Quantum Cognition Beyond Hilbert Space I: Fundamentals
This work addresses a foundational problem in cognitive science by proposing a new mathematical framework to overcome specific modeling challenges, potentially advancing quantum-like theories of cognition.
The paper tackles the limitations of the quantum cognition paradigm in Hilbert space by introducing an operational framework with an extended Bloch representation that does not require the Born rule, and successfully models cognitive phenomena like question order effects and response replicability.
The formalism of quantum theory in Hilbert space has been applied with success to the modeling and explanation of several cognitive phenomena, whereas traditional cognitive approaches were problematical. However, this 'quantum cognition paradigm' was recently challenged by its proven impossibility to simultaneously model 'question order effects' and 'response replicability'. In Part I of this paper we describe sequential dichotomic measurements within an operational and realistic framework for human cognition elaborated by ourselves, and represent them in a quantum-like 'extended Bloch representation' where the Born rule of quantum probability does not necessarily hold. In Part II we apply this mathematical framework to successfully model question order effects, response replicability and unpacking effects, thus opening the way toward quantum cognition beyond Hilbert space.