidential reasoning techniques classically represent support for a hypothesis by a numeric value or an evidential interval. The combination of support is performed by an arithmetic rule which often requires restrictions to be placed on the set of possibilities. These assumptions usually require the hypotheses to be exhausitive and mutually exclusive. Endorsement based classification systems represent support for the alternatives symbolically rather than numerically. A framework for constructing endorsement systems is presented in which transformations are defined to generate and update the knowledge base. The interaction of the knowledge base and transformations produces a non-monotonic reasoning system. Two endorsement based …