Contextuality in Random Variables

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 non-locality and Kochen–Specker contextuality. This systematic introduction requires no prior familiarity with the subject and only minimal 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.

• Introduces the theory of contextuality step by step, with rigorous proofs, extensive explanations, and exercises with solutions
• Presents the theory in abstract mathematical terms, mentioning but not confining the presentation to its applications in specific domains, thus making the book accessible to readers from a broad range of disciplines
• The first systematic presentation of the mathematical foundations of contextuality