There are many books on lattice theory in the field, but none interfaces with the foundations of probability. This book does. It also develops new probability theories with rigorous foundations for decision theory and applies them to specific well-known problematic examples. There is only one other book that attempts this. It uses quantum probability theory from physics. The new probability theories developed in this book are different; they are not borrowed from physics but are explicitly designed for decision theory.

"The book explores the variety of meanings of contextuality across different disciplines, with the emphasis on quantum physics and on psychology."--

Founded in 1985 by Jean-Claude Falmagne and Jean-Paul Doignon, Knowledge Structure Theory (KST) constitutes a rigorous and current mathematical theory for the representation and the assessment of human knowledge. The seminal work of these authors initiated a highly active research strand with an ever-growing literature, mostly scattered across various technical journals.Starting from a concise but comprehensive introduction to its foundations, this volume provides a state-of-the-art review of KST. For the first time the volume brings together the most important theoretical developments and extensions of the last decade and presents new areas of application beyond education, with contributions by key researchers in the field.Among the important advances covered by this book are (1) a comprehensive treatment of probabilistic models in KST; (2) polytomous extensions of the theory; (3) KST-based psychological diagnostics and neuropsychological assessment; (4) the representation and assessment of cognitive skills in problem solving, as well as procedural skills. In addition, this book also includes an overview of available software for the application of KST.

Standard probability theory has been an enormously successful contribution to modern science. However, from many perspectives it is too narrow as a general theory of uncertainty, particularly for issues involving subjective uncertainty. This first-of-its-kind book is primarily based on qualitative approaches to probabilistic-like uncertainty, and includes qualitative theories for the standard theory as well as several of its generalizations.One of these generalizations produces a belief function composed of two functions: a probability function that measures the probabilistic strength of an uncertain event, and another function that measures the amount of ambiguity or vagueness of the event. Another unique approach of the book is to change the event space from a boolean algebra, which is closely linked to classical propositional logic, to a different event algebra that is closely linked to a well-studied generalization of classical propositional logic known as intuitionistic logic. Together, these new qualitative theories succeed where the standard probability theory fails by accounting for a number of puzzling empirical findings in the psychology of human probability judgments and decision making.

This is the first book combining research on the Global Environment, Catastrophic Risks and Economic Theory and Policy. Modern economic theory originated in the middle of the twentieth century when industrial expansion coupled with population growth led to a voracious use of natural resources and global environmental concerns. It is uncontested that, for the first time in recorded history, humans dominate the planet, changing the planet's atmosphere, its bodies of water, and the complex web of species that makes life on earth. This radical change in circumstances led to rethinking of the foundations of human organization and, in particular, the industrial economy and the economic theory behind it. This book brings together new approaches on multiple levels: environmental sustainability requires rethinking in terms of economic theory and policy as well as the considerations of catastrophic risk and extremal events. Leading experts address questions of economic governance, risk management, policy decision making and distribution across time and space.

Over the last ten years, elements of the formalism of quantum mechanics have been successfully applied beyond physics in areas such as psychology (especially cognition), economics and finance (especially in the formalization of so-called ‘decision making’), political science, and molecular biology. An important stream of work along these lines, commonly under the heading of quantum-like modeling, has been published in well regarded scientific journals, and major publishers have devoted entire books to the topic. This Festschrift honors a key figure in this field of research: Andrei Khrennikov, who made momentous contributions to it and to quantum foundations themselves. While honoring these contributions, and in order to do so, this Festschrift orients its reader toward the future rather than focusing on the past: it addresses future challenges and establishes the way forward in both domains, quantum-like modeling and quantum foundations. A while ago, in response to the developments of using the quantum formalism outside of quantum mechanics, the eminent quantum physicist Anton Zeilinger said, ‘Why should it be precisely the quantum mechanics formalism? Maybe its generalization would be more adequate...’ This volume responds to this statement by both showing the reasons for the continuing importance of quantum formalism and yet also considering pathways to such generalizations. Khrennikov’s work has been indispensable in establishing the great promise of quantum and quantum-like thinking in shaping the future of scientific research across the disciplines.

Lack of ability to think probabilistically makes one prone to a variety of irrational fears and vulnerable to scams designed to exploit probabilistic naiveté, impairs decision making under uncertainty, facilitates the misinterpretation of statistical information, and precludes critical evaluation of likelihood claims. Cognition and Chance presents an overview of the information needed to avoid such pitfalls and to assess and respond to probabilistic situations in a rational way. Dr. Nickerson investigates such questions as how good individuals are at thinking probabilistically and how consistent their reasoning under uncertainty is with principles of mathematical statistics and probability theory. He reviews evidence that has been produced in researchers' attempts to investigate these and similar types of questions. Seven conceptual chapters address such topics as probability, chance, randomness, coincidences, inverse probability, paradoxes, dilemmas, and statistics. The remaining five chapters focus on empirical studies of individuals' abilities and limitations as probabilistic thinkers. Topics include estimation and prediction, perception of covariation, choice under uncertainty, and people as intuitive probabilists. Cognition and Chance is intended to appeal to researchers and students in the areas of probability, statistics, psychology, business, economics, decision theory, and social dilemmas.