Quantum Cognition Beyond Hilbert Space I: Fundamentals

摘要

The formalism of quantum theory in Hilbert space has been applied withsuccess to the modeling and explanation of several cognitive phenomena, whereastraditional cognitive approaches were problematical. However, this 'quantumcognition paradigm' was recently challenged by its proven impossibility tosimultaneously model 'question order effects' and 'response replicability'. InPart I of this paper we describe sequential dichotomic measurements within anoperational and realistic framework for human cognition elaborated byourselves, and represent them in a quantum-like 'extended Bloch representation'where the Born rule of quantum probability does not necessarily hold. In PartII we apply this mathematical framework to successfully model question ordereffects, response replicability and unpacking effects, thus opening the waytoward quantum cognition beyond Hilbert space.