Quantum-like dynamics applied to cognition: a consideration of available options

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Keywords: quantum-like dynamics, cognition, Schrödinger evolution, Lindblad evolution 2 Abstract Quantum Probability Theory (QPT) has provided a novel, rich mathematical framework for cognitive modelling, especially for situations which appear paradoxical from classical perspectives. This work concerns the dynamical aspects of QPT, as relevant to cognitive modelling. We aspire to shed light on how the mind's driving potentials (encoded in Hamiltonian and Lindbladian operators) impact the evolution of a mental state. Some existing QPT cognitive models do employ dynamical aspects when considering how a mental state changes with time, but it is often the case that several simplifying assumptions are introduced. What kind of modelling flexibility do QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? Permanent repository linkWe consider a series of nested QPT dynamical models, constructed with a view to accommodate results from a simple, hypothetical experimental paradigm on decision making. We consider Hamiltonians more complex than the ones which have traditionally been employed with a view to explore the putative explanatory value of this additional complexity. We then proceed to compare simple models with extensions regarding both the initial state (e.g., mixed state with a specific orthogonal decomposition; a general mixed state) and the dynamics (by introducing Hamiltonians which destroy the separability of the initial structure and by considering an open-systems extension). We illustrate the relations between these models mathematically and numerically.3

Is There a Conjunction Fallacy in Legal Probabilistic Decision Making?

“…The observed results motivate the consideration of an initial representation for the mental space in a tensor product structure as above, but also a thought process which “mixes” thoughts and beliefs between the two crimes (Pothos and Busemeyer, 2009 ; Broekaert et al, 2017 ). It is not our purpose presently to outline in detail a full cognitive model for the consideration of criminal cases and we focus on the technical elements of QPT potentially relevant for coverage of the results (for more relevant details see Pothos and Busemeyer, 2009 ; Trueblood and Busemeyer, 2011 ; Pothos et al, 2013 ; Wang et al, 2013 ; Narens, 2014 ).…”

Corrigendum: Is There a Conjunction Fallacy in Legal Probabilistic Decision Making?

“…It is not our purpose presently to outline in detail a full cognitive model for the consideration of criminal cases and we focus on the technical elements of QPT that allow for coverage of the results (for more relevant details see e.g., Pothos and Busemeyer, 2009 ; Trueblood and Busemeyer, 2011 ; Pothos et al, 2013 ; Wang et al, 2013 ; Narens, 2014 ). This has been corrected to: The observed results motivate the consideration of an initial representation for the mental space in a tensor product structure as above, but also a thought process which “mixes” thoughts and beliefs between the two crimes (Pothos and Busemeyer, 2009 ; Broekaert et al, 2017 ). It is not our purpose presently to outline in detail a full cognitive model for the consideration of criminal cases and we focus on the technical elements of QPT potentially relevant for coverage of the results (for more relevant details see Pothos and Busemeyer, 2009 ; Trueblood and Busemeyer, 2011 ; Pothos et al, 2013 ; Wang et al, 2013 ; Narens, 2014 ).…”

“…A correction has been made to Discussion , paragraph 10. The original sentences were: The observed results require an initial representation for the mental space in a tensor product structure as above, but also a thought process which “mixes” thoughts and beliefs between the two crimes (Pothos and Busemeyer, 2009 ; Broekaert et al, 2017 ). It is not our purpose presently to outline in detail a full cognitive model for the consideration of criminal cases and we focus on the technical elements of QPT that allow for coverage of the results (for more relevant details see e.g., Pothos and Busemeyer, 2009 ; Trueblood and Busemeyer, 2011 ; Pothos et al, 2013 ; Wang et al, 2013 ; Narens, 2014 ).…”

Quantum-like model of subjective expected utility

“…In Asano et al (2017) each lottery was represented in its own space and the pair of lotteries was represented in the direct sum of these two belief-spaces (cf. Pothos and Busemeyer, 2009;Broekaert et al, 2017), the Cartesian product of the belief-state spaces for individual lotteries. The use of a single belief space gives the possibility (absent in the model by Asano et al (2017)) to represent complementary (incompatible) systems of events corresponding to different lotteries.…”