Logic Versus Approximation

Logic Versus Approximation

Author: Wolfgang Lenski (Ed )

Publisher: Springer Science & Business Media

Published: 2004-10-27

Total Pages: 212

ISBN-13: 3540225625

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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.


Fuzziness and Approximate Reasoning

Fuzziness and Approximate Reasoning

Author: Kofi Kissi Dompere

Publisher: Springer

Published: 2009-07-28

Total Pages: 311

ISBN-13: 3540880879

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We do not perceive the present as it is and in totality, nor do we infer the future from the present with any high degree of dependability, nor yet do we accurately know the consequences of our own actions. In addition, there is a fourth source of error to be taken into account, for we do not execute actions in the precise form in which they are imaged and willed. Frank H. Knight [R4.34, p. 202] The “degree” of certainty of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical signi- cance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon fav- ableness of the opinion itself. The ultimate logic, or psychology, of these deliberations is obscure, a part of the scientifically unfathomable mystery of life and mind. Frank H. Knight [R4.34, p. 226-227] With some inaccuracy, description of uncertain consequences can be classified into two categories, those which use exclusively the language of probability distributions and those which call for some other principle, either to replace or supplement.


Fuzzy Sets in Approximate Reasoning and Information Systems

Fuzzy Sets in Approximate Reasoning and Information Systems

Author: J.C. Bezdek

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 527

ISBN-13: 1461552435

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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.


Approximate Computing

Approximate Computing

Author: Weiqiang Liu

Publisher: Springer Nature

Published: 2022-08-22

Total Pages: 607

ISBN-13: 3030983471

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This book explores the technological developments at various levels of abstraction, of the new paradigm of approximate computing. The authors describe in a single-source the state-of-the-art, covering the entire spectrum of research activities in approximate computing, bridging device, circuit, architecture, and system levels. Content includes tutorials, reviews and surveys of current theoretical/experimental results, design methodologies and applications developed in approximate computing for a wide scope of readership and specialists. Serves as a single-source reference to state-of-the-art of approximate computing; Covers broad range of topics, from circuits to applications; Includes contributions by leading researchers, from academia and industry.


Abstraction, Reformulation, and Approximation

Abstraction, Reformulation, and Approximation

Author: Sven Koenig

Publisher: Springer

Published: 2003-08-02

Total Pages: 360

ISBN-13: 3540456228

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It has been recognized since the inception of Artificial Intelligence (AI) that abstractions, problem reformulations, and approximations (AR&A) are central to human common sense reasoning and problem solving and to the ability of systems to reason effectively in complex domains. AR&A techniques have been used to solve a variety of tasks, including automatic programming, constraint satisfaction, design, diagnosis, machine learning, search, planning, reasoning, game playing, scheduling, and theorem proving. The primary purpose of AR&A techniques in such settings is to overcome computational intractability. In addition, AR&A techniques are useful for accelerating learning and for summarizing sets of solutions. This volume contains the proceedings of SARA 2002, the fifth Symposium on Abstraction, Reformulation, and Approximation, held at Kananaskis Mountain Lodge, Kananaskis Village, Alberta (Canada), August 2 4, 2002. The SARA series is the continuation of two separate threads of workshops: AAAI workshops in 1990 and 1992, and an ad hoc series beginning with the "Knowledge Compilation" workshop in 1986 and the "Change of Representation and Inductive Bias" workshop in 1988 with followup workshops in 1990 and 1992. The two workshop series merged in 1994 to form the first SARA. Subsequent SARAs were held in 1995, 1998, and 2000.


Structure and Approximation in Physical Theories

Structure and Approximation in Physical Theories

Author: A. Hartkamper

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 254

ISBN-13: 1468441094

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The present volume contains 14 contributions presented at a colloquium on "Structure and Approximation in Physical Theories" held at Osnabruck in June 1980. The articles are presented in the revised form written after the colloquium and hence also take account of the results of the discussion at the colloquium. It is a striking feature that the problem of approximation in physical theories has only recently found some attention in the philosophy of science, although the working physicist is con stantly confronted with those questions. No interesting theory of exact science exactly fits its experimental data; almost every relation between different theories is an approximate one. There fore an adequate reconstruction of physical theories must take into account and conceptualize the moment of approximation. The majority of the articles in this book is centered around this subject. There are at least two elaborate, 'structuralistic' approaches to the formalization of physical theories in which the aspect of approximation has been incorporated: the approach due to P. Suppes, J. Sneed, W. Stegmuller ("S-approach") and the approach of G. Lud wig and his co-workers ("L-approach"). The articles in this book correspondingly fall into three classes: presentation, elaboration and critique of the L-approach [Hartkamper/Schmidt, Ludwig, Neumann, Werner, Schmidt, Mayr, Kamiah, Majer, Grafe] or of the S-approach [Moulines, Balzer, Cooke], and articles referring to both approaches or concerned with related matters [Scheibe, Pfarr, Castrigiano]. Of course, this is only a rough classification and each article must be appraised in its own right.


Towards the Future of Fuzzy Logic

Towards the Future of Fuzzy Logic

Author: Rudolf Seising

Publisher: Springer

Published: 2015-05-26

Total Pages: 382

ISBN-13: 3319187503

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This book provides readers with a snapshot of the state-of-the art in fuzzy logic. Throughout the chapters, key theories developed in the last fifty years as well as important applications to practical problems are presented and discussed from different perspectives, as the authors hail from different disciplines and therefore use fuzzy logic for different purposes. The book aims at showing how fuzzy logic has evolved since the first theory formulation by Lotfi A. Zadeh in his seminal paper on Fuzzy Sets in 1965. Fuzzy theories and implementation grew at an impressive speed and achieved significant results, especially on the applicative side. The study of fuzzy logic and its practice spread all over the world, from Europe to Asia, America and Oceania. The editors believe that, thanks to the drive of young researchers, fuzzy logic will be able to face the challenging goals posed by computing with words. New frontiers of knowledge are waiting to be explored. In order to motivate young people to engage in the future development of fuzzy logic, fuzzy methodologies, fuzzy applications, etc., the editors invited a team of internationally respected experts to write the present collection of papers, which shows the present and future potentials of fuzzy logic from different disciplinary perspectives and personal standpoints.


Approximate Reasoning in Intelligent Systems, Decision and Control

Approximate Reasoning in Intelligent Systems, Decision and Control

Author: E. Sanchez

Publisher: Elsevier

Published: 2014-05-23

Total Pages: 208

ISBN-13: 1483294382

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Documents realistic applications of approximate reasoning techniques, with emphasis placed on operational systems. The papers presented explore new areas of practical decision-making and control systems by considering important aspects of fuzzy logic theory and the latest developments in the field of expert systems. Specific fields of application covered include modelling and control, management, planning, diagnostics, finance and software. Contains 12 papers.


Fuzzy Sets, Logics and Reasoning about Knowledge

Fuzzy Sets, Logics and Reasoning about Knowledge

Author: Didier Dubois

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 421

ISBN-13: 9401716528

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Fuzzy Sets, Logics and Reasoning about Knowledge reports recent results concerning the genuinely logical aspects of fuzzy sets in relation to algebraic considerations, knowledge representation and commonsense reasoning. It takes a state-of-the-art look at multiple-valued and fuzzy set-based logics, in an artificial intelligence perspective. The papers, all of which are written by leading contributors in their respective fields, are grouped into four sections. The first section presents a panorama of many-valued logics in connection with fuzzy sets. The second explores algebraic foundations, with an emphasis on MV algebras. The third is devoted to approximate reasoning methods and similarity-based reasoning. The fourth explores connections between fuzzy knowledge representation, especially possibilistic logic and prioritized knowledge bases. Readership: Scholars and graduate students in logic, algebra, knowledge representation, and formal aspects of artificial intelligence.


Logic and Complexity

Logic and Complexity

Author: Richard Lassaigne

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 361

ISBN-13: 0857293923

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Logic and Complexity looks at basic logic as it is used in Computer Science, and provides students with a logical approach to Complexity theory. With plenty of exercises, this book presents classical notions of mathematical logic, such as decidability, completeness and incompleteness, as well as new ideas brought by complexity theory such as NP-completeness, randomness and approximations, providing a better understanding for efficient algorithmic solutions to problems. Divided into three parts, it covers: - Model Theory and Recursive Functions - introducing the basic model theory of propositional, 1st order, inductive definitions and 2nd order logic. Recursive functions, Turing computability and decidability are also examined. - Descriptive Complexity - looking at the relationship between definitions of problems, queries, properties of programs and their computational complexity. - Approximation - explaining how some optimization problems and counting problems can be approximated according to their logical form. Logic is important in Computer Science, particularly for verification problems and database query languages such as SQL. Students and researchers in this field will find this book of great interest.