Classification of quantum-like models depending on interference (in)equalities

For long time the well-developed mathematical formalism of quantum mechanics has been widely and very successfully applied, not only in physics but in economics, biology, and cognitive psychology. This is due to the fact that the quantum probability paradigm is more “context”-based, and, as such, is often more suitable for taking into account various types of uncertainty and contextuality, which are essential elements of cognitive psychology and behavioral economics. Bell’s inequality (1964) for pairwise correlations is the crucial test of “quantumness” of the world of elementary particles. Meanwhile, the loophole-free experiment on Bell’s inequality was finally performed only a year ago. Quantum statistics violates not just Bell’s inequality but also the formula of total probability, as conditioned on two events. While quantum pairwise correlations can be stronger than classical (as demonstrated by Bell’s inequality), they still respect some quantum upper limit. If this limit is exceeded in an experiment, this would mean that the data is neither classical nor quantum. The same conclusion can be drawn from violation of the formula of total probability conditioned on three rather than just two events. We would like to draw an analogy between the three-slit experiment on interfering quantum particles and the 3-satisfiability problem.