"Conflict, Complexity and Mathematical Social Science" provides a foundational mathematical approach to the modelling of social conflict. The book illustrates how theory and evidence can be mathematically deepened and how investigations grounded in social choice theory can provide the evidence needed to inform social practice. Countering criticism from constructivist viewpoints it shows how discourse is grounded in mathematical logic and mathematical structure. The modelling of social conflict is viewed as an application of mathematical social science and relevant models are drawn from each field of mathematical psychology, mathematical sociology, mathematical political science and mathematical economics. Unique in its multidisciplinary focus the book brings together powerful mathematical conceptualisations of the social world from a wide range of separate areas of inquiry, thereby providing a strong conceptual framework and an integrated account of social situations. It is a vital resource for all researchers in peace science, peace and conflict studies, politics, international relations, mathematical modelling in the social sciences and complexity theory.

Can a line be analysed mathematically such a way that it does not fall apart into a set of discrete points? Are there objects of pure mathematics that can change through time? L. E. J. Brouwer argued that the two questions are related and that the answer to both is "yes," introducing the concept of choice sequences. This book subjects Brouwer's choice sequences to a phenomenological critique in the style of Husserl.

This book is about the dynamics of coupled map lattices (CML) and of related spatially extended systems. It will be useful to post-graduate students and researchers seeking an overview of the state-of-the-art and of open problems in this area of nonlinear dynamics. The special feature of this book is that it describes the (mathematical) theory of CML and some related systems and their phenomenology, with some examples of CML modeling of concrete systems (from physics and biology). More precisely, the book deals with statistical properties of (weakly) coupled chaotic maps, geometric aspects of (chaotic) CML, monotonic spatially extended systems, and dynamical models of specific biological systems.

The 2005 BISC International Special Event-BISCSE 05 Forging the frontiers was held in the University of California, Berkeley, Where fuzzy logic began, from November 3-6, 2005. The successful applications of fuzzy logic and it s rapid growth suggest that the impact of fuzzy logic will be felt increasingly in coming years. Fuzzy logic is likely to play an especially important role in science and engineering, but eventually its influence may extend much farther. In many ways, fuzzy logic represents a significant paradigm shift in the aims of computing - a shift which reflects the fact that the human mind, unlike present day computers, possesses a remarkable ability to store and process information which is pervasively imprecise, uncertain and lacking in categoricity.

The chapters of the book are evolved from presentations made by selected participants at the meeting and organized in two books. The papers include reports from the different front of soft computing in various industries and address the problems of different fields of research in fuzzy logic, fuzzy set and soft computing. The book provides a collection of forty four (44) articles in two volumes."

The Equation of Knowledge: From Bayes' Rule to a Unified Philosophy of Science introduces readers to the Bayesian approach to science: teasing out the link between probability and knowledge. The author strives to make this book accessible to a very broad audience, suitable for professionals, students, and academics, as well as the enthusiastic amateur scientist/mathematician. This book also shows how Bayesianism sheds new light on nearly all areas of knowledge, from philosophy to mathematics, science and engineering, but also law, politics and everyday decision-making. Bayesian thinking is an important topic for research, which has seen dramatic progress in the recent years, and has a significant role to play in the understanding and development of AI and Machine Learning, among many other things. This book seeks to act as a tool for proselytising the benefits and limits of Bayesianism to a wider public. Features Presents the Bayesian approach as a unifying scientific method for a wide range of topics Suitable for a broad audience, including professionals, students, and academics Provides a more accessible, philosophical introduction to the subject that is offered elsewhere

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).

In modern society services and support provided by computer-based systems have become ubiquitous and indeed have started to fund amentally alter the way people conduct their business. Moreover, it has become apparent that among the great variety of computer technologies available to potential users a crucial role will be played by concurrent systems. The reason is that many commonly occurring phenomena and computer applications are highly con current : typical examples include control systems, computer networks, digital hardware, business computing, and multimedia systems. Such systems are characterised by ever increasing complexity, which results when large num bers of concurrently active components interact. This has been recognised and addressed within the computing science community. In particular, sev eral form al models of concurrent systems have been proposed, studied, and applied in practice. This book brings together two of the most widely used formalisms for de scribing and analysing concurrent systems: Petri nets and process algebras. On the one hand , process algebras allow one to specify and reason about the design of complex concurrent computing systems by means of algebraic operators corresponding to common programming constructs. Petri nets, on the other hand, provide a graphical representation of such systems and an additional means of verifying their correctness efficiently, as well as a way of expressing properties related to causality and concurrency in system be haviour.

Convexity of sets in linear spaces, and concavity and convexity of functions, lie at the root of beautiful theoretical results that are at the same time extremely useful in the analysis and solution of optimization problems, including problems of either single objective or multiple objectives. Not all of these results rely necessarily on convexity and concavity; some of the results can guarantee that each local optimum is also a global optimum, giving these methods broader application to a wider class of problems. Hence, the focus of the first part of the book is concerned with several types of generalized convex sets and generalized concave functions. In addition to their applicability to nonconvex optimization, these convex sets and generalized concave functions are used in the book's second part, where decision-making and optimization problems under uncertainty are investigated. Uncertainty in the problem data often cannot be avoided when dealing with practical problems. Errors occur in real-world data for a host of reasons. However, over the last thirty years, the fuzzy set approach has proved to be useful in these situations. It is this approach to optimization under uncertainty that is extensively used and studied in the second part of this book. Typically, the membership functions of fuzzy sets involved in such problems are neither concave nor convex. They are, however, often quasiconcave or concave in some generalized sense. This opens possibilities for application of results on generalized concavity to fuzzy optimization. Despite this obvious relation, applying the interface of these two areas has been limited to date. It is hoped that the combination of ideas and results from the field of generalized concavity on the one hand and fuzzy optimization on the other hand outlined and discussed in Generalized Concavity in Fuzzy Optimization and Decision Analysis will be of interest to both communities. Our aim is to broaden the classes of problems that the combination of these two areas can satisfactorily address and solve.

This volume, the 6th volume in the DRUMS Handbook series, is part of the after math of the successful ESPRIT project DRUMS (Defeasible Reasoning and Un certainty Management Systems) which took place in two stages from 1989-1996. In the second stage (1993-1996) a work package was introduced devoted to the topics Reasoning and Dynamics, covering both the topics of 'Dynamics of Rea soning', where reasoning is viewed as a process, and 'Reasoning about Dynamics', which must be understood as pertaining to how both designers of and agents within dynamic systems may reason about these systems. The present volume presents work done in this context. This work has an emphasis on modelling and formal techniques in the investigation of the topic "Reasoning and Dynamics," but it is not mere theory that occupied us. Rather research was aimed at bridging the gap between theory and practice. Therefore also real-life applications of the modelling techniques were considered, and we hope this also shows in this volume, which is focused on the dynamics of reasoning processes. In order to give the book a broader perspective, we have invited a number of well-known researchers outside the project but working on similar topics to contribute as well. We have very pleasant recollections of the project, with its lively workshops and other meetings, with the many sites and researchers involved, both within and outside our own work package."

In the year 2014, both Peter Koepke and Philip Welch are celebrating their 60th birthdays, and this festive occasion is celebrated with this Festschrift in their honour containing scientific contributions of their students, collaborators, colleagues and friends which cover the various different research ares of logic in which Peter and Philip are active.

In the last years, it was observed an increasing interest of computer scientists in the structure of biological molecules and the way how they can be manipulated in vitro in order to define theoretical models of computation based on genetic engineering tools. Along the same lines, a parallel interest is growing regarding the process of evolution of living organisms. Much of the current data for genomes are expressed in the form of maps which are now becoming available and permit the study of the evolution of organisms at the scale of genome for the first time. On the other hand, there is an active trend nowadays throughout the field of computational biology toward abstracted, hierarchical views of biological sequences, which is very much in the spirit of computational linguistics. In the last decades, results and methods in the field of formal language theory that might be applied to the description of biological sequences were pointed out.

Internal logic is the logic of content. The content is here arithmetic and the emphasis is on a constructive logic of arithmetic (arithmetical logic). Kronecker's general arithmetic of forms (polynomials) together with Fermat's infinite descent is put to use in an internal consistency proof. The view is developed in the context of a radical arithmetization of mathematics and logic and covers the many-faceted heritage of Kronecker's work, which includes not only Hilbert, but also Frege, Cantor, Dedekind, Husserl and Brouwer.

The book will be of primary interest to logicians, philosophers and mathematicians interested in the foundations of mathematics and the philosophical implications of constructivist mathematics. It may also be of interest to historians, since it covers a fifty-year period, from 1880 to 1930, which has been crucial in the foundational debates and their repercussions on the contemporary scene.

Fuzzy logic is a relatively new concept in science applications. Hitherto, fuzzy logic has been a conceptual process applied in the field of risk management. Its potential applicability is much wider than that, however, and its particular suitability for expanding our understanding of processes and information in science and engineering in our post-modern world is only just beginning to be appreciated.

Written as a companion text to the author 's earlier volume "An Introduction to Fuzzy Logic Applications," the book is aimed at professional engineers and students and those with an interest in exploring the potential of fuzzy logic as an information processing kit with a wide variety of practical applications in the field of engineering science and develops themes and topics introduced in the author 's earlier text.

Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.

Intelligent Hybrid Systems: Fuzzy Logic, Neural Networks, and Genetic Algorithms is an organized edited collection of contributed chapters covering basic principles, methodologies, and applications of fuzzy systems, neural networks and genetic algorithms. All chapters are original contributions by leading researchers written exclusively for this volume. This book reviews important concepts and models, and focuses on specific methodologies common to fuzzy systems, neural networks and evolutionary computation. The emphasis is on development of cooperative models of hybrid systems. Included are applications related to intelligent data analysis, process analysis, intelligent adaptive information systems, systems identification, nonlinear systems, power and water system design, and many others. Intelligent Hybrid Systems: Fuzzy Logic, Neural Networks, and Genetic Algorithms provides researchers and engineers with up-to-date coverage of new results, methodologies and applications for building intelligent systems capable of solving large-scale problems.

Alfred Tarski was one of the two giants of the twentieth-century development of logic, along with Kurt Goedel. The four volumes of this collection contain all of Tarski's published papers and abstracts, as well as a comprehensive bibliography. Here will be found many of the works, spanning the period 1921 through 1979, which are the bedrock of contemporary areas of logic, whether in mathematics or philosophy. These areas include the theory of truth in formalized languages, decision methods and undecidable theories, foundations of geometry, set theory, and model theory, algebraic logic, and universal algebra.

Supervision of Petri Nets presents supervisory control theory for Petri nets with a legal set as the control goal. Petri nets model discrete event systems - dynamic systems whose evolution is completely determined by the occurrence of discrete events. Control laws, which guarantee that the system meets a set of specifications in the presence of uncontrollable and unobservable events, are studied and constructed, using application areas such as automated manufacturing and transportation systems. Supervision of Petri Nets introduces a new and mathematically sound approach to the subject. Existing results are unified by proposing a general mathematical language that makes extensive use of order theoretical ideas, and numerous new results are described, including ready-to-use algorithms that construct supervisory control laws for Petri nets. Supervision of Petri Nets is an excellent reference for researchers, and may also be used as a supplementary text for advanced courses on control theory.

The Handbook of Deontic Logic and Normative Systems presents a detailed overview of the main lines of research on contemporary deontic logic and related topics. Although building on decades of previous work in the field, it is the first collection to take into account the significant changes in the landscape of deontic logic that have occurred in the past twenty years. These changes have resulted largely, though not entirely, from the interaction of deontic logic with a variety of other fields, including computer science, legal theory, organizational theory, economics, and linguistics. This first volume of the Handbook is divided into three parts, containing nine chapters in all, each written by leading experts in the field. The first part concentrates on historical foundations. The second examines topics of central interest in contemporary deontic logic. The third presents some new logical frameworks that have now become part of the mainstream literature. A second volume of the Handbook is currently in preparation, and there may be a third after that.

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role.

The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.

Mathematical logic is essentially related to computer science. This book describes the aspects of mathematical logic that are closely related to each other, including classical logic, constructive logic, and modal logic. This book is intended to attend to both the peculiarities of logical systems and the requirements of computer science.In this edition, the revisions essentially involve rewriting the proofs, increasing the explanations, and adopting new terms and notations.

The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies.

This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.

Over the last few decades the interest of logicians and mathematicians in constructive and computational aspects of their subjects has been steadily growing, and researchers from disparate areas realized that they can benefit enormously from the mutual exchange of techniques concerned with those aspects. A key figure in this exciting development is the logician and mathematician Helmut Schwichtenberg to whom this volume is dedicated on the occasion of his 70th birthday and his turning emeritus. The volume contains 20 articles from leading experts about recent developments in Constructive set theory, Provably recursive functions, Program extraction, Theories of truth, Constructive mathematics, Classical vs. intuitionistic logic, Inductive definitions, and Continuous functionals and domains.

This volume comprises a collection of twenty written versions of invited as well as contributed papers presented at the conference held from 20-24 May 1996 in Beijing, China. It covers many areas of logic and the foundations of mathematics, as well as computer science. Also included is an article by M. Yasugi on the Asian Logic Conference which first appeared in Japanese, to provide a glimpse into the history and development of the series.