Probabilistic Lattices

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-kn... Read more

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. Contents: Introduction; Basic Lattice Theory; Pseudo Complemented Distributive Lattices; Probability and Coherence; Rationality, Heuristics, and Human Judgments of Probability; Orthomodular Modeling of Psychological Paradigms. Readership: Researchers in probability theory, logic and mathematical psychology. Key Features: Systematic, foundational development of probability theories based on Boolean and non-Boolean algebras; New theoretical foundations for theories of belief that emphasize the logical structure of event spaces; New methods for modeling the Kahnemann and Tversky heuristics and other psychological paradigms based on intuitionistic logic and a generalization of quantum logic Less