Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction ( $\text{CNTF}$ ) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted $\text{CNT}_{2}$ , was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that $\text{CNTF}=2\text{CNT}_{2}$ within a class of systems, called cyclic, that have played a prominent role in contextuality research.Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction ($\text{CNTF}$) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted $\text{CNT}_{2}$, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that $\text{CNTF}=2\text{CNT}_{2}$ within a class of systems, called cyclic, that have played a prominent role in contextuality research.

arXiv:2110.07113Oct 14, 20212 citations

On the Quantum-like Contextuality of Ambiguous Phrases

Daphne Wang, Mehrnoosh Sadrzadeh, Samson Abramsky +1 more

Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible.Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible.

arXiv:2107.14589Jul 19, 20219 citations

Contextuality (or lack thereof) is a property of systems of random variables. Among the measures of the degree of contextuality, two have played important roles. One of them, Contextual Fraction (

\text{CNTF}

) was proposed within the framework of the sheaf-theoretic approach to contextuality, and extended to arbitrary systems in the Contextuality-by-Default approach. The other, denoted

\text{CNT}_{2}

, was proposed as one of the measures within the Contextuality-by-Default approach. In this note, I prove that

\text{CNTF}=2\text{CNT}_{2}

within a class of systems, called cyclic, that have played a prominent role in contextuality research.