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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]

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]