Contextuality is About Identity of Random Variables

Abstract

Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is one and the same under different conditions leads to contradictions when one considers its joint distribution with other random variables (this is the essence of all Bell-type theorems). In our Contextuality-by-Default approach, instead of asking why or how the conditions force "one and the same" random variable to change "its" identity, any two random variables recorded under different conditions are considered different "automatically". They are never the same, nor are they jointly distributed, but one can always impose on them a joint distribution (probabilistic coupling). The special situations when there is a coupling in which these random variables are equal with probability 1 are considered non-contextual. Contextuality means that such couplings do not exist. We argue that the determination of the identity of random variables by conditions under which they are recorded is not a causal relationship and cannot violate laws of physics.

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• Probabilistic Foundations of Contextuality
• On Contextuality in Behavioral Data
• Contextuality-by-Default description of Bell tests: Contextuality as the rule not as an exception
• Contextuality or nonlocality; what would John Bell choose today?
• Neither Contextuality nor Nonlocality Admits Catalysts
• On Joint Distributions, Counterfactual Values, and Hidden Variables in Relation to Contextuality
• Some Examples of Contextuality in Physics: Implications to Quantum Cognition
• Replacing Nothing with Something Special: Contextuality-by-Default and Dummy Measurements
• Quantum Nonlocality: how does Nature do it?
• Advanced Analysis of Quantum Contextuality in a Psychophysical Double-Detection Experiment
• Towards a Quantum-Like Cognitive Architecture for Decision-Making
• More Causes Less Effect: Destructive Interference in Decision Making
• Closing Bell: Boxing black box simulations in the resource theory of contextuality
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
• Modelling contextuality by probabilistic programs with hypergraph semantics
• Commentary: Is the moon there if nobody looks -- Bell inequalities and physical reality
• Response: Commentary: Is the moon there if nobody looks? Bell inequalities and physical reality
• Statistical Contextual Explanation of Quantum Paradoxes
• On Universality of Classical Probability with Contextually Labeled Random Variables
• On contextuality and logic in scientific discourse: Reply to Aliakbarzadeh, Kitto, and Bruza