Matrix Logic

Theory and Applications

Author: A. Stern

Publisher: Elsevier

ISBN: 1483295494

Category: Mathematics

Page: 220

View: 9063

In this pioneering work, the author develops a fundamental formulation of logic in terms of theory of matrices and vector spaces. The discovery of matrix logic represents a landmark in the further formalization of logic. For the first time the power of direct mathematical computation is applied to the whole set of logic operations, allowing the derivation of both the classical and modal logics from the same formal base. The new formalism allows the author to enlarge the alphabet of the truth-values with negative logic antivalues and to link matrix logic descriptions with the Dirac formulation of quantum theory - a result having fundamental implications and repercussions for science as a whole. As a unified language which permits a logical examination of the underlying phenomena of quantum field theory and vice versa, matrix logic opens new avenues for the study of fundamental interactions and gives rise to a revolutionary conclusion that physics as such can be viewed and studied as a logic in the fundamental sense. Finally, modelling itself on exact sciences, matrix logic does not refute the classical logic but instead incorporates it as a special deterministic limit. The book requires multidisciplinary knowledge and will be of interest to physicists, mathematicians, computer scientists and engineers.

An Introduction to Semi-tensor Product of Matrices and Its Applications

Author: Daizhan Cheng,Hongsheng Qi,Yin Zhao

Publisher: World Scientific

ISBN: 9814374687

Category: Mathematics

Page: 587

View: 6776

Proposes a generalization of Conventional Matrix Product (CMP), called the Semi-Tensor Product (STP). This book offers a comprehensive introduction to the theory of STP and its various applications, including logical function, fuzzy control, Boolean networks, analysis and control of nonlinear systems, amongst others.

Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices

Author: Adak, Amal Kumar,Manna, Debashree,Bhowmik, Monoranjan

Publisher: IGI Global

ISBN: 1522509151

Category: Computers

Page: 375

View: 6268

The use of fuzzy logic has become prominent in a variety of fields and applications. By implementing these logic sets, problems and uncertainties are more effectively resolved. Emerging Research on Applied Fuzzy Sets and Intuitionistic Fuzzy Matrices is a pivotal reference source for the latest scholarly perspectives on the interdisciplinary use of fuzzy logic theory, focusing on the application of sets and matrices. Highlighting theoretical framework and empirical research findings, this book is ideally designed for academics, practitioners, upper-level students, and professionals interested in an innovative overview of fuzzy logic sets and matrices.

Fuzzy Logic Theory and Applications

Part I and Part II

Author: Lotfi A Zadeh,Rafik A Aliev

Publisher: World Scientific Publishing

ISBN: 9813238194

Category: Computers

Page: 612

View: 1288

Nowadays, voluminous textbooks and monographs in fuzzy logic are devoted only to separate or some combination of separate facets of fuzzy logic. There is a lack of a single book that presents a comprehensive and self-contained theory of fuzzy logic and its applications. Written by world renowned authors, Lofti Zadeh, also known as the Father of Fuzzy Logic, and Rafik Aliev, who are pioneers in fuzzy logic and fuzzy sets, this unique compendium includes all the principal facets of fuzzy logic such as logical, fuzzy-set-theoretic, epistemic and relational. Theoretical problems are prominently illustrated and illuminated by numerous carefully worked-out and thought-through examples. This invaluable volume will be a useful reference guide for academics, practitioners, graduates and undergraduates in fuzzy logic and its applications.

Type-2 Fuzzy Logic: Theory and Applications

Author: Oscar Castillo,Patricia Melin

Publisher: Springer

ISBN: 3540762841

Category: Mathematics

Page: 244

View: 1858

This book describes new methods for building intelligent systems using type-2 fuzzy logic and soft computing (SC) techniques. The authors extend the use of fuzzy logic to a higher order, which is called type-2 fuzzy logic. Combining type-2 fuzzy logic with traditional SC techniques, we can build powerful hybrid intelligent systems that can use the advantages that each technique offers. This book is intended to be a major reference tool and can be used as a textbook.

Matrices

Theory and Applications

Author: Denis Serre

Publisher: Springer Science & Business Media

ISBN: 9781441976833

Category: Mathematics

Page: 289

View: 9418

In this book, Denis Serre begins by providing a clean and concise introduction to the basic theory of matrices. He then goes on to give many interesting applications of matrices to different aspects of mathematics and also other areas of science and engineering. With forty percent new material, this second edition is significantly different from the first edition. Newly added topics include: • Dunford decomposition, • tensor and exterior calculus, polynomial identities, • regularity of eigenvalues for complex matrices, • functional calculus and the Dunford–Taylor formula, • numerical range, • Weyl's and von Neumann’s inequalities, and • Jacobi method with random choice. The book mixes together algebra, analysis, complexity theory and numerical analysis. As such, this book will provide many scientists, not just mathematicians, with a useful and reliable reference. It is intended for advanced undergraduate and graduate students with either applied or theoretical goals. This book is based on a course given by the author at the École Normale Supérieure de Lyon.

Matrix Preconditioning Techniques and Applications

Author: Ke Chen

Publisher: Cambridge University Press

ISBN: 9780521838283

Category: Mathematics

Page: 568

View: 7594

A comprehensive introduction to preconditioning techniques, now an essential part of successful and efficient iterative solutions of matrices.

Transfer Matrix Method for Multibody Systems

Theory and Applications

Author: Xiaoting Rui,Guoping Wang,Jianshu Zhang

Publisher: Wiley

ISBN: 1118724801

Category: Mathematics

Page: 768

View: 1624

TRANSFER MATRIX METHOD FOR MULTIBODY SYSTEMS: THEORY AND APPLICATIONS Xiaoting Rui, Guoping Wang and Jianshu Zhang - Nanjing University of Science and Technology, China Featuring a new method of multibody system dynamics, this book introduces the transfer matrix method systematically for the first time. First developed by the lead author and his research team, this method has found numerous engineering and technological applications. Readers are first introduced to fundamental concepts like the body dynamics equation, augmented operator and augmented eigenvector before going in depth into precision analysis and computations of eigenvalue problems as well as dynamic responses. The book also covers a combination of mixed methods and practical applications in multiple rocket launch systems, self-propelled artillery as well as launch dynamics of on-ship weaponry. • Comprehensively introduces a new method of analyzing multibody dynamics for engineers • Provides a logical development of the transfer matrix method as applied to the dynamics of multibody systems that consist of interconnected bodies • Features varied applications in weaponry, aeronautics, astronautics, vehicles and robotics Written by an internationally renowned author and research team with many years' experience in multibody systems Transfer Matrix Method of Multibody System and Its Applications is an advanced level text for researchers and engineers in mechanical system dynamics. It is a comprehensive reference for advanced students and researchers in the related fields of aerospace, vehicle, robotics and weaponry engineering.

Guide to Discrete Mathematics

An Accessible Introduction to the History, Theory, Logic and Applications

Author: Gerard O'Regan

Publisher: Springer

ISBN: 3319445618

Category: Computers

Page: 370

View: 9312

This stimulating textbook presents a broad and accessible guide to the fundamentals of discrete mathematics, highlighting how the techniques may be applied to various exciting areas in computing. The text is designed to motivate and inspire the reader, encouraging further study in this important skill. Features: provides an introduction to the building blocks of discrete mathematics, including sets, relations and functions; describes the basics of number theory, the techniques of induction and recursion, and the applications of mathematical sequences, series, permutations, and combinations; presents the essentials of algebra; explains the fundamentals of automata theory, matrices, graph theory, cryptography, coding theory, language theory, and the concepts of computability and decidability; reviews the history of logic, discussing propositional and predicate logic, as well as advanced topics; examines the field of software engineering, describing formal methods; investigates probability and statistics.

Beyond Two: Theory and Applications of Multiple-Valued Logic

Author: Melvin Fitting,Ewa Orlowska

Publisher: Springer Science & Business Media

ISBN: 9783790815412

Category: Mathematics

Page: 374

View: 9939

This volume represents the state of the art for much current research in many-valued logics. Primary researchers in the field are among the authors. Major methodological issues of many-valued logics are treated, as well as applications of many-valued logics to reasoning with fuzzy information. Areas covered include: Algebras of multiple valued logics and their applications, proof theory and automated deduction in multiple valued logics, fuzzy logics and their applications, and multiple valued logics for control theory and rational belief.

Matrix Logic and Mind

A Probe into a Unified Theory of Mind and Matter

Author: A. Stern

Publisher: Elsevier

ISBN: 0080934137

Category: Mathematics

Page: 290

View: 418

In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental physics the author reaches the revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense, as compared with Einstein's view of physics as space-time geometry. This opens new, exciting prospects for the study of fundamental interactions. A formulation of logic in terms of matrix operators and logic vector spaces allows the author to tackle for the first time the intractable problem of cognition in a scientific manner. In the same way as the findings of Heisenberg and Dirac in the 1930s provided a conceptual and mathematical foundation for quantum physics, matrix operator logic supports an important breakthrough in the study of the physics of the mind, which is interpreted as a fractal of quantum mechanics. Introducing a concept of logic quantum numbers, the author concludes that the problem of logic and the intelligence code in general can be effectively formulated as eigenvalue problems similar to those of theoretical physics. With this important leap forward in the study of the mechanism of mind, the author concludes that the latter cannot be fully understood either within classical or quantum notions. A higher-order covariant theory is required to accommodate the fundamental effect of high-level intelligence. The landmark results obtained by the author will have implications and repercussions for the very foundations of science as a whole. Moreover, Stern's Matrix Logic is suitable for a broad spectrum of practical applications in contemporary technologies.

Computer Science – Theory and Applications

6th International Computer Science Symposium in Russia, CSR 2011, St. Petersburg, Russia, June 14-18, 2011. Proceedings

Author: Alexander Kulikov,Nikolay Vereshchagin

Publisher: Springer Science & Business Media

ISBN: 3642207111

Category: Computers

Page: 471

View: 9472

This book constitutes the proceedings of the 6th International Computer Science Symposium in Russia, CSR 2011, held in St. Petersburg, Russia, in June 2011. The 29 papers presented were carefully reviewed and selected from 76 submissions. The scope of topics of the symposium was quite broad and covered basically all areas of the foundations of theoretical computer science.

Linear Algebra and Matrix Analysis for Statistics

Author: Sudipto Banerjee,Anindya Roy

Publisher: CRC Press

ISBN: 1420095382

Category: Mathematics

Page: 580

View: 1224

Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra. The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction. The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Matrix Logic and Mind

A Probe Into a Unified Theory of Mind and Matter

Author: August Stern

Publisher: North Holland

ISBN: N.A

Category: Computers

Page: 290

View: 2700

In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental physics the author reaches the revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense, as compared with Einstein's view of physics as space-time geometry. This opens new, exciting prospects for the study of fundamental interactions. A formulation of logic in terms of matrix operators and logic vector spaces allows the author to tackle for the first time the intractable problem of cognition in a scientific manner. In the same way as the findings of Heisenberg and Dirac in the 1930s provided a conceptual and mathematical foundation for quantum physics, matrix operator logic supports an important breakthrough in the study of the physics of the mind, which is interpreted as a fractal of quantum mechanics. Introducing a concept of logic quantum numbers, the author concludes that the problem of logic and the intelligence code in general can be effectively formulated as eigenvalue problems similar to those of theoretical physics. With this important leap forward in the study of the mechanism of mind, the author concludes that the latter cannot be fully understood either within classical or quantum notions. A higher-order covariant theory is required to accommodate the fundamental effect of high-level intelligence. The landmark results obtained by the author will have implications and repercussions for the very foundations of science as a whole. Moreover, Stern's Matrix Logic is suitable for a broad spectrum of practical applications in contemporary technologies.

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition

Author: N.A

Publisher: ScholarlyEditions

ISBN: 1490110127

Category: Mathematics

Page: 1037

View: 9421

Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Approximation Theory. The editors have built Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Approximation Theory in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Probability, Combinatorics, and Chaos Theory: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Scalar, Vector, and Matrix Mathematics

Theory, Facts, and Formulas

Author: Dennis S. Bernstein

Publisher: Princeton University Press

ISBN: 1400888255

Category: Mathematics

Page: 1600

View: 1954

The essential reference book on matrices—now fully updated and expanded, with new material on scalar and vector mathematics Since its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics. In this revised and expanded edition, Dennis Bernstein combines extensive material on scalar and vector mathematics with the latest results in matrix theory to make this the most comprehensive, current, and easy-to-use book on the subject. Each chapter describes relevant theoretical background followed by specialized results. Hundreds of identities, inequalities, and facts are stated clearly and rigorously, with cross-references, citations to the literature, and helpful comments. Beginning with preliminaries on sets, logic, relations, and functions, this unique compendium covers all the major topics in matrix theory, such as transformations and decompositions, polynomial matrices, generalized inverses, and norms. Additional topics include graphs, groups, convex functions, polynomials, and linear systems. The book also features a wealth of new material on scalar inequalities, geometry, combinatorics, series, integrals, and more. Now more comprehensive than ever, Scalar, Vector, and Matrix Mathematics includes a detailed list of symbols, a summary of notation and conventions, an extensive bibliography and author index with page references, and an exhaustive subject index. Fully updated and expanded with new material on scalar and vector mathematics Covers the latest results in matrix theory Provides a list of symbols and a summary of conventions for easy and precise use Includes an extensive bibliography with back-referencing plus an author index

Matrix Algebra

Theory, Computations, and Applications in Statistics

Author: James E. Gentle

Publisher: Springer Science & Business Media

ISBN: 0387708723

Category: Computers

Page: 528

View: 2021

This much-needed work presents, among other things, the relevant aspects of the theory of matrix algebra for applications in statistics. Written in an informal style, it addresses computational issues and places more emphasis on applications than existing texts.

Fuzzy If-Then Rules in Computational Intelligence

Theory and Applications

Author: Da Ruan,Etienne E. Kerre

Publisher: Springer Science & Business Media

ISBN: 9780792378204

Category: Mathematics

Page: 322

View: 8447

During the last three decades, interest has increased significantly in the representation and manipulation of imprecision and uncertainty. Perhaps the most important technique in this area concerns fuzzy logic or the logic of fuzziness initiated by L. A. Zadeh in 1965. Since then, fuzzy logic has been incorporated into many areas of fundamental science and into the applied sciences. More importantly, it has been successful in the areas of expert systems and fuzzy control. The main body of this book consists of so-called IF-THEN rules, on which experts express their knowledge with respect to a certain domain of expertise. Fuzzy IF-THEN Rules in Computational Intelligence: Theory and Applications brings together contributions from leading global specialists who work in the domain of representation and processing of IF-THEN rules. This work gives special attention to fuzzy IF-THEN rules as they are being applied in computational intelligence. Included are theoretical developments and applications related to IF-THEN problems of propositional calculus, fuzzy predicate calculus, implementations of the generalized Modus Ponens, approximate reasoning, data mining and data transformation, techniques for complexity reduction, fuzzy linguistic modeling, large-scale application of fuzzy control, intelligent robotic control, and numerous other systems and practical applications. This book is an essential resource for engineers, mathematicians, and computer scientists working in fuzzy sets, soft computing, and of course, computational intelligence.

Code Design for Dependable Systems

Theory and Practical Applications

Author: Eiji Fujiwara

Publisher: John Wiley & Sons

ISBN: 047179273X

Category: Science

Page: 660

View: 7259

Theoretical and practical tools to master matrix code design strategy and technique Error correcting and detecting codes are essential to improving system reliability and have popularly been applied to computer systems and communication systems. Coding theory has been studied mainly using the code generator polynomials; hence, the codes are sometimes called polynomial codes. On the other hand, the codes designed by parity check matrices are referred to in this book as matrix codes. This timely book focuses on the design theory for matrix codes and their practical applications for the improvement of system reliability. As the author effectively demonstrates, matrix codes are far more flexible than polynomial codes, as they are capable of expressing various types of code functions. In contrast to other coding theory publications, this one does not burden its readers with unnecessary polynomial algebra, but rather focuses on the essentials needed to understand and take full advantage of matrix code constructions and designs. Readers are presented with a full array of theoretical and practical tools to master the fine points of matrix code design strategy and technique: * Code designs are presented in relation to practical applications, such as high-speed semiconductor memories, mass memories of disks and tapes, logic circuits and systems, data entry systems, and distributed storage systems * New classes of matrix codes, such as error locating codes, spotty byte error control codes, and unequal error control codes, are introduced along with their applications * A new parallel decoding algorithm of the burst error control codes is demonstrated In addition to the treatment of matrix codes, the author provides readers with a general overview of the latest developments and advances in the field of code design. Examples, figures, and exercises are fully provided in each chapter to illustrate concepts and engage the reader in designing actual code and solving real problems. The matrix codes presented with practical parameter settings will be very useful for practicing engineers and researchers. References lead to additional material so readers can explore advanced topics in depth. Engineers, researchers, and designers involved in dependable system design and code design research will find the unique focus and perspective of this practical guide and reference helpful in finding solutions to many key industry problems. It also can serve as a coursebook for graduate and advanced undergraduate students.