Action theory is the object of growing attention in a variety of scientific disciplines and this is the first volume to offer a synthetic view of the range of approaches possible in the topic. The volume focuses on the nexus of formal action theory with a startlingly diverse set of subjects, which range from logic, linguistics, artificial intelligence and automata theory to jurisprudence, deontology and economics. It covers semantic, mathematical and logical aspects of action, showing how the problem of action breaks the boundaries of traditional branches of logic located in syntactics and semantics and now lies on lies on the borderline between logical pragmatics and praxeology. The chapters here focus on specialized tasks in formal action theory, beginning with a thorough description and formalization of the language of action and moving through material on the differing models of action theory to focus on probabilistic models, the relations of formal action theory to deontic logic and its key applications in algorithmic and programming theory. The coverage thus fills a notable lacuna in the literary corpus and offers solid formal underpinning in cognitive science by approaching the problem of cognition as a composite action of mind.

This is the first text and monograph about DNA computing, a molecular approach that might revolutionize our thinking and ideas about computing. Although it is too soon to predict whether computer hardware to change from silicon to carbon and from microchips to DNA molecules, the theoretical premises have already been studied extensively. The book starts with an introduction to DNA-related matters, the basics of biochemistry and language and computation theory, and progresses to the most advanced mathematical theory developed so far in the area. All three authors are pioneers in the theory of DNA computing. Apart from being well-known scientists, they are known for their lucid writing. Many of their previous books have become classics in their field, and this book too is sure to follow their example.

The papers presented at the Symposium focused mainly on two fields of interest. First, there were papers dealing with the theoretical background of fuzzy logic and with applications of fuzzy reasoning to the problems of artificial intelligence, robotics and expert systems. Second, quite a large number of papers were devoted to fuzzy approaches to modelling of decision-making situations under uncertainty and vagueness and their applications to the evaluation of alternatives, system control and optimization.Apart from that, there were also some interesting contributions from other areas, like fuzzy classifications and the use of fuzzy approaches in quantum physics.This volume contains the most valuable and interesting papers presented at the Symposium and will be of use to all those researchers interested in fuzzy set theory and its applications.

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.

The volume analyses and develops David Makinson s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources of classical logic.

Among the contributions included in the volume, one chapter focuses on the inferential preferential method, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the (limited but important) role of logic in philosophy."

Reviews of the first edition: ..".Gerstein wants-very gently-to teach his students to think. He wants to show them how to wrestle with a problem (one that is more sophisticated than "plug and chug"), how to build a solution, and ultimately he wants to teach the students to take a statement and develop a way to prove it...Gerstein writes with a certain flair that I think students will find appealing. For instance, after his discussion of cardinals he has a section entitled Languages and Finite Automata. This allows him to illustrate some of the ideas he has been discussing with problems that almost anyone can understand, but most importantly he shows how these rather transparent problems can be subjected to a mathematical analysis. His discussion of how a machine might determine whether the sequence of words "Celui fromage de la parce que maintenant" is a legitimate French sentence is just delightful (and even more so if one knows a little French.)...I am confident that a student who works through Gerstein's book will really come away with (i) some mathematical technique, and (ii) some mathematical knowledge. -Steven Krantz, American Mathematical Monthly "This very elementary book is intended to be a textbook for a one-term course which introduces students into the basic notions of any higher mathematics courses...The explanations of the basic notions are combined with some main theorems, illustrated by examples (with solutions if necessary) and complemented by exercises. The book is well written and should be easily understandable to any beginning student." -S. Gottwald, Zentralblatt This textbook is intended for a one-term course whose goal is to ease the transition from lower-division calculus courses to upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, combinatorics, etc. It contains a wide-ranging assortment of examples and imagery to motivate and to enhance the underlying intuitions, as well as numerous exercises and a solutions manual for professors. The new material in this second edition includes four more topics in number theory, a brief introduction to complex numbers, and a section on graph theory and combinatorial topics related to graphs. Introducing these additional topics gives the reader an even broader view of the mathematical experience.

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.

Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic structures and deductive systems either of the same or different nature. The issue of preservation of properties is addressed.

The book is about Gentzen calculi for (the main systems of) modal logic. It is divided into three parts. In the first partwe introduce and discuss the main philosophical ideas related to proof theory, and we try to identify criteria for distinguishing good sequent calculi. In the second part we present the several attempts made from the 50's until today to provide modal logic with Gentzen calculi. In the third and and final part we analyse new calculi for modal logics, called tree-hypersequent calculi, which were recently introduced by the author. We show in a precise and clear way the main results that can be proved with and about them.

This is an overview of the current state of knowledge along with open problems and perspectives, clarified in such fields as non-standard inferences in description logics, logic of provability, logical dynamics and computability theory. The book includes contributions concerning the role of logic today, including unexpected aspects of contemporary logic and the application of logic. This book will be of interest to logicians and mathematicians in general.

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."

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.

This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability. The individual contributions touch on most of the core aspects of Davis' work and set it in a contemporary context. They analyse, discuss and develop many of the ideas and concepts that Davis put forward, including such issues as contemporary satisfiability solvers, essential unification, quantum computing and generalisations of Hilbert's tenth problem. The book starts out with a scientific autobiography by Davis, and ends with his responses to comments included in the contributions. In addition, it includes two previously unpublished original historical papers in which Davis and Putnam investigate the decidable and the undecidable side of Logic, as well as a full bibliography of Davis' work. As a whole, this book shows how Davis' scientific work lies at the intersection of computability, theoretical computer science, foundations of mathematics, and philosophy, and draws its unifying vision from his deep involvement in Logic.

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."

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.

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.

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.

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.

This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman's work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman's work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Goedel's incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as "What is logic?" and proposed particular positions regarding the foundations of mathematics including, for example, his "conceptual structuralism." The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman's work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman's distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.

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.

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.