This book examines the philosophical conception of abductive reasoning as developed by Charles S. Peirce, the founder of American pragmatism. It explores the historical and systematic connections of Peirce's original ideas and debates about their interpretations. Abduction is understood in a broad sense which covers the discovery and pursuit of hypotheses and inference to the best explanation. The analysis presents fresh insights into this notion of reasoning, which derives from effects to causes or from surprising observations to explanatory theories. The author outlines some logical and AI approaches to abduction as well as studies various kinds of inverse problems in astronomy, physics, medicine, biology, and human sciences to provide examples of retroductions and abductions. The discussion covers also everyday examples with the implication of this notion in detective stories, one of Peirce's own favorite themes. The author uses Bayesian probabilities to argue that explanatory abduction is a method of confirmation. He uses his own account of truth approximation to reformulate abduction as inference which leads to the truthlikeness of its conclusion. This allows a powerful abductive defense of scientific realism. This up-to-date survey and defense of the Peircean view of abduction may very well help researchers, students, and philosophers better understand the logic of truth-seeking.

This book constitutes a self-contained and unified approach to automated reasoning in multiple-valued logics (MVL) developed by the author. Moreover, it contains a virtually complete account of other approaches to automated reasoning in MVL. This is the first overview of this subfield of automated reasoning ever given. Finally, a variety of applications of automated reasoning in MVL including several short case studies are listed. Automated reasoning in non-classical logics is an essential subtask of many AI applications. Applications of MVL in particular include, for instance, hardware and software verification, reasoning with incomplete or inconsistent knowledge, and natural language processing. Therefore, efficient theorem proving methods in MVL are essential. In the historical part of the book it is demonstrated why existing approaches are inadequate. In the original part a simple, but powerful, concept called 'sets-as-signs' is introduced in the context of semantic tableaux, and subsequently is applied to a variety of calculi including resolution and dissolution. It is shown that 'sets-as-signs' yields a many-valued extension of the well-known relationship between classical logic and integer programming. As a consequence, automated reasoning in infinitely-valued logics can be done uniformly and efficiently for the first time.

This unique and contemporary text not only offers an introduction to proofs with a view towards algebra and analysis, a standard fare for a transition course, but also presents practical skills for upper-level mathematics coursework and exposes undergraduate students to the context and culture of contemporary mathematics. The authors implement the practice recommended by the Committee on the Undergraduate Program in Mathematics (CUPM) curriculum guide, that a modern mathematics program should include cognitive goals and offer a broad perspective of the discipline. Part I offers: An introduction to logic and set theory. Proof methods as a vehicle leading to topics useful for analysis, topology, algebra, and probability. Many illustrated examples, often drawing on what students already know, that minimize conversation about "doing proofs." An appendix that provides an annotated rubric with feedback codes for assessing proof writing. Part II presents the context and culture aspects of the transition experience, including: 21st century mathematics, including the current mathematical culture, vocations, and careers. History and philosophical issues in mathematics. Approaching, reading, and learning from journal articles and other primary sources. Mathematical writing and typesetting in LaTeX. Together, these Parts provide a complete introduction to modern mathematics, both in content and practice. Table of Contents Part I - Introduction to Proofs Logic and Sets Arguments and Proofs Functions Properties of the Integers Counting and Combinatorial Arguments Relations Part II - Culture, History, Reading, and Writing Mathematical Culture, Vocation, and Careers History and Philosophy of Mathematics Reading and Researching Mathematics Writing and Presenting Mathematics Appendix A. Rubric for Assessing Proofs Appendix B. Index of Theorems and Definitions from Calculus and Linear Algebra Bibliography Index Biographies Danilo R. Diedrichs is an Associate Professor of Mathematics at Wheaton College in Illinois. Raised and educated in Switzerland, he holds a PhD in applied mathematical and computational sciences from the University of Iowa, as well as a master's degree in civil engineering from the Ecole Polytechnique Federale in Lausanne, Switzerland. His research interests are in dynamical systems modeling applied to biology, ecology, and epidemiology. Stephen Lovett is a Professor of Mathematics at Wheaton College in Illinois. He holds a PhD in representation theory from Northeastern University. His other books include Abstract Algebra: Structures and Applications (2015), Differential Geometry of Curves and Surfaces, with Tom Banchoff (2016), and Differential Geometry of Manifolds (2019).

This English translation of the author's original work has been thoroughly revised, expanded and updated.

The book covers logical systems known as "type-free" or "self-referential." These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications.

Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered.

Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field.

Prime numbers are beautiful, mysterious, and beguiling mathematical objects. The mathematician Bernhard Riemann made a celebrated conjecture about primes in 1859, the so-called Riemann hypothesis, which remains one of the most important unsolved problems in mathematics. Through the deep insights of the authors, this book introduces primes and explains the Riemann hypothesis. Students with a minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. The first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. The exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. Readers with more mathematical experience will then go deeper into the structure of primes and see how the Riemann hypothesis relates to Fourier analysis using the vocabulary of spectra. Readers with a strong mathematical background will be able to connect these ideas to historical formulations of the Riemann hypothesis.

In this book, leading experts discuss innovative components of complexity theory and chaos theory in economics.

The underlying perspective is that investigations of economic phenomena should view these phenomena not as deterministic, predictable and mechanistic but rather as process dependent, organic and always evolving.

The aim is to highlight the exciting potential of this approach in economics and its ability to overcome the limitations of past research and offer important new insights. The book offers a stimulating mix of theory, examples and policy.

By casting light on a variety of topics in the field, it will provide an ideal platform for researchers wishing to deepen their understanding and identify areas for further investigation.

This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics.

Topos theory provides an important setting and language for much of mathematical logic and set theory. It is well known that a typed language can be given for a topos to be regarded as a category of sets. This enables a fruitful interplay between category theory and set theory. However, one stumbling block to a logical approach to topos theory has been the treatment of geometric morphisms. This book presents a convenient and natural solution to this problem by developing the notion of a frame relative to an elementary topos. The authors show how this technique enables a logical approach to be taken to topics such as category theory relative to a topos and the relative Giraud theorem. The work is self-contained except that the authors presuppose a familiarity with basic category theory and topos theory. Logicians, set and category theorists, and computer scientist working in the field will find this work essential reading.

This book focuses on one of the major challenges of the newly created scientific domain known as data science: turning data into actionable knowledge in order to exploit increasing data volumes and deal with their inherent complexity. Actionable knowledge has been qualitatively and intensively studied in management, business, and the social sciences but in computer science and engineering, its connection has only recently been established to data mining and its evolution, 'Knowledge Discovery and Data Mining' (KDD). Data mining seeks to extract interesting patterns from data, but, until now, the patterns discovered from data have not always been 'actionable' for decision-makers in Socio-Technical Organizations (STO). With the evolution of the Internet and connectivity, STOs have evolved into Cyber-Physical and Social Systems (CPSS) that are known to describe our world today. In such complex and dynamic environments, the conventional KDD process is insufficient, and additional processes are required to transform complex data into actionable knowledge. Readers are presented with advanced knowledge concepts and the analytics and information fusion (AIF) processes aimed at delivering actionable knowledge. The authors provide an understanding of the concept of 'relation' and its exploitation, relational calculus, as well as the formalization of specific dimensions of knowledge that achieve a semantic growth along the AIF processes. This book serves as an important technical presentation of relational calculus and its application to processing chains in order to generate actionable knowledge. It is ideal for graduate students, researchers, or industry professionals interested in decision science and knowledge engineering.

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.

During the past 25 years, set theory has developed in several interesting directions. The most outstanding results cover the application of sophisticated techniques to problems in analysis, topology, infinitary combinatorics and other areas of mathematics. This book contains a selection of contributions, some of which are expository in nature, embracing various aspects of the latest developments. Amongst topics treated are forcing axioms and their applications, combinatorial principles used to construct models, and a variety of other set theoretical tools including inner models, partitions and trees. Audience: This book will be of interest to graduate students and researchers in foundational problems of mathematics.

Nature-Inspired Optimization Algorithms, a comprehensive work on the most popular optimization algorithms based on nature, starts with an overview of optimization going from the classical to the latest swarm intelligence algorithm. Nature has a rich abundance of flora and fauna that inspired the development of optimization techniques, providing us with simple solutions to complex problems in an effective and adaptive manner. The study of the intelligent survival strategies of animals, birds, and insects in a hostile and ever-changing environment has led to the development of techniques emulating their behavior. This book is a lucid description of fifteen important existing optimization algorithms based on swarm intelligence and superior in performance. It is a valuable resource for engineers, researchers, faculty, and students who are devising optimum solutions to any type of problem ranging from computer science to economics and covering diverse areas that require maximizing output and minimizing resources. This is the crux of all optimization algorithms. Features: Detailed description of the algorithms along with pseudocode and flowchart Easy translation to program code that is also readily available in Mathworks website for some of the algorithms Simple examples demonstrating the optimization strategies are provided to enhance understanding Standard applications and benchmark datasets for testing and validating the algorithms are included This book is a reference for undergraduate and post-graduate students. It will be useful to faculty members teaching optimization. It is also a comprehensive guide for researchers who are looking for optimizing resources in attaining the best solution to a problem. The nature-inspired optimization algorithms are unconventional, and this makes them more efficient than their traditional counterparts.

This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.

The International Biometric Society (IBS) was formed at the First International Biometric Conference at Woods Hole on September 6, 1947. The History of the International Biometric Society presents a deep dive into the voluminous archival records, with primary focus on IBS's first fifty years. It contains numerous photos and extracts from the archival materials, and features many photos of important leaders who served IBS across the decades. Features: Describes events leading up to and at Woods Hole on September 6, 1947 that led to the formation of IBS Outlines key markers that shaped IBS after the 1947 formation through to the modern day Describes the regional and national group structure, and the formation of regions and national groups Describes events surrounding the key scientific journal of IBS, Biometrics, including the transfer of ownership to IBS, content, editors, policies, management, and importance Describes the other key IBS publications - Biometric Bulletin, Journal of Agricultural Biological and Environmental Statistics, and regional publications Provides details of International Biometric Conferences and key early symposia Describes IBS constitution and by-laws processes, and the evolution of business arrangements Provides a record of international officers, including regional presidents, national group secretaries, journal editors, and the locations of meetings Includes a gallery of international Presidents, and a gallery of Secretaries and Treasurers The History of the International Biometric Society will appeal to anyone interested in the activities of our statistical and biometrical forebearers. The focus is on issues and events that engaged the attention of the officers of IBS. Some of these records are riveting, some entertaining, some intriguing, and some colorful. Some of the issues covered were difficult to handle, but even these often resulted in changes that benefited IBS.

The International Biometric Society (IBS) was formed at the First International Biometric Conference at Woods Hole on September 6, 1947. The History of the International Biometric Society presents a deep dive into the voluminous archival records, with primary focus on IBS's first fifty years. It contains numerous photos and extracts from the archival materials, and features many photos of important leaders who served IBS across the decades. Features: Describes events leading up to and at Woods Hole on September 6, 1947 that led to the formation of IBS Outlines key markers that shaped IBS after the 1947 formation through to the modern day Describes the regional and national group structure, and the formation of regions and national groups Describes events surrounding the key scientific journal of IBS, Biometrics, including the transfer of ownership to IBS, content, editors, policies, management, and importance Describes the other key IBS publications - Biometric Bulletin, Journal of Agricultural Biological and Environmental Statistics, and regional publications Provides details of International Biometric Conferences and key early symposia Describes IBS constitution and by-laws processes, and the evolution of business arrangements Provides a record of international officers, including regional presidents, national group secretaries, journal editors, and the locations of meetings Includes a gallery of international Presidents, and a gallery of Secretaries and Treasurers The History of the International Biometric Society will appeal to anyone interested in the activities of our statistical and biometrical forebearers. The focus is on issues and events that engaged the attention of the officers of IBS. Some of these records are riveting, some entertaining, some intriguing, and some colorful. Some of the issues covered were difficult to handle, but even these often resulted in changes that benefited IBS.

In order to perform effective analysis of today’s information security systems, numerous components must be taken into consideration. This book presents a well-organized, consistent solution created by the author, which allows for precise multilevel analysis of information security systems and accounts for all of the significant details. Enabling the multilevel modeling of secure systems, the quality of protection modeling language (QoP-ML) approach provides for the abstraction of security systems while maintaining an emphasis on quality protection. This book introduces the basis of the QoP modeling language along with all the advanced analysis modules, syntax, and semantics. It delineates the steps used in cryptographic protocols and introduces a multilevel protocol analysis that expands current understanding. Introduces quality of protection evaluation of IT Systems Covers the financial, economic, and CO2 emission analysis phase Supplies a multilevel analysis of Cloud-based data centers Details the structures for advanced communication modeling and energy analysis Considers security and energy efficiency trade-offs for the protocols of wireless sensor network architectures Includes case studies that illustrate the QoP analysis process using the QoP-ML Examines the robust security metrics of cryptographic primitives Compares and contrasts QoP-ML with the PL/SQL, SecureUML, and UMLsec approaches by means of the SEQUAL framework The book explains the formal logic for representing the relationships between security mechanisms in a manner that offers the possibility to evaluate security attributes. It presents the architecture and API of tools that ensure automatic analysis, including the automatic quality of protection analysis tool (AQoPA), crypto metrics tool (CMTool), and security mechanisms evaluation tool (SMETool). The book includes a number of examples and case studies that illustrate the QoP analysis process by the QoP-ML. Every operation defined by QoP-ML is described within parameters of security metrics to help you better evaluate the impact of each operation on your system's security.

We humans are collectively driven by a powerful - yet not fully explained - instinct to understand. We would like to see everything established, proven, laid bare. The more important an issue, the more we desire to see it clarified, stripped of all secrets, all shades of gray. What could be more important than to understand the Universe and ourselves as a part of it? To find a window onto our origin and our destiny? This book examines how far our modern cosmological theories - with their sometimes audacious models, such as inflation, cyclic histories, quantum creation, parallel universes - can take us towards answering these questions. Can such theories lead us to ultimate truths, leaving nothing unexplained? Last, but not least, Heller addresses the thorny problem of why and whether we should expect to find theories with all-encompassing explicative power.

This open access book is the first ever collection of Karl Popper's writings on deductive logic. Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics. This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.

This volume presents the main results of the 4th International Conference on Multivariate Approximation, which was held at Witten-Bommerholz, September 24-29, 2000. Nineteen selected, peer-reviewed contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision.
Features and Topics:
interpolation and approximation on compact sets, kergin interpolation
error asymptotics
radial basis functions
energy minimizing configurations on the sphere
quadrature and cubature formulae
harmonic functions near a zero
blending functions
frames and approximation of inverse frame operators
The book is an essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.

Soft computing encompasses various computational methodologies, which, unlike conventional algorithms, are tolerant of imprecision, uncertainty, and partial truth. Soft computing technologies offer adaptability as a characteristic feature and thus permit the tracking of a problem through a changing environment. Besides some recent developments in areas like rough sets and probabilistic networks, fuzzy logic, evolutionary algorithms, and artificial neural networks are core ingredients of soft computing, which are all bio-inspired and can easily be combined synergetically.This book presents a well-balanced integration of fuzzy logic, evolutionary computing, and neural information processing. The three constituents are introduced to the reader systematically and brought together in differentiated combinations step by step. The text was developed from courses given by the authors and offers numerous illustrations as

This book presents the construction and resolution of 50 practical optimization problems and covers an exceptionally wide range, including games-associated problems (Unblock Me, Sudokus), logistical problems, and problems concerning plant distribution, production, operations scheduling, management and resource allocation. The problems are divided into 5 difficulty levels. Problems in the first few levels are focused on learning the model construction methodology, while those in the last level include complex optimization environments. For each problem solution, the specific steps are illustrated, promoting reader comprehension. In addition, all the models are implemented in an optimization library, LINGO, their solutions have been analyzed and their correct construction has been verified. The book also includes a simple guide to implementing models in LINGO in a straightforward manner and in any input data format (text files, spreadsheets or databases). As an ideal companion to the author's previously published work Modelling in Mathematical Programming, the book is intended as a basic tool for students of operations research, and for researchers in any advanced area involving mathematical programming.

Distributed and peer-to-peer (P2P) applications are increasing daily, and cyberattacks are constantly adopting new mechanisms to threaten the security and privacy of users in these Internet of Things (IoT) environments. Blockchain, a decentralized cryptographic-based technology, is a promising element for IoT security in manufacturing, finance, healthcare, supply chain, identity management, e-governance, defence, education, banking, and trading. Blockchain has the potential to secure IoT through repetition, changeless capacity, and encryption. Blockchain for Information Security and Privacy provides essential knowledge of blockchain usage in the mainstream areas of security, trust, and privacy in decentralized domains. This book is a source of technical information regarding blockchain-oriented software and applications. It provides tools to researchers and developers in both computing and software engineering to develop solutions and automated systems that can promote security, trust, and privacy in cyberspace. FEATURES Applying blockchain-based secured data management in confidential cyberdefense applications Securing online voting systems using blockchain Safeguarding electronic healthcare record (EHR) management using blockchain Impacting security and privacy in digital identity management Using blockchain-based security and privacy for smart contracts By providing an overview of blockchain technology application domains in IoT (e.g., vehicle web, power web, cloud internet, and edge computing), this book features side-by-side comparisons of modern methods toward secure and privacy-preserving blockchain technology. It also examines safety objectives, efficiency, limitations, computational complexity, and communication overhead of various applications using blockchain. This book also addresses the combination of blockchain and industrial IoT. It explores novel various-levels of information sharing systems.

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject. Volumes III and IV cover papers written in 1963-84 and are the result of a long collaboration with I. M. Singer on the Index Theory of elliptic operators.

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject. Volumes III and IV cover papers written in 1963-84 and are the result of a long collaboration with I. M. Singer on the Index Theory of elliptic operators.