  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.
