Bell’s inequality for conditional probabilities as a test for quantum-like behaviour of mind

We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an experimental test for quantum-like cognitive behaviour based on a generalization of the famous Bell’s inequality. This generalization is an analogue of Bell’s inequality, but for conditional probabilities. The use of conditional probabilities (instead of simultaneous probability distributions for pairs of observables in the original Bell’s inequality) gives the possibility to separate two problems which are mixed in the original Bell’s framework: nonlocality and nonclassical (quantum-like) probabilistic behaviour. Our inequality for conditional probabilities can be used for experiments with a single system (so we need not to prepare pairs of correlated systems) to find quantum-like behaviour. This possibility is extremely important in cognitive sciences where it is practically impossible to prepare pairs of precisely correlated cognitive systems. Thus the test of the original Bell’s inequality in cognitive and social sciences, or psychology is the problem of huge complexity. On the other hand, our test based on an analogue of Bell’s inequality for conditional probabilities can be easily performed in, e.g., psychological experiments or cognitive tasks.