The Contextuality-by-Default View of the Sheaf-Theoretic Approach to Contextuality

Dzhafarov, Ehtibar N.

doi:10.1007/978-3-031-24117-8_15

Cited by 3 publications

(9 citation statements)

References 19 publications

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“…Together, these two results show the proportionality of all but one of these measures. The measure CNT3 based on negative probabilities was conjectured to be proportional to CNT2 in [9]. In this paper, we prove the truth of this conjecture by means of showing that false(n−1false)CNT3=CNTF.…”

Section: Introductionmentioning

confidence: 74%

“…In this section, we present the Contextuality-by-Default (CbD) approach to contextuality analysis [7,9–13]. A system of random variables is a set of double-indexed random variables Rqc, where c∈C is the context of the random variable, the conditions under which it is recorded, and q∈Q denotes its content , the property of which the random variable is a measurement.…”

Section: Contextuality-by-defaultmentioning

confidence: 99%

“…If a system scriptRn is consistently connected, the contextual fraction proposed by Abramsky et al [29,30] can be computed solving the following linear programming task: center center center4pt1emsolid none nonenone nonesolidfindmaximizingsubject toboldz1⊺boldzM(.)boldz≤p(.)∗ boldz≥0 1⊺boldz≤1. For any solution boldz∗, CNTFfalse(scriptRnfalse)=1−bold1⊺boldz∗. The previous task is equivalent to the one presented in [30] which uses a simpler representation of the system [9]. A solution boldz∗ generally does not define a probability distribution.…”

Section: Contextuality-by-defaultmentioning

confidence: 99%

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Measures of contextuality in cyclic systems and the negative probabilities measure CNT ₃

Camillo,

Cervantes

2024

Phil. Trans. R. Soc. A.

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Several principled measures of contextuality have been proposed for general systems of random variables (i.e. inconsistently connected systems). One such measure is based on quasi-couplings using negative probabilities (here denoted by CNT 3 , Dzhafarov & Kujala, 2016 Quantum interaction ). Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377 , 20190149. ( doi:10.1098/rsta.2019.0149 )) introduced a measure of contextuality, CNT 2 , that naturally generalizes to a measure of non-contextuality. Dzhafarov & Kujala (Dzhafarov & Kujala 2019 Phil. Trans. R. Soc. A 377 , 20190149. ( doi:10.1098/rsta.2019.0149 )) additionally conjectured that in the class of cyclic systems these two measures are proportional. Here we prove that conjecture is correct. Recently, Cervantes (Cervantes 2023 J. Math. Psychol . 112 , 102726. ( doi:10.1016/j.jmp.2022.102726 )) showed the proportionality of CNT 2 and the Contextual Fraction measure introduced by Abramsky & Brandenburger (Abramsky & Brandenburger 2011 New J. Phys . 13 , 113036. ( doi:10.1088/1367-2630/13/11/113036 )). The present proof completes the description of the interrelations of all contextuality measures proposed within or translated into the Contextuality-by-Default framework so far as they pertain to cyclic systems. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

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Section: Introductionmentioning

confidence: 74%

Section: Contextuality-by-defaultmentioning

confidence: 99%

Section: Contextuality-by-defaultmentioning

confidence: 99%

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Measures of contextuality in cyclic systems and the negative probabilities measure CNT ₃

Camillo,

Cervantes

2024

Phil. Trans. R. Soc. A.

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“…However, this difficulty can be easily remedied if one replaces a system under consideration with its consistified equivalent [8,9]. A consistified equivalent R † of a system R is a consistently connected system that depicts the same empirical or theoretical situation and is contextual if and only if R is contextual.…”

Section: Consistified Systemsmentioning

confidence: 99%

“…While this is the central issue for the Contextuality-by-Default (CbD) theory [4][5][6][7], the difference between disturbance and contextuality is not apparent in the formulations of the HVMs. However, one can effectively separate disturbance from contextuality by using the consistified systems introduced in Dzhafarov [8,9]. Any system of random variables can be reformulated as an equivalent, in a well-defined sense, system that has no disturbance (is consistently connected, in the CbD terminology).…”

Section: Introductionmentioning

confidence: 99%

Hidden variables, free choice, context-independence and all that

Dzhafarov

2024

Phil. Trans. R. Soc. A.

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This paper provides a systematic account of the hidden variable models (HVMs) formulated to describe systems of random variables with mutually exclusive contexts. Any such system can be described either by a model with free choice but generally context-dependent mapping of the hidden variables into observable ones, or by a model with context-independent mapping but generally compromised free choice. These two types of HVMs are equivalent, one can always be translated into another. They are also unfalsifiable, applicable to all possible systems. These facts, the equivalence and unfalsifiability, imply that freedom of choice and context-independent mapping are no assumptions at all, and they tell us nothing about freedom of choice or physical influences exerted by contexts as these notions would be understood in science and philosophy. The conjunction of these two notions, however, defines a falsifiable HVM that describes non-contextuality when applied to systems with no disturbance or to consistifications of arbitrary systems. This HVM is most adequately captured by the term ‘context-irrelevance’, meaning that no distribution in the model changes with context. This article is part of the theme issue ‘Quantum contextuality, causality and freedom of choice’.

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Generalised Winograd Schema and its Contextuality

Lo,

Sadrzadeh,

Mansfield

2023

Electron. Proc. Theor. Comput. Sci.

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Ambiguities in natural language give rise to probability distributions over interpretations. The distributions are often over multiple ambiguous words at a time; a multiplicity which makes them a suitable topic for sheaf-theoretic models of quantum contextuality. Previous research showed that different quantitative measures of contextuality correlate well with Psycholinguistic research on lexical ambiguities. In this work, we focus on coreference ambiguities and investigate the Winograd Schema Challenge (WSC), a test proposed by Levesque in 2011 to evaluate the intelligence of machines. The WSC consists of a collection of multiple-choice questions that require disambiguating pronouns in sentences structured according to the Winograd schema, in a way that makes it difficult for machines to determine the correct referents but remains intuitive for human comprehension. In this study, we propose an approach that analogously models the Winograd schema as an experiment in quantum physics. However, we argue that the original Winograd Schema is inherently too simplistic to facilitate contextuality. We introduce a novel mechanism for generalising the schema, rendering it analogous to a Bell-CHSH measurement scenario. We report an instance of this generalised schema, complemented by the human judgements we gathered via a crowdsourcing platform. The resulting model violates the Bell-CHSH inequality by 0.192, thus exhibiting contextuality in a coreference resolution setting.

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The Contextuality-by-Default View of the Sheaf-Theoretic Approach to Contextuality

Cited by 3 publications

References 19 publications

Measures of contextuality in cyclic systems and the negative probabilities measure CNT ₃

Measures of contextuality in cyclic systems and the negative probabilities measure CNT ₃

Hidden variables, free choice, context-independence and all that

Generalised Winograd Schema and its Contextuality

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The Contextuality-by-Default View of the Sheaf-Theoretic Approach to Contextuality

Cited by 3 publications

References 19 publications

Measures of contextuality in cyclic systems and the negative probabilities measure CNT 3

Measures of contextuality in cyclic systems and the negative probabilities measure CNT 3

Hidden variables, free choice, context-independence and all that

Generalised Winograd Schema and its Contextuality

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Product

Resources

About

Measures of contextuality in cyclic systems and the negative probabilities measure CNT ₃

Measures of contextuality in cyclic systems and the negative probabilities measure CNT ₃