  We present the fundamentals of the quantum theoretical approach we have
developed in the last decade to model cognitive phenomena that resisted
modeling by means of classical logical and probabilistic structures, like
Boolean, Kolmogorovian and, more generally, set theoretical structures. We
firstly sketch the operational-realistic foundations of conceptual entities,
i.e. concepts, conceptual combinations, propositions, decision-making entities,
etc. Then, we briefly illustrate the application of the quantum formalism in
Hilbert space to represent combinations of natural concepts, discussing its
success in modeling a wide range of empirical data on concepts and their
conjunction, disjunction and negation. Next, we naturally extend the quantum
theoretical approach to model some long-standing `fallacies of human
reasoning', namely, the `conjunction fallacy' and the `disjunction effect'.
Finally, we put forward an explanatory hypothesis according to which human
reasoning is a defined superposition of `emergent reasoning' and `logical
reasoning', where the former generally prevails over the latter. The quantum
theoretical approach explains human fallacies as the consequence of genuine
quantum structures in human reasoning, i.e. `contextuality', `emergence',
`entanglement', `interference' and `superposition'. As such, it is alternative
to the Kahneman-Tversky research programme, which instead aims to explain human
fallacies in terms of `individual heuristics and biases'.
