I reflect on several aspects of the general claim that a quantum-like approach to Cognitive Science is advantageous over classical approaches. The classical approaches refer to the symbolic approaches including models using a classical (Kolmogorov) probability calculus. The general claim seems to be right from a descriptive viewpoint but not necessarily from an explanatory viewpoint. The explanatory perspective needs a more careful analysis since adding some additional arbitrary parameters (such as phase shift parameters in quantum probabilities) does not automatically increase the explanatory value of the approach; rather, it seems to decrease it. I argue further that there is another class of traditional models - the class of geometric models of cognition. These models have a much longer tradition than the symbolic models. Interestingly, quantum mechanics does not contradict the geometric models. Hence, real progress at the meeting between quantum mechanics and cognitive science could be made by unifying these geometric models with ideas from quantum theory.
I reflect on several aspects of the general claim that a quantum-like approach to Cognitive Science is advantageous over classical approaches. The classical approaches refer to the symbolic approaches including models using a classical (Kolmogorov) probability calculus. The general claim seems to be right from a descriptive viewpoint but not necessarily from an explanatory viewpoint. The explanatory perspective needs a more careful analysis since adding some additional arbitrary parameters (such as phase shift parameters in quantum probabilities) does not automatically increase the explanatory value of the approach; rather, it seems to decrease it. I argue further that there is another class of traditional models - the class of geometric models of cognition. These models have a much longer tradition than the symbolic models. Interestingly, quantum mechanics does not contradict the geometric models. Hence, real progress at the meeting between quantum mechanics and cognitive science could be made by unifying these geometric models with ideas from quantum theory.
We reflect on several aspects of the general claim that a quantum-like approach to Cognitive Science is advantageous over classical approaches. The classical approaches refer to the symbolic approaches including models using a classical (Kolmogorov) probability calculus. The general claim seems to be right from a descriptive viewpoint but not necessarily from an explanatory viewpoint. The explanatory perspective needs a more careful analysis since adding some additional arbitrary parameters (such as phase shift parameters in quantum probabilities) does not automatically increase the explanatory value of the approach; rather, it seems to decrease it. We argue further that there is another class of traditional models - the class of geometric models of cognition. These models have a much longer tradition than the symbolic models. Interestingly, quantum mechanics does not contradict the geometric models. Hence, real progress at the meeting between quantum mechanics and cognitive science could be made by unifying these geometric models with ideas from quantum theory.
Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be bizarre and even ridiculous to apply ideas of quantum physics in order to improve current psychological and linguistic or semantic ideas. However, a closer look shows that there are some parallels in the development of quantum physics and advanced theories of cognitive science. In psychology, geometric models of meaning have a long tradition. However, they suffer from many shortcomings which are illustrated by discussing several puzzles of bounded rationality. In the first part of this article, we argue that the present account of quantum cognition - taking quantum probabilities rather than classical probabilities - can give a more systematic description of these puzzles than the alternate and rather eclectic treatments in the traditional framework of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always and does not automatically provide a deeper understanding and a true explanation of these puzzles. In the second part of this article, we explain the foundational issue from the perspective of Piron, Foulis, Randall, and others, and we apply it to the foundation of quantum cognition. In this connection, we show that quantum probabilities are of (virtual) conceptual necessity if grounded in an abstract algebraic framework of orthomodular lattices. This framework is motivated by assuming partial Boolean algebras (describing particular perspectives) that are combined into a uniform system while considering certain capacity restrictions. It is at this point that one important aspect of the whole idea of bounded rationality directly enters the theoretical scenery of quantum cognition: resource limitation.
The mathematical formalism of quantum mechanics has been successfully employed in the last years to model situations in which the use of classical structures gives rise to problematical situations, and where typically quantum effects, such as 'contextuality' and 'entanglement', have been recognized. This 'Quantum Interaction Approach' is briefly reviewed in this paper focusing, in particular, on the quantum models that have been elaborated to describe how concepts combine in cognitive science, and on the ensuing identification of a quantum structure in human thought. We point out that these results provide interesting insights toward the development of a unified theory for meaning and knowledge formalization and representation. Then, we analyze the technological aspects and implications of our approach, and a particular attention is devoted to the connections with symbolic artificial intelligence, quantum computation and robotics.
Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and finances. To distinguish such models from genuine quantum physical models, they often called quantum-like (although often people simply speak about, e.g., "quantum cognition"). These novel applications generate a number of foundational questions. Nowadays we can speak about a new science - foundations of quantum-like modeling. At the first stage this science was mainly about comparison of classical and quantum models, mainly in the probabilistic setting. It was found that statistical data from cognitive psychology violate some basic constraints posed on data by classical probability theory (Kolmogorov, 1933); in particular, the constraints given by the formula of total probability and Bell's type inequalities. Recently another question attracted some attention. In spite of real success in applications, there are no reason to believe that the quantum probability would cover completely all problems of, e.g., cognition. May be more general probability models have to be explored. A similar problem attracted a lot of attention in foundations of quantum physics culminating in a series of experiments to check Sorkin's equality for the triple-slit experiment by Weihs' group. In this note we present a similar test in the cognitive experimental setting. Performance of this test would either give further confirmation of the adequacy of the quantum probability model to cognitive applications or rejection of the conventional quantum model. Thus this note opens the door for a series of exciting experimental tests for the quantum-like model of cognition.
Abstract Quantum logics are non-classical logics defined from the mathematical formalism of quantum mechanics. While they are conventionally used to model inferential processes in physics, their scope of application is potentially much broader. We argue that quantum logics can serve as a framework to model human cognition, as their semantics seem able to capture not only how people make inferences about quantum mechanics, but also how they reason in general. We begin by defining quantum logics from an algebraic perspective in a classical first-order setting. Next, we present findings from cognitive science that suggest these logics are apt to characterize human reasoning. We then consider how such a connection between quantum logics and cognition contributes to longstanding philosophical debates about the epistemological status of logic and the problem of adoption. Finally, we discuss how cognitive applications of quantum logics could advance our understanding of human psychology and even quantum foundations.
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'.