153,569 research outputs found
Cognitive Foundations of Probability
Prediction is based on past cases. We assume that a predictor can rank eventualities according to their plausibility given any memory that consists of repetitions of past cases. In a companion paper, we show that under mild consistency requirements, these rankings can be represented by numerical functions, such that the function corresponding to each eventuality is linear in the number of case repetitions. In this paper we extend the analysis to rankings of events. Our main result is that a cancellation condition a la de Finetti implies that these functions are additive with respect to union of disjoint sets. If the set of past cases coincides with the set of possible eventualities, natural conditions are equivalent to ranking events by their empirical frequencies. More generally, our results may describe how individuals form probabilistic beliefs given cases that are only partially pertinent to the prediction problem at hand, and how this subjective measure of pertinence can be derived from likelihood rankings.Bayesian prior, case-based decision theory, qualitative probabilities
Extended Tensor Products and Generalization of the Notion of Entanglement
Motivated by the novel applications of the mathematical formalism of quantum
theory and its generalizations in cognitive science, psychology, social and
political sciences, and economics, we extend the notion of the tensor product
and entanglement. We also study the relation between conventional entanglement
of complex qubits and our generalized entanglement. Our construction can also
be used to describe entanglement in the framework of non-Archimedean physics.
It is also possible to construct tensor products of non-Archimedean (e.g.,
-adic) and complex Hilbert spaces.Comment: Proceedings of AIP, conference Foundations of Probability and Physics
6, Vaxjo, Sweden, June 2011, volume 142
Applying Quantum Principles to Psychology
This article starts out with a detailed example illustrating the utility of
applying quantum probability to psychology. Then it describes several
alternative mathematical methods for mapping fundamental quantum concepts (such
as state preparation, measurement, state evolution) to fundamental
psychological concepts (such as stimulus, response, information processing).
For state preparation, we consider both pure states and densities with
mixtures. For measurement, we consider projective measurements and positive
operator valued measurements. The advantages and disadvantages of each method
with respect to applications in psychology are discussed.Comment: one of the aims of this review paper is to attract attention of
experts in quantum information and probability (as well as in quantum
foundations) to a new rapidly growing field of applications of quantum
theory. The paper establishes the correspondence between concepts of quantum
theory and concepts of cognitive science and psychology. Submitted to Physica
Script
Cognitive Processes Involved in Solving Information Systems (IS) Design Problems
The author characterizes systems analysis and design as a cognitive problem-solving process and suggests that many implementations fail because Information Systems (IS) designers do not adequately understand the cognitive processes involved. The author explores problem understanding as well as the dynamic relationship between it and plan development and points to areas in which research will not only increase the probability of successful IS implementations but will also contribute to the theoretical foundations of IS
Operational Axioms for Quantum Mechanics
The mathematical formulation of Quantum Mechanics in terms of complex Hilbert
space is derived for finite dimensions, starting from a general definition of
"physical experiment" and from five simple Postulates concerning "experimental
accessibility and simplicity". For the infinite dimensional case, on the other
hand, a C*-algebra representation of physical transformations is derived,
starting from just four of the five Postulates via a Gelfand-Naimark-Segal
(GNS) construction. The present paper simplifies and sharpens the previous
derivation in version 1. The main ingredient of the axiomatization is the
postulated existence of "faithful states" that allows one to calibrate the
experimental apparatus. Such notion is at the basis of the operational
definitions of the scalar product and of the "transposed" of a physical
transformation. What is new in the present paper with respect to
quant-ph/0603011 is the operational deduction of an involution corresponding to
the "complex-conjugation" for effects, whose extension to transformations
allows to define the "adjoint" of a transformation when the extension is
composition-preserving.Comment: New improvements have been made. Work presented at the conference
"Foundations of Probability and Physics-4, Quantum Theory: Reconsideration of
Foundations-3" held on 4-9 June at the International Centre for Mathematical
Modelling in Physics, Engineering and Cognitive Sciences, Vaxjo University,
Sweden. Also contains an errata to "How to Derive the Hilbert-Space
Formulation of Quantum Mechanics From Purely Operational Axioms",
quant-ph/060301
On the Foundations of the Brussels Operational-Realistic Approach to Cognition
The scientific community is becoming more and more interested in the research
that applies the mathematical formalism of quantum theory to model human
decision-making. In this paper, we provide the theoretical foundations of the
quantum approach to cognition that we developed in Brussels. These foundations
rest on the results of two decade studies on the axiomatic and
operational-realistic approaches to the foundations of quantum physics. The
deep analogies between the foundations of physics and cognition lead us to
investigate the validity of quantum theory as a general and unitary framework
for cognitive processes, and the empirical success of the Hilbert space models
derived by such investigation provides a strong theoretical confirmation of
this validity. However, two situations in the cognitive realm, 'question order
effects' and 'response replicability', indicate that even the Hilbert space
framework could be insufficient to reproduce the collected data. This does not
mean that the mentioned operational-realistic approach would be incorrect, but
simply that a larger class of measurements would be in force in human
cognition, so that an extended quantum formalism may be needed to deal with all
of them. As we will explain, the recently derived 'extended Bloch
representation' of quantum theory (and the associated 'general
tension-reduction' model) precisely provides such extended formalism, while
remaining within the same unitary interpretative framework.Comment: 21 page
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