Originally published in 1966. Professor Rescher's aim is to develop a "logic of commands" in exactly the same general way which standard logic has already developed a "logic of truth-functional statement compounds" or a "logic of quantifiers". The object is to present a tolerably accurate and precise account of the logically relevant facets of a command, to study the nature of "inference" in reasonings involving commands, and above all to establish a viable concept of validity in command inference, so that the logical relationships among commands can be studied with something of the rigour to which one is accustomed in other branches of logic.

Putting the G into CAGD, the authors provide a much-needed practical and basic introduction to computer-aided geometric design. This book will help readers understand and use the elements of computer-aided geometric design, curves and surfaces, without the mathematical baggage that is necessary only for more advanced work. Though only minimal background in mathematics is needed to understand the bookis concepts, the book covers an amazing array of topics such as Bezier and B-spline curves and their corresponding surfaces, subdivision surfaces, and NURBS (Non-Uniform Rational B-Splines). Also included are techniques such as interpolation and least squares methods.

The book's objectives are to expose students to analyzing and formulating various patterns such as linear, quadratic, geometric, piecewise, alternating, summation-type, product-type, recursive and periodic patterns. The book will present various patterns graphically and analytically and show the connections between them. Graphical presentations include patterns at same scale, patterns at diminishing scale and alternating patterns.The book's goals are to train and expand students' analytical skills by presenting numerous repetitive-type problems that will lead to formulating results inductively and to the proof by induction method. These will start with formulating basic sequences and piecewise functions and transition to properties of Pascal's Triangle that are horizontally and diagonally oriented and formulating solutions to recursive sequences. The book will start with relatively straight forward problems and gradually transition to more challenging problems and open-ended research questions. The book's aims are to prepare students to establish a base of recognition and formulation of patterns that will navigate to study further mathematics such as Calculus, Discrete Mathematics, Matrix Algebra, Abstract Algebra, Difference Equations, and to potential research projects. The primary aims out of all are to make mathematics accessible and multidisciplinary for students with different backgrounds and from various disciplines.

Goedel's Incompleteness Theorems are among the most significant results in the foundation of mathematics. These results have a positive consequence: any system of axioms for mathematics that we recognize as correct can be properly extended by adding as a new axiom a formal statement expressing that the original system is consistent. This suggests that our mathematical knowledge is inexhaustible, an essentially philosophical topic to which this book is devoted. Basic material in predicate logic, set theory and recursion theory is presented, leading to a proof of incompleteness theorems. The inexhaustibility of mathematical knowledge is treated based on the concept of transfinite progressions of theories as conceived by Turing and Feferman. All concepts and results necessary to understand the arguments are introduced as needed, making the presentation self-contained and thorough.

Algorithms that control the computational processes relating sensors and actuators are indispensable for robot navigation and the perception of the world in which they move. Therefore, a deep understanding of how algorithms work to achieve this control is essential for the development of efficient and usable robots in a broad field of applications. An interdisciplinary group of scientists gathers every two years to document the progress in algorithmic foundations of robotics. This volume addresses in particular the areas of control theory, computational and differential geometry in robotics, and applications to core problems such as motion planning, navigation, sensor-based planning, and manipulation.

Intellectual property owners must continually exploit new ways of reproducing, distributing, and marketing their products. However, the threat of piracy looms as a major problem with digital distribution and storage technologies. Multimedia Watermarking Techniques and Applications covers all current and future trends in the design of modern systems that use watermarking to protect multimedia content. Containing the works of contributing authors who are worldwide experts in the field, this volume is intended for researchers and practitioners, as well as for those who want a broad understanding of multimedia security. In the wake of the explosive growth of digital entertainment and Internet applications, this book is the definitive resource on the subject for scientists, researchers, programmers, engineers, business managers, entrepreneurs, and investors.

Originally published in 1973. This book is directed to the student of philosophy whose background in mathematics is very limited. The author strikes a balance between material of a philosophical and a formal kind, and does this in a way that will bring out the intricate connections between the two. On the formal side, he gives particular care to provide the basic tools from set theory and arithmetic that are needed to study systems of logic, setting out completeness results for two, three, and four valued logic, explaining concepts such as freedom and bondage in quantificational logic, describing the intuitionistic conception of the logical operators, and setting out Zermelo's axiom system for set theory. On the philosophical side, he gives particular attention to such topics as the problem of entailment, the import of the Loewenheim-Skolem theorem, the expressive powers of quantificational logic, the ideas underlying intuitionistic logic, the nature of set theory, and the relationship between logic and set theory. There are exercises within the text, set out alongside the theoretical ideas that they involve.

Originally published in 1962. A clear and simple account of the growth and structure of Mathematical Logic, no earlier knowledge of logic being required. After outlining the four lines of thought that have been its roots - the logic of Aristotle, the idea of all the parts of mathematics as systems to be designed on the same sort of plan as that used by Euclid and his Elements, and the discoveries in algebra and geometry in 1800-1860 - the book goes on to give some of the main ideas and theories of the chief writers on Mathematical Logic: De Morgan, Boole, Jevons, Pierce, Frege, Peano, Whitehead, Russell, Post, Hilbert and Goebel. Written to assist readers who require a general picture of current logic, it will also be a guide for those who will later be going more deeply into the expert details of this field.

Originally published in 1937. A short account of the traditional logic, intended to provide the student with the fundamentals necessary for the specialized study. Suitable for working through individualy, it will provide sufficient knowledge of the elements of the subject to understand materials on more advanced and specialized topics. This is an interesting historic perspective on this area of philosophy and mathematics.

Originally published in 1934. This fourth edition originally published 1954., revised by C. W. K. Mundle. "It must be the desire of every reasonable person to know how to justify a contention which is of sufficient importance to be seriously questioned. The explicit formulation of the principles of sound reasoning is the concern of Logic". This book discusses the habit of sound reasoning which is acquired by consciously attending to the logical principles of sound reasoning, in order to apply them to test the soundness of arguments. It isn't an introduction to logic but it encourages the practice of logic, of deciding whether reasons in argument are sound or unsound. Stress is laid upon the importance of considering language, which is a key instrument of our thinking and is imperfect.

Recognized as a "Recommended" title by Choice for their April 2021 issue. Choice is a publishing unit at the Association of College & Research Libraries (ACR&L), a division of the American Library Association. Choice has been the acknowledged leader in the provision of objective, high-quality evaluations of nonfiction academic writing. Metaheuristic optimization is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity. This is usually applied when two or more objectives are to be optimized simultaneously. This book is presented with two major objectives. Firstly, it features chapters by eminent researchers in the field providing the readers about the current status of the subject. Secondly, algorithm-based optimization or advanced optimization techniques, which are applied to mostly non-engineering problems, are applied to engineering problems. This book will also serve as an aid to both research and industry. Usage of these methodologies would enable the improvement in engineering and manufacturing technology and support an organization in this era of low product life cycle. Features: Covers the application of recent and new algorithms Focuses on the development aspects such as including surrogate modeling, parallelization, game theory, and hybridization Presents the advances of engineering applications for both single-objective and multi-objective optimization problems Offers recent developments from a variety of engineering fields Discusses Optimization using Evolutionary Algorithms and Metaheuristics applications in engineering

Algorithms and Theory of Computation Handbook, Second Edition: Special Topics and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many of the existing chapters, this second edition contains more than 15 new chapters. This edition now covers self-stabilizing and pricing algorithms as well as the theories of privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics.

This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency. It also presents several systems of non-standard logics with paraconsistent features.

This book is a history of artificial intelligence, that audacious effort to duplicate in an artifact what we consider to be our most important property-our intelligence. It is an invitation for anybody with an interest in the future of the human race to participate in the inquiry.

A revised and expanded advanced-undergraduate/graduate text (first ed., 1978) about optimization algorithms for problems that can be formulated on graphs and networks. This edition provides many new applications and algorithms while maintaining the classic foundations on which contemporary algorithm

The study of graph structure has advanced in recent years with great strides: finite graphs can be described algebraically, enabling them to be constructed out of more basic elements. Separately the properties of graphs can be studied in a logical language called monadic second-order logic. In this book, these two features of graph structure are brought together for the first time in a presentation that unifies and synthesizes research over the last 25 years. The authors not only provide a thorough description of the theory, but also detail its applications, on the one hand to the construction of graph algorithms, and, on the other to the extension of formal language theory to finite graphs. Consequently the book will be of interest to graduate students and researchers in graph theory, finite model theory, formal language theory, and complexity theory.

In this 1987 text Professor Jech gives a unified treatment of the various forcing methods used in set theory, and presents their important applications. Product forcing, iterated forcing and proper forcing have proved powerful tools when studying the foundations of mathematics, for instance in consistency proofs. The book is based on graduate courses though some results are also included, making the book attractive to set theorists and logicians.

As the famous Pythagorean statement reads, 'Number rules the universe', and its veracity is proven in the many mathematical discoveries that have accelerated the development of science, engineering, and even philosophy. A so called "art of the mind", mathematics has guided and stimulated many aspects of human innovation down through the centuries. In this book, Marcel Danesi presents a historical overview of the ten greatest achievements in mathematics, and dynamically explores their importance and effects on our daily lives. Considered as a chain of events rather than isolated incidents, Danesi takes us from the beginnings of modern day mathematics with Pythagoras, through the concept of zero, right the way up to modern computational algorithms. Loaded with thought-provoking practical exercises and puzzles, Pythagoras' Legacy allows the reader to apply their knowledge and discover the significance of mathematics in their everyday lives.

This comprehensive two-volume work is devoted to the most general beginnings of mathematics. It goes back to Hausdorff's classic Set Theory (2nd ed., 1927), where set theory and the theory of functions were expounded as the fundamental parts of mathematics in such a way that there was no need for references to other sources. Along the lines of Hausdorff's initial work (1st ed., 1914), measure and integration theory is also included here as the third fundamental part of contemporary mathematics. The material about sets and numbers is placed in Volume 1 and the material about functions and measures is placed in Volume 2. Contents Historical foreword on the centenary after Felix Hausdorff's classic Set Theory Fundamentals of the theory of functions Fundamentals of the measure theory Historical notes on the Riesz - Radon - Frechet problem of characterization of Radon integrals as linear functionals

Neutrices and External Numbers: A Flexible Number System introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form of an extension of the nonstandard set of real numbers. Many illustrative examples are given. The book starts with detailed presentation of the algebraic structure of external numbers, then deals with the generalized Dedekind completeness property, applications in analysis, domains of validity of approximations of solutions of differential equations, particularly singular perturbations. Finally, it describes the family of algebraic laws characterizing the practice of calculations with external numbers. Features Presents scalar neutrices and external numbers, a mathematical model of order of magnitude within the real number system. Outlines complete algebraic rules for the neutrices and external numbers Conducts operational analysis of convergence and integration of functions known up to orders of magnitude Formalises a calculus of error propagation, covariant with algebraic operations Presents mathematical models of phenomena incorporating their necessary imprecisions, in particular related to the Sorites paradox

Future Data and Knowledge Base Systems will require new functionalities: richer data modelling capabilities, more powerful query languages, and new concepts of query answers. Future query languages will include functionalities such as hypothetical reasoning, abductive reasoning, modal reasoning, and metareasoning, involving knowledge and belief. Intentional answers will lead to cooperative query answering in which the answer to a query takes into consideration user's expectations. Non-classical logic plays an important role in this book for the formalization of new queries and new answers. It is shown how logic permits precise definitions for concepts like cooperative answers, subjective queries, or reliable sources of information, and gives a precise framework for reasoning about these complex concepts. It is worth noting that advances in knowledge management are not just an application domain for existing results in logic, but also require new developments in logic. The book is organized into 10 chapters which cover the areas of cooperative query answering (in the first three chapters), metareasoning and abductive reasoning (chapters 5 to 7), and, finally, hypothetical and subjunctive reasoning (last three chapters).

Dirk van Dalen's biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer's main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name 'intuitionism'. This made him one of the main protagonists in the 'foundation crisis' of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

Introduction to Mathematical Modeling and Chaotic Dynamics focuses on mathematical models in natural systems, particularly ecological systems. Most of the models presented are solved using MATLAB (R). The book first covers the necessary mathematical preliminaries, including testing of stability. It then describes the modeling of systems from natural science, focusing on one- and two-dimensional continuous and discrete time models. Moving on to chaotic dynamics, the authors discuss ways to study chaos, types of chaos, and methods for detecting chaos. They also explore chaotic dynamics in single and multiple species systems. The text concludes with a brief discussion on models of mechanical systems and electronic circuits. Suitable for advanced undergraduate and graduate students, this book provides a practical understanding of how the models are used in current natural science and engineering applications. Along with a variety of exercises and solved examples, the text presents all the fundamental concepts and mathematical skills needed to build models and perform analyses.

The rapidly expanding area of structural graph theory uses ideas of connectivity to explore various aspects of graph theory and vice versa. It has links with other areas of mathematics, such as design theory and is increasingly used in such areas as computer networks where connectivity algorithms are an important feature. Although other books cover parts of this material, none has a similarly wide scope. Ortrud R. Oellermann (Winnipeg), internationally recognised for her substantial contributions to structural graph theory, acted as academic consultant for this volume, helping shape its coverage of key topics. The result is a collection of thirteen expository chapters, each written by acknowledged experts. These contributions have been carefully edited to enhance readability and to standardise the chapter structure, terminology and notation throughout. An introductory chapter details the background material in graph theory and network flows and each chapter concludes with an extensive list of references.

'Points, questions, stories, and occasional rants introduce the 24 chapters of this engaging volume. With a focus on mathematics and peppered with a scattering of computer science settings, the entries range from lightly humorous to curiously thought-provoking. Each chapter includes sections and sub-sections that illustrate and supplement the point at hand. Most topics are self-contained within each chapter, and a solid high school mathematics background is all that is needed to enjoy the discussions. There certainly is much to enjoy here.'CHOICEEver notice how people sometimes use math words inaccurately? Or how sometimes you instinctively know a math statement is false (or not known)?Each chapter of this book makes a point like those above and then illustrates the point by doing some real mathematics through step-by-step mathematical techniques.This book gives readers valuable information about how mathematics and theoretical computer science work, while teaching them some actual mathematics and computer science through examples and exercises. Much of the mathematics could be understood by a bright high school student. The points made can be understood by anyone with an interest in math, from the bright high school student to a Field's medal winner.