Quantum Mechanics Is Compatible with Counterfactual Definiteness.

Counterfactual definiteness (CFD) means that if some property is measured in some context, then the outcome of the measurement would have been the same had this property been measured in a different context. A context includes all other measurements made together with the one in question, and the spatiotemporal relations among them. The proviso for CFD is non-disturbance: any physical influence of the contexts on the property being measured is excluded by the laws of nature, so that no one measuring this property has a way of ascertaining its context.

Contextuality with Disturbance and without: Neither Can Violate Substantive Requirements the Other Satisfies.

Contextuality was originally defined only for consistently connected systems of random variables (those without disturbance/signaling). Contextuality-by-Default theory (CbD) offers an extension of the notion of contextuality to inconsistently connected systems (those with disturbance) by defining it in terms of the systems' couplings subject to certain constraints. Such extensions are sometimes met with skepticism.

Contextuality and Informational Redundancy.

A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of contextuality, and its demonstration is trivial for inconsistently connected systems (i.e.

Measures of contextuality and non-contextuality.

We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with 'disturbance' allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of non-contextuality in non-contextual systems.

Contextuality Analysis of the Double Slit Experiment (with a Glimpse into Three Slits).

The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: Has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the Einsten-Podolsky-Rosen-Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.

Contextuality in canonical systems of random variables.

Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under which it is recorded). Two random variables are jointly distributed if and only if they share a context. In a canonical representation of a system, all random variables are binary, and every content-sharing pair of random variables has a unique maximal coupling (the joint distribution imposed on them so that they coincide with maximal possible probability).

On contextuality in behavioural data.

Dzhafarovet al.(Dzhafarovet al.2016Phil.

Is there contextuality in behavioural and social systems?

Most behavioural and social experiments aimed at revealing contextuality are confined to cyclic systems with binary outcomes. In quantum physics, this broad class of systems includes as special cases Klyachko-Can-Binicioglu-Shumovsky-type, Einstein-Podolsky-Rosen-Bell-type and Suppes-Zanotti-Leggett-Garg-type systems. The theory of contextuality known as contextuality-by-default allows one to define and measure contextuality in all such systems, even if there are context-dependent errors in measurements, or if something in the contexts directly interacts with the measurements.

Necessary and Sufficient Conditions for an Extended Noncontextuality in a Broad Class of Quantum Mechanical Systems.

The notion of (non)contextuality pertains to sets of properties measured one subset (context) at a time. We extend this notion to include so-called inconsistently connected systems, in which the measurements of a given property in different contexts may have different distributions, due to contextual biases in experimental design or physical interactions (signaling): a system of measurements has a maximally noncontextual description if they can be imposed a joint distribution on in which the measurements of any one property in different contexts are equal to each other with the maximal probability allowed by their different distributions. We derive necessary and sufficient conditions for the existence of such a description in a broad class of systems including Klyachko-Can-Binicioğlu-Shumvosky-type (KCBS), EPR-Bell-type, and Leggett-Garg-type systems.

Embedding quantum into classical: contextualization vs conditionalization.

We compare two approaches to embedding joint distributions of random variables recorded under different conditions (such as spins of entangled particles for different settings) into the framework of classical, Kolmogorovian probability theory. In the contextualization approach each random variable is "automatically" labeled by all conditions under which it is recorded, and the random variables across a set of mutually exclusive conditions are probabilistically coupled (imposed a joint distribution upon). Analysis of all possible probabilistic couplings for a given set of random variables allows one to characterize various relations between their separate distributions (such as Bell-type inequalities or quantum-mechanical constraints).

On selective influences, marginal selectivity, and bell/CHSH inequalities.

The Bell/CHSH inequalities of quantum physics are identical with the inequalities derived in mathematical psychology for the problem of selective influences in cases involving two binary experimental factors and two binary random variables recorded in response to them. The following points are made regarding cognitive science applications: (1) compliance of data with these inequalities is informative only if the data satisfy the requirement known as marginal selectivity; (2) both violations of marginal selectivity and violations of the Bell/CHSH inequalities are interpretable as indicating that at least one of the two responses is influenced by both experimental factors.

An electrophysiological study of print processing in kindergarten: the contribution of the visual n1 as a predictor of reading outcome.

Sensitivity to print is characterized by a left occipito-temporal negativity to words in the event-related potential N1. This sensitivity is modulated by reading skills and may thus represent a neural marker of reading competence. Here we studied the development of the N1 in regular and poor readers from preschool age to school age to test whether the amplitude of the N1 predicts children's reading outcomes.

Beyond quantum probability: another formalism shared by quantum physics and psychology.

There is another meeting place for quantum physics and psychology, both within and outside of cognitive modeling. In physics it is known as the issue of classical (probabilistic) determinism, and in psychology it is known as the issue of selective influences. The formalisms independently developed in the two areas for dealing with these issues turn out to be identical, opening ways for mutually beneficial interactions.

All-possible-couplings approach to measuring probabilistic context.

From behavioral sciences to biology to quantum mechanics, one encounters situations where (i) a system outputs several random variables in response to several inputs, (ii) for each of these responses only some of the inputs may "directly" influence them, but (iii) other inputs provide a "context" for this response by influencing its probabilistic relations to other responses. These contextual influences are very different, say, in classical kinetic theory and in the entanglement paradigm of quantum mechanics, which are traditionally interpreted as representing different forms of physical determinism. One can mathematically construct systems with other types of contextuality, whether or not empirically realizable: those that form special cases of the classical type, those that fall between the classical and quantum ones, and those that violate the quantum type.

The joint distribution criterion and the distance tests for selective probabilistic causality.

A general definition and a criterion (a necessary and sufficient condition) are formulated for an arbitrary set of external factors to selectively influence a corresponding set of random entities (generalized random variables, with values in arbitrary observation spaces), jointly distributed at every treatment (a set of factor values containing precisely one value of each factor). The random entities are selectively influenced by the corresponding factors if and only if the following condition, called the joint distribution criterion, is satisfied: there is a jointly distributed set of random entities, one entity for every value of every factor, such that every subset of this set that corresponds to a treatment is distributed as the original variables at this treatment. The distance tests (necessary conditions) for selective influence previously formulated for two random variables in a two-by-two factorial design (Kujala and Dzhafarov, 2008, J.

Adaptive design optimization: a mutual information-based approach to model discrimination in cognitive science.

Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps.

In search of a science-based application: a learning tool for reading acquisition.

This is a story about the fate of a psychological application: from its conception to the optimistic vision surrounding its future. We hope that this application - an enjoyable learning game (www or mobile phone-based, available free of charge to the end users) for children - can at best help millions of children in their reading acquisition in the future. Its basis was created by following intensively the development of children with (N = 107) and without (N = 92) genetic (familial) risk for dyslexia from birth to puberty in the Jyväskylä Longitudinal study of Dyslexia (JLD)-project.

Solutions for certain number-conserving deterministic cellular automata.

We explain the unexpected behavior of the generalizations of cellular automation traffic models introduced in [H. Fukś and N. Boccara, Int.