From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality

Abstract

J. A tale of contextuality... K. ...and its logical implications III. Mathematical proofs of contextuality A. The Kochen-Specker Bell theorem B. KCBS inequality C. Peres-Mermin Square IV. The graph-theoretic approach of Cabello, Severini and Winter (CSW) A. General definitions B. The case of KCBS as a paradigmatic example C. Generalisation D. Link with Bell inequalities V. A sheaf-category theoretic approach to contextuality A. Pictorial representation 1. Probabilistic contextuality 2. Logical contextuality 3. Strong contextuality B. A brief presentation of the mathematical frameworks of the model 1. Correlation experiments in sheaf-theoretic approach 2. Compatibility of marginals 3. Hierarchy of contextuality C. New questions D. An illustration of contextuality VI. A hypergrah approach to contextuality VII. An operational version of contextuality A. A toy model B. An operational theory of contextuality C. Application to quantum mechanics D. Reinterpretation of the Kochen-Specker results VIII. Contextuality-by-Default A.

Contextuality and context-sensitivity in probabilistic models of cognition

“…Realism is bound up with the assumption that quantum observables (or cognitive properties) have definite values at all times. In the literature, this assumption is variously referred to as "realism" (Hermens, 2011), "outcome determinism" (Masse, 2021), "value definiteness" (Held, 2018). We will henceforth refer to the assumption as "determinism".…”