Victor H. Cervantes

Ehtibar N. Dzhafarov, Victor H. Cervantes

We introduce a new notion, that of a contextuality profile of a system. Rather than characterizing a system's contextuality by a single number, its overall degree of contextuality, we show how it can be characterized by a curve relating degree of contextuality to level at which the system is considered,\begin{array}{c|c|c|c|c|c|c|c} \textnormal{level} & 1 & \cdots & n-1 & n>1 & n+1 & \cdots & N\\ \hline \textnormal{degree} & 0 & \cdots & 0 & d_{n}>0 & d_{n+1}\geq d_{n} & \cdots & d_{N}\geq d_{N-1} \end{array},where N is the maximum number of variables per system's context. A system is represented at level n if one only considers the joint distributions with k\leq n variables, ignoring higher-order joint distributions. We show that the level-wise contextuality analysis can be used in conjunction with any well-constructed measure of contextuality. We present a method of concatenated systems to explore contextuality profiles systematically, and we apply it to the contextuality profiles for three major measures of contextuality proposed in the literature.

Daphne Wang, Mehrnoosh Sadrzadeh, Samson Abramsky et al.

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.