Joint probabilities and quantum cognition

In this paper we discuss the existence of joint probability distributions for quantum-like response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.

[1]  Emmanuel Haven.  The wave-equivalent of the Black–Scholes option price: an interpretation , 2004 .

[2]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[3]  Patrick Suppes,et al.  Phase-oscillator computations as neural models of stimulus–response conditioning and response selection ☆ , 2010, 1010.3063.

[4]  James T. Townsend,et al.  Quantum dynamics of human decision-making , 2006 .

[5]  Patrick Suppes,et al.  Learning Pattern Recognition Through Quasi-Synchronization of Phase Oscillators , 2011, IEEE Transactions on Neural Networks.

[6]  J. Acacio de Barros,et al.  Quantum-like model of behavioral response computation using neural oscillators , 2012, Biosyst..

[7]  Patrick Suppes,et al.  When are Probabilistic Explanations Possible , 1981 .

[8]  Masanori Ohya,et al.  Quantum-Like Model for Decision Making Process in Two Players Game , 2011 .

[9]  Emmanuel Haven,et al.  The importance of probability interference in social science: rationale and experiment , 2007, 0709.2802.

[10]  P A Robinson,et al.  Interrelating anatomical, effective, and functional brain connectivity using propagators and neural field theory. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Jerome R. Busemeyer,et al.  Quantum Models of Cognition and Decision , 2012 .

[12]  Andrei Khrennikov,et al.  Bell's inequality: Physics meets Probability , 2007, 0709.3909.

[13]  P. Suppes,et al.  Quantum Mechanics and the Brain , 2007 .

[14]  Patrick Suppes,et al.  Diffraction with well-defined photon trajectories: A foundational analysis , 1994 .

[15]  Andrei Khrennikov,et al.  Ubiquitous Quantum Structure , 2010 .

[16]  Patrick Suppes,et al.  Probabilistic Results for Six Detectors in a Three-Particle GHZ Experiment , 2001 .

[17]  J. Busemeyer,et al.  Introduction to the special issue on quantum cognition , 2009, 1309.5673.

[18]  Emmanuel Haven,et al.  A discussion on embedding the Black-Scholes option pricing model in a quantum physics setting , 2002 .

[19]  E. Specker,et al.  The Problem of Hidden Variables in Quantum Mechanics , 1967 .

[20]  Patrick Suppes,et al.  Probabilistic inequalities and upper probabilities in quantum mechanical entanglement , 2010, 1010.3064.

[21]  N Gisin,et al.  No-signaling condition and quantum dynamics. , 2001, Physical review letters.

[22]  Emmanuel Haven.  Pilot-Wave Theory and Financial Option Pricing , 2005 .

[23]  Acacio De Barros J,et al.  Inequalities for dealing with detector inefficiencies in greenberger-horne-zeilinger-type experiments , 2000, Physical review letters.

[24]  Andrei Khrennikov,et al.  Quantum-like Description of Probabilistic Data from Shafir-Tversky Experiments: evidence of trigonometric and hyperbolic (!) interference , 2007, 0708.2993.

[25]  Patrick Suppes,et al.  A random-walk approach to interference , 1994 .

[26]  Patrick Suppes,et al.  A Proposed Experiment Showing that Classical Fields Can Violate Bell's Inequalities , 1996 .

[27]  Andrei Khrennikov.  Can fluctuations of classical random field produce quantum averages? , 2009, Optical Engineering + Applications.

[28]  J. Busemeyer,et al.  Empirical Comparison of Markov and Quantum models of decision-making , 2009 .

[29]  Patrick Suppes,et al.  Photons, billiards and chaos , 1996 .

[30]  Patrick Suppes,et al.  Violation of bell's inequalities with a local theory of photons , 1996 .

[31]  Patrick Suppes,et al.  A particle theory of the Casimir effect , 1995, quant-ph/9510010.

[32]  A. Tversky,et al.  The Disjunction Effect in Choice under Uncertainty , 1992 .

[33]  H. Stowell.  The emperor's new mind R. Penrose, Oxford University Press, New York (1989) 466 pp. $24.95 , 1990, Neuroscience.

[34]  Patrick Suppes,et al.  Quantum mechanics, interference, and the brain , 2009 .

[35]  Patrick Suppes,et al.  A Collection of Probabilistic Hidden-Variable Theorems and Counterexamples , 1996 .

[36]  Emmanuel Haven.  A Black-Scholes Schrödinger option price: ‘bit’ versus ‘qubit’ , 2003 .

[37]  Diederik Aerts,et al.  Quantum Structure in Cognition , 2008, 0805.3850.

[38]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[39]  J. Busemeyer,et al.  A quantum probability explanation for violations of ‘rational’ decision theory , 2009, Proceedings of the Royal Society B: Biological Sciences.

[40]  Emmanuel Haven,et al.  The quantum-like description of the dynamics of party governance in the US political system , 2012, 1206.2888.

[41]  Andrei Khrennikov,et al.  Quantum-like model of cognitive decision making and information processing , 2009, Biosyst..

[42]  Zheng Wang,et al.  Quantum Information Processing Explanation for Interactions between Inferences and Decisions , 2007, AAAI Spring Symposium: Quantum Interaction.

[43]  Abraham Pais,et al.  Inward bound : of matter and forces in the physical world / Abraham Pais , 1986 .

[44]  Emmanuel Haven,et al.  Quantum mechanics and violations of the sure-thing principle: The use of probability interference and other concepts , 2009 .