13 research outputs found
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
Entanglement as a Method to Reduce Uncertainty
In physics, entanglement 'reduces' the entropy of an entity, because the (von
Neumann) entropy of, e.g., a composite bipartite entity in a pure entangled
state is systematically lower than the entropy of the component sub-entities.
We show here that this 'genuinely non-classical reduction of entropy as a
result of composition' also holds whenever two concepts combine in human
cognition and, more generally, it is valid in human culture. We exploit these
results and make a 'new hypothesis' on the nature of entanglement, namely, the
production of entanglement in the preparation of a composite entity can be seen
as a 'dynamical process of collaboration between its sub-entities to reduce
uncertainty', because the composite entity is in a pure state while its
sub-entities are in a non-pure, or density, state, as a result of the
preparation. We identify within the nature of this entanglement a mechanism of
contextual updating and illustrate the mechanism in the example we analyze. Our
hypothesis naturally explains the 'non-classical nature' of some quantum
logical connectives, as due to Bell-type correlations.Comment: 15 page
Modeling Meaning Associated with Documental Entities: Introducing the Brussels Quantum Approach
We show that the Brussels operational-realistic approach to quantum physics
and quantum cognition offers a fundamental strategy for modeling the meaning
associated with collections of documental entities. To do so, we take the World
Wide Web as a paradigmatic example and emphasize the importance of
distinguishing the Web, made of printed documents, from a more abstract meaning
entity, which we call the Quantum Web, or QWeb, where the former is considered
to be the collection of traces that can be left by the latter, in specific
measurements, similarly to how a non-spatial quantum entity, like an electron,
can leave localized traces of impact on a detection screen. The double-slit
experiment is extensively used to illustrate the rationale of the modeling,
which is guided by how physicists constructed quantum theory to describe the
behavior of the microscopic entities. We also emphasize that the superposition
principle and the associated interference effects are not sufficient to model
all experimental probabilistic data, like those obtained by counting the
relative number of documents containing certain words and co-occurrences of
words. For this, additional effects, like context effects, must also be taken
into consideration.Comment: 27 pages, 6 figures, Late
Quantum entanglement in physical and cognitive systems: a conceptual analysis and a general representation
We provide a general description of the phenomenon of entanglement in
bipartite systems, as it manifests in micro and macro physical systems, as well
as in human cognitive processes. We do so by observing that when genuine
coincidence measurements are considered, the violation of the 'marginal laws',
in addition to the Bell-CHSH inequality, is also to be expected. The situation
can be described in the quantum formalism by considering the presence of
entanglement not only at the level of the states, but also at the level of the
measurements. However, at the "local'" level of a specific joint measurement, a
description where entanglement is only incorporated in the state remains always
possible, by adopting a fine-tuned tensor product representation. But
contextual tensor product representations should only be considered when there
are good reasons to describe the outcome-states as (non-entangled) product
states. This will not in general be true, hence, the entangement resource will
have to generally be allocated both in the states and in the measurements. In
view of the numerous violations of the marginal laws observed in physics'
laboratories, it remains unclear to date if entanglement in micro-physical
systems is to be understood only as an 'entanglement of the states', or also as
an 'entanglement of the measurements'. But even if measurements would also be
entangled, the corresponding violation of the marginal laws (no-signaling
conditions) would not for this imply that a superluminal communication would be
possible
Representing Attitudes Towards Ambiguity in Hilbert Space: Foundations and Applications
We provide here a general mathematical framework to model attitudes towards
ambiguity which uses the formalism of quantum theory as a ``purely mathematical
formalism, detached from any physical interpretation''. We show that the
quantum-theoretic framework enables modelling of the "Ellsberg paradox", but it
also successfully applies to more concrete human decision-making (DM) tests
involving financial, managerial and medical decisions. In particular, we
elaborate a mathematical representation of various empirical studies which
reveal that attitudes of managers towards uncertainty shift from "ambiguity
seeking" to "ambiguity aversion", and viceversa, thus exhibiting "hope effects"
and "fear effects". The present framework provides a promising direction
towards the development of a unified theory of decisions in the presence of
uncertainty.Comment: 23 pages, standard LaTeX, 1 figur
Applicazioni del Formalismo Quantistico alle Scienze Cognitive
In questo articolo verranno presentati alcuni risultati recenti sull'applicazione del formalismo matematico della meccanica quantistica (QM) ai domini cognitivi e socioeconomici, ottenuti nell'ambito di una decennale collaborazione tra i gruppi di ricerca di Bruxelles e Leicester. In particolare, si mostrerĂ come il formalismo quantistico in spazi di Hilbert permetta di modellizzare e fornire una spiegazione unitaria per una serie di fenomeni cognitivi complessi, compresi i giudizi e le decisioni in presenza di incertezza, per i quali l'applicazione di formalismi di tipo classico porta invece a risultati paradossali. I risultati presentati in questo articolo supportano un programma di ricerca emergente, noto con il nome di quantum cognition programme, che presuppone l'esistenza di strutture quantistiche in domini non-fisici