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arXiv:1611.09212

Towards a new quantum cognition model

Riccardo Franco

Published Nov 23, 2016• 5 citations
arXivHTMLPDF

Abstract

This article presents a new quantum-like model for cognition explicitly based on knowledge. It is shown that this model, called QKT (quantum knowledge-based theory), is able to coherently describe some experimental results that are problematic for the prior quantum-like decision models. In particular, I consider the experimental results relevant to the post-decision cognitive dissonance, the problems relevant to the question order effect and response replicability, and those relevant to the grand-reciprocity equations. A new set of postulates is proposed, which evidence the different meaning given to the projectors and to the quantum states. In the final part, I show that the use of quantum gates can help to better describe and understand the evolution of quantum-like models.

DOI
10.48550/arxiv.1611.09212

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Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Oct 2, 2017•36 citations
This article presents a new quantum-like model for cognition explicitly based on knowledge. It is shown that this model, called QKT (quantum knowledge-based theory), is able to coherently describe some experimental results that are problematic for the prior quantum-like decision models. In particular, I consider the experimental results relevant to the post-decision cognitive dissonance, the problems relevant to the question order effect and response replicability, and those relevant to the grand-reciprocity equations. A new set of postulates is proposed, which evidence the different meaning given to the projectors and to the quantum states. In the final part, I show that the use of quantum gates can help to better describe and understand the evolution of quantum-like models.
Lately, so-called 'quantum models' based on parts of the mathematics of quantum mechanics, have been developed in decision theory and cognitive sciences to account for seemingly irrational or paradoxical human judgments. In this paper, we limit ourselves to such quantum-like models that address order effects. It has been argued that such models are able to account for existing and new empirical data, and meet some a priori predictions. From the quantum law of reciprocity, we derive new empirical predictions that we call the Grand Reciprocity equations, that must be satisfied by quantum-like models on the condition that they are non-degenerate. We show that existing non-degenerate quantum-like models for order effects fail this test on several existing data sets. We take it to suggest that degenerate quantum-like models should be the focus of forthcoming research in the area.
Uncertainty is an intrinsic part of life; most events, affairs, and questions are uncertain. A key problem in behavioral sciences is how the mind copes with uncertain information. Quantum probability theory offers a set of principles for inference, which align well with intuition about psychological processes in certain cases: cases when it appears that inference is contextual, the mental state changes as a result of previous judgments, or there is interference between different possibilities. We motivate the use of quantum theory in cognition and its key characteristics. For each of these characteristics, we review relevant quantum cognitive models and empirical support. The scope of quantum cognitive models encompasses fallacies in decision-making (such as the conjunction fallacy or the disjunction effect), question order effects, conceptual combination, evidence accumulation, perception, over-/underdistribution effects in memory, and more. Quantum models often formalize psychological ideas previously expressed in heuristic terms, allow unified explanations of previously disparate findings, and have led to several surprising, novel predictions. We also cast a critical eye on quantum models and consider some of their shortcomings and issues regarding their further development.
Quantum theory has inspired many new ideas for understanding Cognition and decision making. Given the nascent state of this field, many new challenges still remain. What are the strengths and unique contributions of these ideas? What are likely next steps in its development? How can it be applied to practical problems in cognitive science? Is this a rational or an irrational system of reasoning? What, if any, are its connections to neuroscience? Should the hard problem of consciousness be considered? These are questions that we try to address in this chapter, albeit at times in a limited way. We end with a debate with a fictitious skeptic (actually previous reviewers) of these ideas. Let us start by reviewing what we have covered so far. Contributions to cognition and decision We begin by summarizing the conclusions reached in previous chapters regarding the usefulness of quantum theory for modelling phenomena in cognition and decision. Chapter 1 provided some motivation and Chapter 2 provided a theoretical introduction to quantum theory. Chapter 3 presented a quantum model to account for question order effects on survey research. An exact and parameter-free test was derived from the model, which produced surprisingly accurate predictions for results obtained from three different large Gallup poll survey studies. Chapter 4 described a quantum model of probability judgments to account for findings that produce violations of classic probability theory, including conjunction and disjunction fallacies and order effects on inference.
This article examines the empirical evidence for interference effects in psychological experiments. It also reviews the competing interpretation of these effects with respect to traditional cognitive models and new quantum cognition models. The conclusion is that quantum theory provides unifying principles for explaining interference effects found in a wide variety of different experimental paradigms, and it provides a viable new theoretical approach for understanding cognition and decision making.
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision-making)—quantum-like modelling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects (RREs), cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely, sharp repeatable non-projective measurements — S R P ¯ . This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modelling is not the automatic borrowing of the quantum formalism. Exploring the class S R P ¯ highlights the role of non-commutativity of the state-update maps generated by measurement back action . Thus, ‘non-classicality’ in quantum physics as well as quantum-like modelling for cognition is based on two different types of non-commutativity, of operators (observables) and instruments (state-update maps): observable non-commutativity versus state-update-non-commutativity . We speculate that distinguishing quantum-like properties of the cognitive effects is the expression of the latter, or possibly both. This article is part of the theme issue ‘Quantum theory and topology in models of decision making (Part 1)’.
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 does QPT dynamics offer without any simplifying assumptions and is it likely that such flexibility will be relevant in cognitive modelling? We 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. a 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-system extension). We illustrate the relations between these models mathematically and numerically.This article is part of the themed issue 'Second quantum revolution: foundational questions'.