Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1911.01750

On contextuality and logic in scientific discourse: Reply to Aliakbarzadeh, Kitto, and Bruza

Ehtibar N. Dzhafarov

Published Nov 5, 2019• 0 citations
arXivHTMLPDF

Abstract

Aliakbarzadeh, Kitto, and Bruza (arXiv:1909.13048v1) criticize the Contextuality-by-Default (CbD) theory in three ways: (1) they claim an internal contradiction within the theory, that consists in both denying and accepting the equality of stochastically unrelated random variables; (2) they find CbD deficient because when one confines one's attention to consistently connected systems (those with no disturbance/signaling) one can dispense with the double-indexation of random variables; and (3) they see no relationship between double-indexation and ontic states. This commentary shows that (re$\:$1) the contradiction is inserted in the presentation of CbD by the authors of the paper; (re$\:$2) in the case of consistently connected systems CbD properly specializes to traditional understanding of contextuality; and (re$\:$3) if ontic states are understood as quantum states, they are simply not within the language of CbD, and if they are understood as domain probability spaces for context-sharing random variables, they can be trivially reconstructed.

DOI
10.48550/arxiv.1911.01750

Related papers

Measures of contextuality and non-contextuality

Janne V. Kujala, Ehtibar N. Dzhafarov

We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with 'disturbance' allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of non-contextuality in non-contextual systems. The other two CbD-based measures do not suggest ways in which degree of non-contextuality of a non-contextual system can be quantified. We find the same to be true for the contextual fraction measure developed by Abramsky, Barbosa and Mansfield. This measure of contextuality is confined to consistently connected systems, but CbD allows one to generalize it to arbitrary systems. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

arXiv:1903.07170•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Sep 16, 2019•36 citations

Contextuality with Disturbance and without: Neither Can Violate Substantive Requirements the Other Satisfies

Ehtibar N. Dzhafarov, Janne V. Kujala

Contextuality was originally defined only for consistently connected systems of random variables (those without disturbance/signaling). Contextuality-by-Default theory (CbD) offers an extension of the notion of contextuality to inconsistently connected systems (those with disturbance) by defining it in terms of the systems' couplings subject to certain constraints. Such extensions are sometimes met with skepticism. We pose the question of whether it is possible to develop a set of substantive requirements (i.e., those addressing a notion itself rather than its presentation form) such that (1) for any consistently connected system, these requirements are satisfied, but (2) they are violated for some inconsistently connected systems. We show that no such set of requirements is possible, not only for CbD but for all possible CbD-like extensions of contextuality. This follows from the fact that any extended contextuality theory T is contextually equivalent to a theory T' in which all systems are consistently connected. The contextual equivalence means the following: there is a bijective correspondence between the systems in T and T' such that the corresponding systems in T and T' are, in a well-defined sense, mere reformulations of each other, and they are contextual or noncontextual together.

arXiv:2302.11995•Entropy•Mar 28, 2023•4 citations

Contextuality and Indistinguishability

J. Acácio de Barros, Federico Holik, Décio Krause

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent.Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities.In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability.In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same.We will discuss how the consequences of this move may help us understand quantum contextuality.

•Jan 1, 2017•25 citations

Contextuality and Indistinguishability

J. Acácio de Barros, Federico Holik, Décio Krause

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen–Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality.

arXiv:1707.04656•Entropy•Aug 23, 2017•0 citations

Relating causal and probabilistic approaches to contextuality

Matt Jones

A primary goal in recent research on contextuality has been to extend this concept to cases of inconsistent connectedness, where observables have different distributions in different contexts. This article proposes a solution within the framework of probabi- listic causal models, which extend hidden-variables theories, and then demonstrates an equivalence to the contextuality-by-default (CbD) framework. CbD distinguishes contextuality from direct influences of context on observables, defining the latter purely in terms of probability distributions. Here, we take a causal view of direct influences, defining direct influence within any causal model as the probability of all latent states of the system in which a change of context changes the outcome of a measurement. Model-based contextuality (M-contextuality) is then defined as the necessity of stronger direct influences to model a full system than when considered individually. For consistently connected systems, M-contextuality agrees with standard contextuality. For general systems, it is proved that M-contextuality is equivalent to the property that any model of a system must contain 'hidden influences', meaning direct influences that go in opposite directions for different latent states, or equivalently signalling between observers that carries no information. This criterion can be taken as formalizing the 'no-conspiracy' principle that has been proposed in connection with CbD. M-contextuality is then proved to be equivalent to CbD-contextuality, thus providing a new interpretation of CbD-contextuality as the non-existence of a model for a system without hidden direct influences. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.

arXiv:1906.02716•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Sep 16, 2019•14 citations

Probabilistic foundations of contextuality

Ehtibar N. Dzhafarov, Janne V. Kujala

Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint, contextuality is mathematically impossible even if one generally allows (as one must) for random variables not to be jointly distributed. To avoid contradictions one has to adopt the Contextuality‐by‐Default approach: measurements made in different contexts are always distinct and stochastically unrelated to each other. Contextuality is reformulated then in terms of the (im)possibility of imposing on all the measurements in a system a joint distribution of a particular kind: such that any measurements of one and the same property made in different contexts satisfy a specified property, . In the traditional analysis of contextuality means “are equal to each other with probability 1”. However, if the system of measurements violates the “no‐disturbance principle”, due to signaling or experimental biases, then the meaning of has to be generalized, and the proposed generalization is “are equal to each other with maximal possible probability” (applied to any set of measurements of one and the same property). This approach is illustrated on arbitrary systems of binary measurements, including most of quantum systems of traditional interest in contextuality studies (irrespective of whether the “no‐disturbance” principle holds in them).

arXiv:1604.08412•Fortschritte der Physik•Sep 7, 2016•34 citations
Aliakbarzadeh, Kitto, and Bruza (arXiv:1909.13048v1) criticize the Contextuality-by-Default (CbD) theory in three ways: (1) they claim an internal contradiction within the theory, that consists in both denying and accepting the equality of stochastically unrelated random variables; (2) they find CbD deficient because when one confines one's attention to consistently connected systems (those with no disturbance/signaling) one can dispense with the double-indexation of random variables; and (3) they see no relationship between double-indexation and ontic states. This commentary shows that (re \:1) the contradiction is inserted in the presentation of CbD by the authors of the paper; (re \:2) in the case of consistently connected systems CbD properly specializes to traditional understanding of contextuality; and (re \:3) if ontic states are understood as quantum states, they are simply not within the language of CbD, and if they are understood as domain probability spaces for context-sharing random variables, they can be trivially reconstructed.
We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with 'disturbance' allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of non-contextuality in non-contextual systems. The other two CbD-based measures do not suggest ways in which degree of non-contextuality of a non-contextual system can be quantified. We find the same to be true for the contextual fraction measure developed by Abramsky, Barbosa and Mansfield. This measure of contextuality is confined to consistently connected systems, but CbD allows one to generalize it to arbitrary systems. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.
Contextuality was originally defined only for consistently connected systems of random variables (those without disturbance/signaling). Contextuality-by-Default theory (CbD) offers an extension of the notion of contextuality to inconsistently connected systems (those with disturbance) by defining it in terms of the systems' couplings subject to certain constraints. Such extensions are sometimes met with skepticism. We pose the question of whether it is possible to develop a set of substantive requirements (i.e., those addressing a notion itself rather than its presentation form) such that (1) for any consistently connected system, these requirements are satisfied, but (2) they are violated for some inconsistently connected systems. We show that no such set of requirements is possible, not only for CbD but for all possible CbD-like extensions of contextuality. This follows from the fact that any extended contextuality theory T is contextually equivalent to a theory T' in which all systems are consistently connected. The contextual equivalence means the following: there is a bijective correspondence between the systems in T and T' such that the corresponding systems in T and T' are, in a well-defined sense, mere reformulations of each other, and they are contextual or noncontextual together.
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent.Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities.In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability.In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen-Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same.We will discuss how the consequences of this move may help us understand quantum contextuality.
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen–Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality.
A primary goal in recent research on contextuality has been to extend this concept to cases of inconsistent connectedness, where observables have different distributions in different contexts. This article proposes a solution within the framework of probabi- listic causal models, which extend hidden-variables theories, and then demonstrates an equivalence to the contextuality-by-default (CbD) framework. CbD distinguishes contextuality from direct influences of context on observables, defining the latter purely in terms of probability distributions. Here, we take a causal view of direct influences, defining direct influence within any causal model as the probability of all latent states of the system in which a change of context changes the outcome of a measurement. Model-based contextuality (M-contextuality) is then defined as the necessity of stronger direct influences to model a full system than when considered individually. For consistently connected systems, M-contextuality agrees with standard contextuality. For general systems, it is proved that M-contextuality is equivalent to the property that any model of a system must contain 'hidden influences', meaning direct influences that go in opposite directions for different latent states, or equivalently signalling between observers that carries no information. This criterion can be taken as formalizing the 'no-conspiracy' principle that has been proposed in connection with CbD. M-contextuality is then proved to be equivalent to CbD-contextuality, thus providing a new interpretation of CbD-contextuality as the non-existence of a model for a system without hidden direct influences. This article is part of the theme issue 'Contextuality and probability in quantum mechanics and beyond'.
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint, contextuality is mathematically impossible even if one generally allows (as one must) for random variables not to be jointly distributed. To avoid contradictions one has to adopt the Contextuality‐by‐Default approach: measurements made in different contexts are always distinct and stochastically unrelated to each other. Contextuality is reformulated then in terms of the (im)possibility of imposing on all the measurements in a system a joint distribution of a particular kind: such that any measurements of one and the same property made in different contexts satisfy a specified property, . In the traditional analysis of contextuality means “are equal to each other with probability 1”. However, if the system of measurements violates the “no‐disturbance principle”, due to signaling or experimental biases, then the meaning of has to be generalized, and the proposed generalization is “are equal to each other with maximal possible probability” (applied to any set of measurements of one and the same property). This approach is illustrated on arbitrary systems of binary measurements, including most of quantum systems of traditional interest in contextuality studies (irrespective of whether the “no‐disturbance” principle holds in them).