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Cambridge University Press eBooks

Context-Dependence and Contextuality

Ehtibar N. Dzhafarov, Janne V. Kujala, Victor Hernando Cervantes

Published Feb 28, 2026• 0 citations
Publisher
DOI
10.1017/9781009742221.003

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True contextuality beats direct influences in human decision making.

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In quantum physics there are well-known situations when measurements of the same property in different contexts (under different conditions) have the same probability distribution but cannot be represented by one and the same random variable. Such systems of random variables are called contextual. More generally, true contextuality is observed when different contexts force measurements of the same property (in psychology, responses to the same question) to be more dissimilar random variables than warranted by the difference of their distributions. The difference in distributions is itself a form of context-dependence but of another nature: it is attributable to direct causal influences exerted by contexts upon the random variables. The Contextuality-by-Default theory allows one to separate true contextuality from direct influences in the overall context-dependence. The Contextuality-by-Default analysis of numerous previous attempts to demonstrate contextuality in human judgments shows that all context-dependence in them can be accounted for by direct influences, with no true contextuality present. However, contextual systems in human behavior can be found. In this paper we present a series of crowd-sourcing experiments that exhibit true contextuality in simple decision making. The design of these experiments is an elaboration of one introduced in the Snow Queen experiment (Decision 5, 193-204, 2018), in which contextuality was for the first time demonstrated unequivocally. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

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The context-sensitivity of cognition has been demonstrated across a wide range of cognitive functions such as perception, memory, judgement and decision making. A related term, 'contextuality', has appeared from the field of quantum cognition, with mounting empirical evidence demonstrating that cognitive phenomena are sometimes contextual. Contextuality is a subtle notion that influences how we must view the properties of the cognitive phenomenon being studied. This article addresses the questions: What does it mean for a cognitive phenomenon to be contextual? What are the implications of contextuality for probabilistic models of cognition? How does contextuality differ from context-sensitivity? Starting from George Boole's "conditions of possible experience", we argue that a probabilistic model of a cognitive phenomenon is necessarily subject to an assumption of realism. By this we mean that the phenomenon being studied is assumed to have cognitive properties with a definite value independent of observation. In contrast, quantum cognition holds that a cognitive property maybe indeterminate, i.e., its properties do not have well established values prior to observation. We argue that indeterminacy is sufficient for incompatibility between cognitive properties. In turn, incompatibility is necessary for their contextuality. The significance of this argument for cognitive psychology is the following:if a cognitive phenomenon is found to be contextual, then there is reason to believe it may be indeterminate. We illustrate by means of two crowdsourced experiments how context-sensitivity and contextuality of cognitive properties in the form of facial trait judgements can be characterized from empirical data. Finally, we conceptually and formally contrast contextuality with context-sensitivity. We propose that both involve a form of context dependence, with causality being the differentiating factor: the context dependence in context-sensitivity has a causal basis, whereas the context dependence in contextuality is acausal. The resulting implications for probabilistic models of cognition are discussed.

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Contextuality and Sequential Measurement Order: Distinct Obstructions with a Shared MTT Interface

Peter Nero

Quantum contextuality and measurement order dependence are usually treated as distinct foundational problems. Contextuality is formulated as a logical obstruction to noncontextual value assignment, while order dependence is treated as a dynamical effect of sequential measurement. We show that these two phenomena arise from the same structural source. Within Modal Triplet Theory, each operational measurement context induces a context-dependent reduced dynamics, admissible domain, and associated basin atlas on the reduced state space. Contextuality corresponds to the impossibility of constructing a single global admissible basin assignment compatible with all contexts. Measurement order dependence is the dynamical manifestation of the same obstruction: sequential enforcement of incompatible basin atlases yields history-dependent outcome selection with positive probability. We prove an equivalence theorem establishing that contextuality and order dependence are two shadows—static and dynamical—of the same incompatibility. The framework aligns with Kochen–Specker theorems, contextuality inequalities, weak measurements, and sequential measurement experiments, while remaining consistent with projection-based outcome selection and the basin-measure reconstruction of the Born rule.

•Jan 15, 2026•0 citations

Contextuality

Springer eBooks•Jan 1, 2002•1 citation
In quantum physics there are well-known situations when measurements of the same property in different contexts (under different conditions) have the same probability distribution but cannot be represented by one and the same random variable. Such systems of random variables are called contextual. More generally, true contextuality is observed when different contexts force measurements of the same property (in psychology, responses to the same question) to be more dissimilar random variables than warranted by the difference of their distributions. The difference in distributions is itself a form of context-dependence but of another nature: it is attributable to direct causal influences exerted by contexts upon the random variables. The Contextuality-by-Default theory allows one to separate true contextuality from direct influences in the overall context-dependence. The Contextuality-by-Default analysis of numerous previous attempts to demonstrate contextuality in human judgments shows that all context-dependence in them can be accounted for by direct influences, with no true contextuality present. However, contextual systems in human behavior can be found. In this paper we present a series of crowd-sourcing experiments that exhibit true contextuality in simple decision making. The design of these experiments is an elaboration of one introduced in the Snow Queen experiment (Decision 5, 193-204, 2018), in which contextuality was for the first time demonstrated unequivocally. (PsycINFO Database Record (c) 2019 APA, all rights reserved).
The context-sensitivity of cognition has been demonstrated across a wide range of cognitive functions such as perception, memory, judgement and decision making. A related term, 'contextuality', has appeared from the field of quantum cognition, with mounting empirical evidence demonstrating that cognitive phenomena are sometimes contextual. Contextuality is a subtle notion that influences how we must view the properties of the cognitive phenomenon being studied. This article addresses the questions: What does it mean for a cognitive phenomenon to be contextual? What are the implications of contextuality for probabilistic models of cognition? How does contextuality differ from context-sensitivity? Starting from George Boole's "conditions of possible experience", we argue that a probabilistic model of a cognitive phenomenon is necessarily subject to an assumption of realism. By this we mean that the phenomenon being studied is assumed to have cognitive properties with a definite value independent of observation. In contrast, quantum cognition holds that a cognitive property maybe indeterminate, i.e., its properties do not have well established values prior to observation. We argue that indeterminacy is sufficient for incompatibility between cognitive properties. In turn, incompatibility is necessary for their contextuality. The significance of this argument for cognitive psychology is the following:if a cognitive phenomenon is found to be contextual, then there is reason to believe it may be indeterminate. We illustrate by means of two crowdsourced experiments how context-sensitivity and contextuality of cognitive properties in the form of facial trait judgements can be characterized from empirical data. Finally, we conceptually and formally contrast contextuality with context-sensitivity. We propose that both involve a form of context dependence, with causality being the differentiating factor: the context dependence in context-sensitivity has a causal basis, whereas the context dependence in contextuality is acausal. The resulting implications for probabilistic models of cognition are discussed.
Quantum contextuality and measurement order dependence are usually treated as distinct foundational problems. Contextuality is formulated as a logical obstruction to noncontextual value assignment, while order dependence is treated as a dynamical effect of sequential measurement. We show that these two phenomena arise from the same structural source. Within Modal Triplet Theory, each operational measurement context induces a context-dependent reduced dynamics, admissible domain, and associated basin atlas on the reduced state space. Contextuality corresponds to the impossibility of constructing a single global admissible basin assignment compatible with all contexts. Measurement order dependence is the dynamical manifestation of the same obstruction: sequential enforcement of incompatible basin atlases yields history-dependent outcome selection with positive probability. We prove an equivalence theorem establishing that contextuality and order dependence are two shadows—static and dynamical—of the same incompatibility. The framework aligns with Kochen–Specker theorems, contextuality inequalities, weak measurements, and sequential measurement experiments, while remaining consistent with projection-based outcome selection and the basin-measure reconstruction of the Born rule.