9 research outputs found
A New Fundamental Evidence of Non-Classical Structure in the Combination of Natural Concepts
We recently performed cognitive experiments on conjunctions and negations of
two concepts with the aim of investigating the combination problem of concepts.
Our experiments confirmed the deviations (conceptual vagueness, underextension,
overextension, etc.) from the rules of classical (fuzzy) logic and probability
theory observed by several scholars in concept theory, while our data were
successfully modeled in a quantum-theoretic framework developed by ourselves.
In this paper, we isolate a new, very stable and systematic pattern of
violation of classicality that occurs in concept combinations. In addition, the
strength and regularity of this non-classical effect leads us to believe that
it occurs at a more fundamental level than the deviations observed up to now.
It is our opinion that we have identified a deep non-classical mechanism
determining not only how concepts are combined but, rather, how they are
formed. We show that this effect can be faithfully modeled in a two-sector Fock
space structure, and that it can be exactly explained by assuming that human
thought is the supersposition of two processes, a 'logical reasoning', guided
by 'logic', and a 'conceptual reasoning' guided by 'emergence', and that the
latter generally prevails over the former. All these findings provide a new
fundamental support to our quantum-theoretic approach to human cognition.Comment: 14 pages. arXiv admin note: substantial text overlap with
arXiv:1503.0426
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
Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought
We analyze different aspects of our quantum modeling approach of human
concepts, and more specifically focus on the quantum effects of contextuality,
interference, entanglement and emergence, illustrating how each of them makes
its appearance in specific situations of the dynamics of human concepts and
their combinations. We point out the relation of our approach, which is based
on an ontology of a concept as an entity in a state changing under influence of
a context, with the main traditional concept theories, i.e. prototype theory,
exemplar theory and theory theory. We ponder about the question why quantum
theory performs so well in its modeling of human concepts, and shed light on
this question by analyzing the role of complex amplitudes, showing how they
allow to describe interference in the statistics of measurement outcomes, while
in the traditional theories statistics of outcomes originates in classical
probability weights, without the possibility of interference. The relevance of
complex numbers, the appearance of entanglement, and the role of Fock space in
explaining contextual emergence, all as unique features of the quantum
modeling, are explicitly revealed in this paper by analyzing human concepts and
their dynamics.Comment: 31 pages, 5 figure
Conjunction and Negation of Natural Concepts: A Quantum-theoretic Modeling
We perform two experiments with the aim to investigate the effects of
negation on the combination of natural concepts. In the first experiment, we
test the membership weights of a list of exemplars with respect to two
concepts, e.g., {\it Fruits} and {\it Vegetables}, and their conjunction {\it
Fruits And Vegetables}. In the second experiment, we test the membership
weights of the same list of exemplars with respect to the same two concepts,
but negating the second, e.g., {\it Fruits} and {\it Not Vegetables}, and again
their conjunction {\it Fruits And Not Vegetables}. The collected data confirm
existing results on conceptual combination, namely, they show dramatic
deviations from the predictions of classical (fuzzy set) logic and probability
theory. More precisely, they exhibit conceptual vagueness, gradeness of
membership, overextension and double overextension of membership weights with
respect to the given conjunctions. Then, we show that the quantum probability
model in Fock space recently elaborated to model Hampton's data on concept
conjunction (Hampton, 1988a) and disjunction (Hampton, 1988b) faithfully
accords with the collected data. Our quantum-theoretic modeling enables to
describe these non-classical effects in terms of genuine quantum effects,
namely `contextuality', `superposition', `interference' and `emergence'. The
obtained results confirm and strenghten the analysis in Aerts (2009a) and Sozzo
(2014) on the identification of quantum aspects in experiments on conceptual
vagueness. Our results can be inserted within the general research on the
identification of quantum structures in cognitive and decision processes.Comment: 32 pages, standard latex, no figures, 16 tables. arXiv admin note:
text overlap with arXiv:1311.6050; and text overlap with arXiv:0805.3850 by
other author
Quantum Structure of Negation and Conjunction in Human Thought
We analyse in this paper the data collected in a set of experiments performed
on human subjects on the combination of natural concepts. We investigate the
mutual influence of conceptual conjunction and negation by measuring the
membership weights of a list of exemplars with respect to two concepts, e.g.,
'Fruits' and 'Vegetables', and their conjunction 'Fruits And Vegetables', but
also their conjunction when one or both concepts are negated, namely, 'Fruits
And Not Vegetables', 'Not Fruits And Vegetables' and 'Not Fruits And Not
Vegetables'. Our findings sharpen existing analysis on conceptual combinations,
revealing systematic and remarkable deviations from classical (fuzzy set) logic
and probability theory. And, more important, our results give further
considerable evidence to the validity of our quantum-theoretic framework for
the combination of two concepts. Indeed, the representation of conceptual
negation naturally arises from the general assumptions of our two-sector Fock
space model, and this representation faithfully agrees with the collected data.
In addition, we find a further significant deviation and a priori unexpected
from classicality, which can exactly be explained by assuming that human
reasoning is the superposition of an 'emergent reasoning' and a 'logical
reasoning', and that these two processes can be successfully represented in a
Fock space algebraic structure.Comment: 44 pages. arXiv admin note: text overlap with arXiv:1406.235
The Potential of Quantum Probability for Modeling Cognitive Processes
Quantum probability (QP) theory is a theory for how to assign probabilities to observables. In the context of physics, it has been successfully employed by researchers for over 100 years and has been the basis for some of the most impressive discoveries of the human mind (e.g., the transistor, and so the microchip, and the laser). But the applicability of QP theory is not limited to physical phenomena and, indeed, there has been growing interest in exploring the potential of QP theory in areas as diverse as economics (Baaquie, 2004), information theory (e.g., Grover, 1997), and psychology