Quantum Interaction Approach in Cognition, Artificial Intelligence and Robotics

The use of the mathematical formalism of quantum mechanics as a modeling instrument in disciplines different from physics is now a well established practice and has historically been motivated by different reasons. Firstly, this is due to the flexibility and richness of quantum structures (vector spaces, inner products, quantum probability, quantum logic connectives, etc.). Secondly, there are two aspects that are seemingly characteristic of quantum entities, i.e. contextuality and entanglement, and that appear instead independently of the microscopic nature of these entities. Thirdly, the fact that since the fifties and sixties several effects have been recognized in a variety of areas, such as, economics, biology, psychology ... in which the application of classical structures (set theory, classical logic, Kolmogorovian probability, etc.) is problematical and generates paradoxes. The Allais [1] and Ellsberg [2] paradoxes in economics, the conjunction fallacy [3] and disjunction effect [4] in decision theory, the representation of concepts and the formalization of meaning in cognitive science [5], are the most important examples of situations in which classical structures do not provide satisfactory results, but more general structures are needed. In particular, the impossibility of formalizing and structuring human and artificial knowledge slackened, notwithstanding the impressive technological success, in the development of some applied research fields, such as artificial intelligence and robotics.