Logic Versus Approximation

Logic versus Approximation

Nowadays knowledge-based systems research and development essentially employs two paradigms of reasoning. There are on the one hand the logic-based approaches where logic is to be understood in a rather broad sense; usually these approaches are used in symbolic domains where numerical calculations are not the core challenge. On the other hand we find approximation oriented reasoning; methods of these kinds are mainly applied in numerical domains where approximation is part of the scientific methodology itself. However, from an abstract level all these approaches do focus on similar topics and arise on various levels such as problem modeling, inference and problem solving techniques, algorithms and mathematical methods, mathematical relations between discrete and continuous properties, and are integrated in tools and applications. In accordance with the unifying vision and research interest of Michael M. Richter and in correspondence to his scientific work, this book presents 13 revised full papers advocating the integration of logic-based and approximation-oriented approaches in knowledge processing.

Fuzzy Sets in Approximate Reasoning and Information Systems

Approximate reasoning is a key motivation in fuzzy sets and possibility theory. This volume provides a coherent view of this field, and its impact on database research and information retrieval. First, the semantic foundations of approximate reasoning are presented. Special emphasis is given to the representation of fuzzy rules and specialized types of approximate reasoning. Then syntactic aspects of approximate reasoning are surveyed and the algebraic underpinnings of fuzzy consequence relations are presented and explained. The second part of the book is devoted to inductive and neuro-fuzzy methods for learning fuzzy rules. It also contains new material on the application of possibility theory to data fusion. The last part of the book surveys the growing literature on fuzzy information systems. Each chapter contains extensive bibliographical material. Fuzzy Sets in Approximate Reasoning and Information Systems is a major source of information for research scholars and graduate students in computer science and artificial intelligence, interested in human information processing.

Logic Versus Approximation