Representation of Super-Quantum probability

[DarMM]

Classical probability theory can be represented with measure spaces and functions over them. Quantum Probability is given as the theory of Hilbert spaces and operators over them. Both more abstractly are handled by the theory of C*-algebras and their duals.

However I know of no structure for Super-Quantum Correlations violating Tsirelson's bound, such as those found in PR boxes. I've always seen them presented merely as a matrix of probabilities attached to events, but never seen a general mathematical theory. I was just wondering if there is one?

 

[atyy]

Poses the same question as the OP, but adds some context: https://arxiv.org/abs/1403.4621