Uncertainty about the value of quantum probability for cognitive modeling

2013 ◽  
Vol 36 (3) ◽  
pp. 279-280 ◽  
Author(s):  
Christina Behme
Keyword(s):  
Probability Theory ◽  
Cognitive Modeling ◽  
Quantum Probability ◽  
Convincing Evidence ◽  
Logical Possibility ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Human Rationality

AbstractI argue that the overly simplistic scenarios discussed by Pothos & Busemeyer (P&B) establish at best that quantum probability theory (QPT) is a logical possibility allowing distinct predictions from classical probability theory (CPT). The article fails, however, to provide convincing evidence for the proposal that QPT offers unique insights regarding cognition and the nature of human rationality.

scholarly journals Probabilistic frames for non-Boolean phenomena

2016 ◽  
Vol 374 (2058) ◽  
pp. 20150102 ◽  
Author(s):  
Louis Narens
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Quantum Probability ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Foundations Of Probability ◽  
Quantifying Uncertainty ◽  
Behavioural Sciences ◽  
Generalized Probability ◽  
Provided Examples

Classical probability theory, as axiomatized in 1933 by Andrey Kolmogorov, has provided a useful and almost universally accepted theory for describing and quantifying uncertainty in scientific applications outside quantum mechanics. Recently, cognitive psychologists and mathematical economists have provided examples where classical probability theory appears inadequate but the probability theory underlying quantum mechanics appears effective. Formally, quantum probability theory is a generalization of classical probability. This article explores relationships between generalized probability theories, in particular quantum-like probability theories and those that do not have full complementation operators (e.g. event spaces based on intuitionistic logic), and discusses how these generalizations bear on important issues in the foundations of probability and the development of non-classical probability theories for the behavioural sciences.

scholarly journals Perspectives on Correctness in Probabilistic Inference from Psychology

2019 ◽  
Vol 22 ◽  
Author(s):  
Emmanuel M. Pothos ◽  
Irina Basieva ◽  
Andrei Khrennikov ◽  
James M. Yearsley
Keyword(s):  
Decision Making ◽  
Information Theory ◽  
Probability Theory ◽  
Probabilistic Inference ◽  
Quantum Probability ◽  
Conjunction Fallacy ◽  
Selection Task ◽  
Classical Probability ◽  
Wason Selection Task ◽  
Classical Probability Theory

Abstract Research into decision making has enabled us to appreciate that the notion of correctness is multifaceted. Different normative framework for correctness can lead to different insights about correct behavior. We illustrate the shifts for correctness insights with two tasks, the Wason selection task and the conjunction fallacy task; these tasks have had key roles in the development of logical reasoning and decision making research respectively. The Wason selection task arguably has played an important part in the transition from understanding correctness using classical logic to classical probability theory (and information theory). The conjunction fallacy has enabled a similar shift from baseline classical probability theory to quantum probability. The focus of this overview is the latter, as it represents a novel way for understanding probabilistic inference in psychology. We conclude with some of the current challenges concerning the application of quantum probability theory in psychology in general and specifically for the problem of understanding correctness in decision making.

Quantum probability and cognitive modeling: Some cautions and a promising direction in modeling physics learning

2013 ◽  
Vol 36 (3) ◽  
pp. 284-285
Author(s):  
Donald R. Franceschetti ◽  
Elizabeth Gire
Keyword(s):  
Probability Theory ◽  
Cognitive Modeling ◽  
Quantum Probability ◽  
Viable Alternative ◽  
Classical Probability ◽  
Physics Learning ◽  
Promising Direction ◽  
Quantum Formalism

AbstractQuantum probability theory offers a viable alternative to classical probability, although there are some ambiguities inherent in transferring the quantum formalism to a less determined realm. A number of physicists are now looking at the applicability of quantum ideas to the assessment of physics learning, an area particularly suited to quantum probability ideas.

scholarly journals Quantum mechanics as a generalized probability theory

2020 ◽  
Author(s):  
William Icefield
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Quantum Probability ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Principle Of Maximum Entropy ◽  
Principle Of Indifference ◽  
Reconstruction Project ◽  
Principle Of Maximum ◽  
Generalized Probability

When quantum mechanics is understood as a new generalized theory of probability - to be called the quantum probability theory - mysteries and controversies regarding quantum mechanics are dissolved. In the classical probability theory, that a measurement of some system requires an additional measurement apparatus is of insignificant importance - in the quantum probability theory, this comes to change. For one central single reason around a particular classical probability equation, the generalized probability view has not gained much traction, despite the fact that this essentially echoes (and provides logical underpinnings of) the conventional wisdom that `quantum mechanics just works as it is.' A classical probability axiom is just an initial intuition - there is no reason why we have to dogmatically cling onto axioms that can clearly be generalized. Issues with the principle of indifference in the classical probability theory are emphasized, along with the quantum reconstruction project of deriving quantum mechanics from epistemic requirements and potential quantum gravity consequences from the principle of maximum entropy.

If quantum probability = classical probability + bounded cognition; is this good, bad, or unnecessary?

2013 ◽  
Vol 36 (3) ◽  
pp. 304-305
Author(s):  
Tim Rakow
Keyword(s):  
Probability Theory ◽  
Probabilistic Models ◽  
Current Knowledge ◽  
Quantum Probability ◽  
Model Specification ◽  
Probability Models ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Knowledge States

AbstractQuantum probability models may supersede existing probabilistic models because they account for behaviour inconsistent with classical probability theory that are attributable to normal limitations of cognition. This intriguing position, however, may overstate weaknesses in classical probability theory by underestimating the role of current knowledge states and may under-employ available knowledge about the limitations of cognitive processes. In addition, flexibility in model specification has risks for the use of quantum probability.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Classical Probability ◽  
Quantum Process ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years Man’ko and co-authors have successfully reconciled quantum and classical probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely that mathematically the interference term in the squared amplitude of superposed wavefunctions has the form of a variance of a sum of correlated random variables and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classical probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. This hidden generic variable appears to be such an archetype.

scholarly journals Upgrading Probability via Fractions of Events

2016 ◽  
Vol 24 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Roman Frič ◽  
Martin Papčo
Keyword(s):  
Probability Theory ◽  
Random Variables ◽  
Random Variable ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Black And White ◽  
Random Events ◽  
Indicator Functions ◽  
Quantum Phenomena ◽  
Special Case

Abstract The influence of “Grundbegriffe” by A. N. Kolmogorov (published in 1933) on education in the area of probability and its impact on research in stochastics cannot be overestimated. We would like to point out three aspects of the classical probability theory “calling for” an upgrade: (i) classical random events are black-and-white (Boolean); (ii) classical random variables do not model quantum phenomena; (iii) basic maps (probability measures and observables { dual maps to random variables) have very different “mathematical nature”. Accordingly, we propose an upgraded probability theory based on Łukasiewicz operations (multivalued logic) on events, elementary category theory, and covering the classical probability theory as a special case. The upgrade can be compared to replacing calculations with integers by calculations with rational (and real) numbers. Namely, to avoid the three objections, we embed the classical (Boolean) random events (represented by the f0; 1g-valued indicator functions of sets) into upgraded random events (represented by measurable {0; 1}-valued functions), the minimal domain of probability containing “fractions” of classical random events, and we upgrade the notions of probability measure and random variable.

Reasoning About Measurements

2021 ◽  
pp. 31-92
Author(s):  
Jochen Rau
Keyword(s):  
Probability Theory ◽  
Quantum Theory ◽  
Physical Theory ◽  
Logical Structure ◽  
Statistical Independence ◽  
Classical Probability ◽  
Multiple Systems ◽  
Classical Probability Theory ◽  
Operational Requirement

This chapter explains the approach of ‘operationalism’, which in a physical theory admits only concepts associated with concrete experimental procedures, and lays out its consequences for propositions about measurements, their logical structure, and states. It illustrates these with toy examples where the ability to perform measurements is limited by design. For systems composed of several constituents this chapter introduces the notions of composite and reduced states, statistical independence, and correlations. It examines what it means for multiple systems to be prepared identically, and how this is represented mathematically. The operational requirement that there must be procedures to measure and prepare a state is examined, and the ensuing constraints derived. It is argued that these constraint leave only one alternative to classical probability theory that is consistent, universal, and fully operational, namely, quantum theory.

scholarly journals Algebras with two multiplications and their cumulants

2019 ◽  
Vol 52 (2) ◽  
pp. 157-186
Author(s):  
Adam Burchardt
Keyword(s):  
Probability Theory ◽  
Linear Space ◽  
Structure Constant ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Sum Of Products ◽  
Probabilistic Concept ◽  
Algebraic Formula

Abstract Cumulants are a notion that comes from the classical probability theory; they are an alternative to a notion of moments. We adapt the probabilistic concept of cumulants to the setup of a linear space equipped with two multiplication structures. We present an algebraic formula which involves those two multiplications as a sum of products of cumulants. In our approach, beside cumulants, we make use of standard combinatorial tools as forests and their colourings. We also show that the resulting statement can be understood as an analogue of Leonov–Shiryaev’s formula. This purely combinatorial presentation leads to some conclusions about structure constant of Jack characters.

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