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This paper illustrates applications of a new, modern version of quantum logic in quantum cognition. The new logic uses ‘effects’ as predicates, instead of the more restricted interpretation of predicates as projections — which is used so far in this area. Effect logic involves states and predicates, validity and conditioning, and also state and predicate transformation via channels. The main aim of this paper is to demonstrate the usefulness of this effect logic in quantum cognition, via many high-level reformulations of standard examples. The usefulness of the logic is greatly increased by its implementation in the programming language Python . [ABSTRACT FROM AUTHOR]

In intertemporal choice, it has been found that if the receipt time is closer to the present, then people tend to grow increasingly or decreasingly impatient. This paper develops an axiom system to construct a weighted additive model reflecting nonconstant impatience. By presupposing that an increment in duration is subjectively assessed according to the periods at which advancement occurs, we denote the one-period advanced receipt of outcomes by multiplying the outcomes by the increment on the right. By this right multiplication, we can regard the effect of advance as the decomposition into two factors, i.e., the factor of step-by-step advance accompanied by subdivided durations and the factor of advance based on the total duration. First, the conditions for enabling right multiplication are proposed for the Cartesian product of the underlying set of a generalized extensive structure and a set of durations. Second, the properties derived under these conditions yield a right action on the generalized extensive structure. Finally, the weighted additive model is obtained as a representation of the generalized extensive structure equipped with the right action. [ABSTRACT FROM AUTHOR]

This paper provides an easy to follow tutorial on the free-energy framework for modelling perception developed by Friston, which extends the predictive coding model of Rao and Ballard. These models assume that the sensory cortex infers the most likely values of attributes or features of sensory stimuli from the noisy inputs encoding the stimuli. Remarkably, these models describe how this inference could be implemented in a network of very simple computational elements, suggesting that this inference could be performed by biological networks of neurons. Furthermore, learning about the parameters describing the features and their uncertainty is implemented in these models by simple rules of synaptic plasticity based on Hebbian learning. This tutorial introduces the free-energy framework using very simple examples, and provides step-by-step derivations of the model. It also discusses in more detail how the model could be implemented in biological neural circuits. In particular, it presents an extended version of the model in which the neurons only sum their inputs, and synaptic plasticity only depends on activity of pre-synaptic and post-synaptic neurons. [ABSTRACT FROM AUTHOR]

The Rescorla–Wagner model has been a leading theory of animal causal induction for nearly 30 years, and human causal induction for the past 15 years. Recent theories (especially Psychol. Rev. 104 (1997) 367) have provided alternative explanations of how people draw causal conclusions from covariational data. However, theoretical attempts to compare the Rescorla–Wagner model with more recent models have been hampered by the fact that the Rescorla–Wagner model is an algorithmic theory, while the more recent theories are all computational. This paper provides a detailed derivation of the long-run behavior of the Rescorla–Wagner model under a wide range of parameters and experimental setups, so that the model can be compared with computational theories. It also shows that the model agrees with competing theories on a wider range of cases than had previously been thought. The paper concludes by showing how recently suggested modifications of the Rescorla–Wagner model impact the long-run behavior of the model. [Copyright &y& Elsevier]

This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for the unknown parameters based on one’s prior beliefs. It is shown that in most typical situations in psychological research (when either observing no, small, medium or large effects) default Bayes factors are asymmetric in information, i.e., they result in unequal error probabilities. The tendency to either prefer the null hypothesis or the alternative hypothesis varies for different default Bayes factors. Although this asymmetry in information is a natural property of a Bayes factor, severe cases of asymmetry may be undesirable in a default setting because the underlying default priors are not a translation of one’s prior beliefs. A calibration scheme is presented to make a default Bayes factor symmetric in information under certain conditions. [ABSTRACT FROM AUTHOR]

This note is a discussion commenting on the paper by Ly et al. on “Harold Jeffreys’s Default Bayes Factor Hypothesis Tests: Explanation, Extension, and Application in Psychology” and on the perceived shortcomings of the classical Bayesian approach to testing, while reporting on an alternative approach advanced by Kamary et al. (2014) as a solution to this quintessential inference problem. [ABSTRACT FROM AUTHOR]

We analyze the interaction between two classical tenets of economic rationality: transitivity and completeness. For a single binary relation, the combination of these properties yields a total preorder. For two binary relations, their interplay entails a NaP -preference: this is a nested pair ≿ N , ≿ P of relations satisfying mixed forms of transitivity and completeness. It is known that a NaP -preference ≿ N , ≿ P is characterized by a family of total preorders having ≿ N and ≿ P as their intersection and union, respectively. This paper examines extensions of this approach to more than two relations. First we define generalized NaP -preferences (GNaP -preferences): these are diamond-shaped quadruples of binary relations on a set such that transitivity and completeness are suitably spread throughout all four components. Then we characterize a GNaP -preference by a family of total preorders witnessing all relations by different combinations of union and intersection. We also show that a suitable amalgamation of NaP -preferences generates a GNaP -preference, and vice versa each GNaP -preference arises by this procedure. Finally, we introduce modal preference structures: these are lattices of binary relations such that the satisfaction of transitivity and completeness is guided by the action of the universal and the existential quantifiers over a family of total preorders. Applications of these novel preference structures to economics and psychology emerge naturally. [ABSTRACT FROM AUTHOR]

Abstract: The ability to understand the goals that drive another person’s actions is an important social and cognitive skill. This is no trivial task, because any given action may in principle be explained by different possible goals (e.g., one may wave ones arm to hail a cab or to swat a mosquito). To select which goal best explains an observed action is a form of abduction. To explain how people perform such abductive inferences, Baker, Tenenbaum, and Saxe (2007) proposed a computational-level theory that formalizes goal inference as Bayesian inverse planning (BIP). It is known that general Bayesian inference–be it exact or approximate–is computationally intractable (NP-hard). As the time required for computationally intractable computations grows excessively fast when scaled from toy domains to the real world, it seems that such models cannot explain how humans can perform Bayesian inferences quickly in real world situations. In this paper we investigate how the BIP model can nevertheless explain how people are able to make goal inferences quickly. The approach that we propose builds on taking situational constraints explicitly into account in the computational-level model. We present a methodology for identifying situational constraints that render the model tractable. We discuss the implications of our findings and reflect on how the methodology can be applied to alternative models of goal inference and Bayesian models in general. [Copyright &y& Elsevier]

Abstract: Experimentation is ubiquitous in the field of psychology and fundamental to the advancement of its science, and one of the biggest challenges for researchers is designing experiments that can conclusively discriminate the theoretical hypotheses or models under investigation. The recognition of this challenge has led to the development of sophisticated statistical methods that aid in the design of experiments and that are within the reach of everyday experimental scientists. This tutorial paper introduces the reader to an implementable experimentation methodology, dubbed Adaptive Design Optimization, that can help scientists to conduct “smart” experiments that are maximally informative and highly efficient, which in turn should accelerate scientific discovery in psychology and beyond. [Copyright &y& Elsevier]

Abstract: Sequential measurements of non-commuting observables produce order effects that are well-known in quantum physics. But their conceptual basis, a significant measurement interaction, is relevant for far more general situations. We argue that non-commutativity is ubiquitous in psychology where almost every interaction with a mental system changes that system in an uncontrollable fashion. Psychological order effects for sequential measurements are therefore to be expected as a rule. In this paper we focus on the theoretical basis of such effects. We classify several families of order effects theoretically, relate them to psychological observations, and predict effects yet to be discovered empirically. We assess the complexity, related to the predictive power, of particular (Hilbert space) models of order effects and discuss possible limitations of such models. [Copyright &y& Elsevier]

Abstract: Choice confidence is a central measure in psychological decision research, often being reported on a probabilistic scale. Simple mechanisms that describe the psychological processes underlying choice confidence, including those based on error and confirmation biases, have typically received support via fits to data averaged over subjects. While averaged data ease model development, they can also destroy important aspects of the confidence data distribution. In this paper, we develop a hierarchical model of raw confidence judgments using the beta distribution, and we implement two simple confidence mechanisms within it. We use Bayesian methods to fit the hierarchical model to data from a two-alternative confidence experiment, and we use a variety of Bayesian tools to diagnose shortcomings of the simple mechanisms that are overlooked when applied to averaged data. Bugs code for estimating the models is also supplied. [Copyright &y& Elsevier]

Abstract: This paper continues the development of the Dissimilarity Cumulation theory and its main psychological application, Universal Fechnerian Scaling [Dzhafarov, E.N and Colonius, H. (2007). Dissimilarity Cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290–304]. In arc-connected spaces the notion of a chain length (the sum of the dissimilarities between the chain’s successive elements) can be used to define the notion of a path length, as the limit inferior of the lengths of chains converging to the path in some well-defined sense. The class of converging chains is broader than that of converging inscribed chains. Most of the fundamental results of the metric-based path length theory (additivity, lower semicontinuity, etc.) turn out to hold in the general dissimilarity-based path length theory. This shows that the triangle inequality and symmetry are not essential for these results, provided one goes beyond the traditional scheme of approximating paths by inscribed chains. We introduce the notion of a space with intermediate points which generalizes (and specializes to when the dissimilarity is a metric) the notion of a convex space in the sense of Menger. A space is with intermediate points if for any distinct there is a different point such that (where is dissimilarity). In such spaces the metric induced by is intrinsic: coincides with the infimum of lengths of all arcs connecting to In Universal Fechnerian Scaling stands for either of the two canonical psychometric increments and ( denoting discrimination probability). The choice between the two makes no difference for the notions of arc-connectedness, convergence of chains and paths, intermediate points, and other notions of the Dissimilarity Cumulation theory. [Copyright &y& Elsevier]

Abstract: This is the third paper in the series introducing the Dissimilarity Cumulation theory and its main psychological application, Universal Fechnerian Scaling. The previously developed dissimilarity-based theory of path length is used to construct the notion of a smooth path, defined by the property that the ratio of the dissimilarity between its points to the length of the subtended fragment of the path tends to unity as the points get closer to each other. We consider a class of stimulus spaces in which for every path there is a series of piecewise smooth paths converging to it pointwise and in length; and a subclass of such spaces where any two sufficiently close points can be connected by a smooth “geodesic in the small”. These notions are used to construct a broadly understood Finslerian geometry of stimulus spaces representable by regions of Euclidean -spaces. With an additional assumption of comeasurability in the small between the canonical psychometric increments of the first and second kind, this establishes a link between Universal Fechnerian Scaling and Multidimensional Fechnerian Scaling in Euclidean -spaces. The latter was a starting point for our theoretical program generalizing Fechner’s idea that sensation magnitudes can be computed by integration of a local discriminability measure. [Copyright &y& Elsevier]

Abstract: We study the recently discovered phenomenon [Conder, M. D. E., & Slinko, A. M. (2004). A counterexample to Fishburn''s conjecture. Journal of Mathematical Psychology, 48(6), 425–431] of existence of comparative probability orderings on finite sets that violate the Fishburn hypothesis [Fishburn, P. C. (1996). Finite linear qualitative probability. Journal of Mathematical Psychology, 40, 64–77; Fishburn, P. C. (1997). Failure of cancellation conditions for additive linear orders. Journal of Combinatorial Designs, 5, 353–365]—we call such orderings and the discrete cones associated with them extremal. Conder and Slinko constructed an extremal discrete cone on a set of elements and showed that no extremal cones exist on a set of elements. In this paper we construct an extremal cone on a finite set of prime cardinality p if p satisfies a certain number theoretical condition. This condition has been computationally checked to hold for 1725 of the 1842 primes between 132 and 16,000, hence for all these primes extremal cones exist. [Copyright &y& Elsevier]

Abstract: Adaptive learning models are used to predict behavior in repeated choice tasks. Predictions can be based on previous payoffs or previous choices of the player. The current paper proposes a new method for evaluating the degree of reliance on past choices, called equal payoff series extraction (EPSE). Under this method a simulated player has the same exact choices as the player but receives equal constant payoffs from all of the alternatives. Success in predicting the next choice ahead for this simulated player therefore relies strictly on mimicry of previous choices of the actual player. This allows determining the marginal fit of predictions that are not based on the actual task payoffs. To evaluate the reliance on past choices under different models, an experiment was conducted in which 48 participants completed a three-alternative choice task in four task conditions. Two different learning rules were evaluated: an interference rule and a decay rule. The results showed that while the predictions of the decay rule relied more on past choices, only the reliance on past payoffs was associated with improved parameter generality. Moreover, we show that the Equal Payoff Series can be used as a criterion for optimizing parameters resulting in better parameter generalizability. [Copyright &y& Elsevier]

Psychological constructs can only be measured indirectly in terms overt behavior, often by means of changes in the level of performance on tasks they are presumed to affect. However, the exact relationship between constructs and the tasks they are presumed to affect is usually not known, which often requires non-essential auxiliary assumptions to be added to a psychological model to allow it to contact the data. Signed difference analysis is a method of deriving testable consequences from psychological models under the general assumption that the relationship between task performance and the constructs or combinations of constructs postulated by the model is at least monotonic. The predictions derived using signed difference analysis do not depend upon estimation of either model parameters or explicit functional relationships. In the present paper, the mathematical theory of signed difference analysis is presented and applied to illustrative problems drawn from research in memory, spatial attention, and reading. The relationships between signed difference analysis and related inferential procedures such as conjoint measurement, state-trace analysis, and double dissociation are discussed. [Copyright &y& Elsevier]