12 research outputs found
Noncontextuality with Marginal Selectivity in Reconstructing Mental Architectures
We present a general theory of series-parallel mental architectures with
selectively influenced stochastically non-independent components. A mental
architecture is a hypothetical network of processes aimed at performing a task,
of which we only observe the overall time it takes under variable parameters of
the task. It is usually assumed that the network contains several processes
selectively influenced by different experimental factors, and then the question
is asked as to how these processes are arranged within the network, e.g.,
whether they are concurrent or sequential. One way of doing this is to consider
the distribution functions for the overall processing time and compute certain
linear combinations thereof (interaction contrasts). The theory of selective
influences in psychology can be viewed as a special application of the
interdisciplinary theory of (non)contextuality having its origins and main
applications in quantum theory. In particular, lack of contextuality is
equivalent to the existence of a "hidden" random entity of which all the random
variables in play are functions. Consequently, for any given value of this
common random entity, the processing times and their compositions (minima,
maxima, or sums) become deterministic quantities. These quantities, in turn,
can be treated as random variables with (shifted) Heaviside distribution
functions, for which one can easily compute various linear combinations across
different treatments, including interaction contrasts. This mathematical fact
leads to a simple method, more general than the previously used ones, to
investigate and characterize the interaction contrast for different types of
series-parallel architectures.Comment: published in Frontiers in Psychology: Cognition 1:12 doi:
10.3389/fpsyg.2015.00735 (special issue "Quantum Structures in Cognitive and
Social Science"
A Qualified Kolmogorovian Account of Probabilistic Contextuality
We describe a mathematical language for determining all possible patterns of
contextuality in the dependence of stochastic outputs of a system on its
deterministic inputs. The central notion is that of all possible couplings for
stochastically unrelated outputs indexed by mutually incompatible values of
inputs. A system is characterized by a pattern of which outputs can be
"directly influenced" by which inputs (a primitive relation, hypothetical or
normative), and by certain constraints imposed on the outputs (such as
Bell-type inequalities or their quantum analogues). The set of couplings
compatible with these constraints represents a form of contextuality in the
dependence of outputs on inputs with respect to the declared pattern of direct
influences.Comment: Lecture Notes in Computer Science 8369, 201-212 (2014
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Quantum probability in decision making from quantum information representation of neuronal states
The recent wave of interest to modeling the process of decision making with the aid of the quantum formalism gives rise to the following question: ‘How can neurons generate quantum-like statistical data?’ (There is a plenty of such data in cognitive psychology and social science.) Our model is based on quantum-like representation of uncertainty in generation of action potentials. This uncertainty is a consequence of complexity of electrochemical processes in the brain; in particular, uncertainty of triggering an action potential by the membrane potential. Quantum information state spaces can be considered as extensions of classical information spaces corresponding to neural codes; e.g., 0/1, quiescent/firing neural code. The key point is that processing of information by the brain involves superpositions of such states. Another key point is that a neuronal group performing some psychological function F is an open quantum system. It interacts with the surrounding electrochemical environment. The process of decision making is described as decoherence in the basis of eigenstates of F. A decision state is a steady state. This is a linear representation of complex nonlinear dynamics of electrochemical states. Linearity guarantees exponentially fast convergence to the decision state
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