The mathematical essence of contextuality lies in the similarity of random variables answering the same question in different contexts: contextuality means they are less similar when considered within their respective contexts than when isolated from them. This book presents a principled way of measuring this similarity and distinguishing two forms of context-dependence: contextuality and disturbance. While applicable across a broad range of disciplines, the concept of contextuality in this book is closest to that in quantum physics, where its special forms in the absence of disturbance are known as Bell nonlocality and KochenSpecker contextuality. This systematic introduction requires no prior familiarity with the subject and a very modest mathematical background. Structured as a textbook, complete with exercises and solutions, it is accessible to a broad readership and suitable for teaching. It will be useful to researchers and students in quantum mechanics, philosophy of science, psychology, computer science, linguistics, and probability theory.
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This book presents a rigorous and accessible introduction to the mathematical foundations of context-dependence and contextuality.
1. Preliminaries;
2. Context-dependence and contextuality;
3. Random
variables;
4. Systems and their couplings;
5. Contextuality I: basic
properties;
6. Contextuality II: dichotomizations and criteria of
contextuality;
7. Cyclic systems;
8. Consistently connected and consistified
systems;
9. Hidden variable models;
10. Measures of the degree of
contextuality;
11. Noncontextuality polytopes for cyclic systems; Index.
Ehtibar N. Dzhafarov is Professor Emeritus at Purdue University, USA. He has published over 170 papers in psychology, mathematics, philosophy, and foundations of quantum mechanics, and he has edited six books and four special journal issues. He served as President of the Society for Mathematical Psychology and has received a Humboldt Research Award. Janne V. Kujala is Associate Professor at the University of Turku, Finland. He has published over 60 papers in computational statistics, applied probability, foundations of quantum mechanics, mathematical psychology, and learning analytics, and has edited one special journal issue. He received the William K. Estes Early Career award in mathematical psychology. Víctor H. Cervantes is Assistant Professor at the University of Illinois Urbana-Champaign, USA. He was awarded a Fulbright Scholarship in 2014, and he received his doctoral degree in mathematical and computational cognitive science from Purdue University.
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