  Recently the mathematical formalism of quantum mechanics, especially methods
of quantum probability theory, started to be widely used in a variety of
applications outside of physics, e.g., cognition and psychology as well as
economy and finances. To distinguish such models from genuine quantum physical
models, they often called quantum-like (although often people simply speak
about, e.g., "quantum cognition"). These novel applications generate a number
of foundational questions. Nowadays we can speak about a new science -
foundations of quantum-like modeling. At the first stage this science was
mainly about comparison of classical and quantum models, mainly in the
probabilistic setting. It was found that statistical data from cognitive
psychology violate some basic constraints posed on data by classical
probability theory (Kolmogorov, 1933); in particular, the constraints given by
the formula of total probability and Bell's type inequalities. Recently another
question attracted some attention. In spite of real success in applications,
there are no reason to believe that the quantum probability would cover
completely all problems of, e.g., cognition. May be more general probability
models have to be explored. A similar problem attracted a lot of attention in
foundations of quantum physics culminating in a series of experiments to check
Sorkin's equality for the triple-slit experiment by Weihs' group. In this note
we present a similar test in the cognitive experimental setting. Performance of
this test would either give further confirmation of the adequacy of the quantum
probability model to cognitive applications or rejection of the conventional
quantum model. Thus this note opens the door for a series of exciting
experimental tests for the quantum-like model of cognition.

Neurons and Cognition;Probability;Quantum Physics