368 research outputs found
Contextualizing concepts using a mathematical generalization of the quantum formalism
We outline the rationale and preliminary results of using the State Context
Property (SCOP) formalism, originally developed as
a generalization of quantum mechanics, to describe the contextual manner in
which concepts are evoked, used, and combined to
generate meaning. The quantum formalism was developed to cope with problems
arising in the description of (1) the measurement
process, and (2) the generation of new states with new properties when
particles become entangled. Similar problems arising
with concepts motivated the formal treatment introduced here. Concepts are
viewed not as fixed representations, but entities
existing in states of potentiality that require interaction with a
context---a stimulus or another concept---to `collapse' to
observable form as an exemplar, prototype, or other (possibly imaginary)
instance. The stimulus situation plays the role of
the measurement in physics, acting as context that induces a change of the
cognitive state from
superposition state to collapsed state. The collapsed state is
more likely to consist of a conjunction of
concepts for associative than analytic thought because more stimulus or
concept properties take part in the
collapse. We provide two contextual measures of conceptual distance---one
using collapse probabilities and the other weighted
properties---and show how they can be applied to conjunctions using the pet
fish problem
Contextual Risk and Its Relevance in Economics
Uncertainty in economics still poses some fundamental problems illustrated,
e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties,
economists have introduced an interesting distinction between 'risk' and
'ambiguity' depending on the existence of a (classical Kolmogorovian)
probabilistic structure modeling these uncertainty situations. On the other
hand, evidence of everyday life suggests that 'context' plays a fundamental
role in human decisions under uncertainty. Moreover, it is well known from
physics that any probabilistic structure modeling contextual interactions
between entities structurally needs a non-Kolmogorovian quantum-like framework.
In this paper we introduce the notion of 'contextual risk' with the aim of
modeling a substantial part of the situations in which usually only 'ambiguity'
is present. More precisely, we firstly introduce the essentials of an
operational formalism called 'the hidden measurement approach' in which
probability is introduced as a consequence of fluctuations in the interaction
between entities and contexts. Within the hidden measurement approach we
propose a 'sphere model' as a mathematical tool for situations in which
contextual risk occurs. We show that a probabilistic model of this kind is
necessarily non-Kolmogorovian, hence it requires either the formalism of
quantum mechanics or a generalization of it. This insight is relevant, for it
explains the presence of quantum or, better, quantum-like, structures in
economics, as suggested by some authors, and can serve to solve the
aforementioned paradoxes.Comment: 6 pages, 2 figure
Entanglement of Conceptual Entities in Quantum Model Theory (QMod)
We have recently elaborated 'Quantum Model Theory' (QMod) to model situations
where the quantum effects of contextuality, interference, superposition,
entanglement and emergence, appear without the entities giving rise to these
situations having necessarily to be of microscopic nature. We have shown that
QMod models without introducing linearity for the set of the states. In this
paper we prove that QMod, although not using linearity for the state space,
provides a method of identification for entangled states and an intuitive
explanation for their occurrence. We illustrate this method for entanglement
identification with concrete examples
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
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