225,576 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
Quantum Structure in Cognition, Origins, Developments, Successes and Expectations
We provide an overview of the results we have attained in the last decade on
the identification of quantum structures in cognition and, more specifically,
in the formalization and representation of natural concepts. We firstly discuss
the quantum foundational reasons that led us to investigate the mechanisms of
formation and combination of concepts in human reasoning, starting from the
empirically observed deviations from classical logical and probabilistic
structures. We then develop our quantum-theoretic perspective in Fock space
which allows successful modeling of various sets of cognitive experiments
collected by different scientists, including ourselves. In addition, we
formulate a unified explanatory hypothesis for the presence of quantum
structures in cognitive processes, and discuss our recent discovery of further
quantum aspects in concept combinations, namely, 'entanglement' and
'indistinguishability'. We finally illustrate perspectives for future research.Comment: 25 pages. arXiv admin note: text overlap with arXiv:1412.870
Classical Logical versus Quantum Conceptual Thought: Examples in Economics, Decision theory and Concept Theory
Inspired by a quantum mechanical formalism to model concepts and their
disjunctions and conjunctions, we put forward in this paper a specific
hypothesis. Namely that within human thought two superposed layers can be
distinguished: (i) a layer given form by an underlying classical deterministic
process, incorporating essentially logical thought and its indeterministic
version modeled by classical probability theory; (ii) a layer given form under
influence of the totality of the surrounding conceptual landscape, where the
different concepts figure as individual entities rather than (logical)
combinations of others, with measurable quantities such as 'typicality',
'membership', 'representativeness', 'similarity', 'applicability', 'preference'
or 'utility' carrying the influences. We call the process in this second layer
'quantum conceptual thought', which is indeterministic in essence, and contains
holistic aspects, but is equally well, although very differently, organized
than logical thought. A substantial part of the 'quantum conceptual thought
process' can be modeled by quantum mechanical probabilistic and mathematical
structures. We consider examples of three specific domains of research where
the effects of the presence of quantum conceptual thought and its deviations
from classical logical thought have been noticed and studied, i.e. economics,
decision theory, and concept theories and which provide experimental evidence
for our hypothesis.Comment: 14 page
A Potentiality and Conceptuality Interpretation of Quantum Physics
We elaborate on a new interpretation of quantum mechanics which we introduced
recently. The main hypothesis of this new interpretation is that quantum
particles are entities interacting with matter conceptually, which means that
pieces of matter function as interfaces for the conceptual content carried by
the quantum particles. We explain how our interpretation was inspired by our
earlier analysis of non-locality as non-spatiality and a specific
interpretation of quantum potentiality, which we illustrate by means of the
example of two interconnected vessels of water. We show by means of this
example that philosophical realism is not in contradiction with the recent
findings with respect to Leggett's inequalities and their violations. We
explain our recent work on using the quantum formalism to model human concepts
and their combinations and how this has given rise to the foundational ideas of
our new quantum interpretation. We analyze the equivalence of meaning in the
realm of human concepts and coherence in the realm of quantum particles, and
how the duality of abstract and concrete leads naturally to a Heisenberg
uncertainty relation. We illustrate the role played by interference and
entanglement and show how the new interpretation explains the problems related
to identity and individuality in quantum mechanics. We put forward a possible
scenario for the emergence of the reality of macroscopic objects.Comment: 20 pages, 1 figur
Experimental Evidence for Quantum Structure in Cognition
We proof a theorem that shows that a collection of experimental data of
membership weights of items with respect to a pair of concepts and its
conjunction cannot be modeled within a classical measure theoretic weight
structure in case the experimental data contain the effect called
overextension. Since the effect of overextension, analogue to the well-known
guppy effect for concept combinations, is abundant in all experiments testing
weights of items with respect to pairs of concepts and their conjunctions, our
theorem constitutes a no-go theorem for classical measure structure for common
data of membership weights of items with respect to concepts and their
combinations. We put forward a simple geometric criterion that reveals the non
classicality of the membership weight structure and use experimentally measured
membership weights estimated by subjects in experiments to illustrate our
geometrical criterion. The violation of the classical weight structure is
similar to the violation of the well-known Bell inequalities studied in quantum
mechanics, and hence suggests that the quantum formalism and hence the modeling
by quantum membership weights can accomplish what classical membership weights
cannot do.Comment: 12 pages, 3 figure
Quantum Interaction Approach in Cognition, Artificial Intelligence and Robotics
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.Comment: 10 page
Quantum Structure in Cognition: Why and How Concepts are Entangled
One of us has recently elaborated a theory for modelling concepts that uses
the state context property (SCoP) formalism, i.e. a generalization of the
quantum formalism. This formalism incorporates context into the mathematical
structure used to represent a concept, and thereby models how context
influences the typicality of a single exemplar and the applicability of a
single property of a concept, which provides a solution of the 'Pet-Fish
problem' and other difficulties occurring in concept theory. Then, a quantum
model has been worked out which reproduces the membership weights of several
exemplars of concepts and their combinations. We show in this paper that a
further relevant effect appears in a natural way whenever two or more concepts
combine, namely, 'entanglement'. The presence of entanglement is explicitly
revealed by considering a specific example with two concepts, constructing some
Bell's inequalities for this example, testing them in a real experiment with
test subjects, and finally proving that Bell's inequalities are violated in
this case. We show that the intrinsic and unavoidable character of entanglement
can be explained in terms of the weights of the exemplars of the combined
concept with respect to the weights of the exemplars of the component concepts.Comment: 10 page
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