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We use quantum probability (QP) theory to investigate individual differences in causal reasoning. By analyzing datasets from Rehder (2014) on comparative judgments, and from Rehder and Waldmann (2016) on absolute judgments, we show that a QP model can both account for individual differences in causal judgments, and why these judgments sometimes violate the properties of causal Bayes nets. We implement this and previously proposed models of causal reasoning (including classical probability models) within the same hierarchical Bayesian inferential framework to provide a detailed comparison between these models, including computing Bayes factors. Analysis of the inferred parameters of the QP model illustrates how these can be interpreted in terms of putative cognitive mechanisms of causal reasoning. Additionally, we implement a latent classification mechanism that identifies subcategories of reasoners based on properties of the inferred cognitive process, rather than post hoc clustering. The QP model also provides a parsimonious explanation for aggregate behavior, which alternatively can only be explained by a mixture of multiple existing models. Investigating individual differences through the lens of a QP model reveals simple but strong alternatives to existing explanations for the dichotomies often observed in how people make causal inferences. These alternative explanations arise from the cognitive interpretation of the parameters and structure of the quantum probability model.

Rational agents should update their beliefs in the light of newevidence. Equally, changes in belief should depend only onthe quality of the evidence, and not on factors such as the or-der in which the evidence is acquired, or whether intermedi-ate judgements are requested during evidence acquisition. Incontrast we show that requests for intermediate judgments caninhibit belief updating for real decision makers, which repre-sents a new type of decision making fallacy. This behaviour isparadoxical from the point of view of classical Bayesian mod-els, but we show that it is consistent with an a priori, parameterfree prediction of a cognitive model based on quantum theory.

We discuss recent progress towards an empirical test of ‘realism’in cognition, ‘realism’ in this context being the propertythat cognitive variables always have well defined (if unknown)values at all times. Our main result is an inequality obeyed byrealist theories, which could be tested by a suitable experiment.We focus our attention in this contribution on two particularissues. The first is the exact notion of realism which is to betested, as this has received less attention in earlier work. Thesecond is an important technical issue about the inequality weuse; in earlier work Atmanspacher and Filk (2010) considereda different expression, and we explain why our inequality ismore suitable for use under realistic experimental conditions

We present progress towards a novel theoretical approach forunderstanding Tversky’s famous ‘diagnosticity’ effect in similarityjudgments, and an initial empirical validation. Our approachuses a model for similarity judgments based on quantumprobability theory. The model predicts a diagnosticity effectunder certain conditions only. Our model also predicts thatchanges to the set of stimuli to be compared can cause the diagnosticityeffect to break down or reverse. In one experiment,we test and confirm one of our key predictions

We develop a quantum probability model that can account forsituations where people’s causal judgments violate theproperties of causal Bayes nets and demonstrate how theparameters of our model can be interpreted to provideinformation about underlying cognitive processes. Weimplement this model within a hierarchical Bayesianinference framework that allows us to systematically identifyindividual differences and also provide a latent classificationof individuals into categories of causal and associativereasoners. Finally, we implement a basic normative causalBayes net within the same inference framework that allows usto directly compare quantum and classical probability modelsusing Bayes factors

Decisions can sometimes have a constructive role, so that the act of, for example, choosing one option over another creates a preference for that option (e.g., Ariely & Norton, 2008; Payne, Bettman, & Johnson, 1993; Sharot, Velasquez, & Dolan, 2010; Sherman, 1980 ). In this work we explore the constructive role of just articulating an impression, for a presented visual stimulus, as opposed to making a choice (specifically, the judgments we employ are affective evaluations). Using quantum probability theory, we outline a cognitive model formalizing such a constructive process. We predict a simple interaction, in relation to how a second image is evaluated, following the presentation of a first image, depending on whether there is a rating for the first image or not. The interaction predicted by the quantum model was confirmed across three experiments and a variety of control manipulations. The advantages of using quantum probability theory to model the present results, compared with existing models of sequence order effects in judgment (e.g., Hogarth & Einhorn, 1992 ) or other theories of constructive processes when a choice is made (e.g., Festinger, 1957; Sharot et al., 2010 ) are discussed. [ABSTRACT FROM AUTHOR]

The term 'vagueness' describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon. [ABSTRACT FROM AUTHOR]

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. [ABSTRACT FROM AUTHOR]

No other study has had as great an impact on the development of the similarity literature as that of Tversky (1977), which provided compelling demonstrations against all the fundamental assumptions of the popular, and extensively employed, geometric similarity models. Notably, similarity judgments were shown to violate symmetry and the triangle inequality and also be subject to context effects, so that the same pair of items would be rated differently, depending on the presence of other items. Quantum theory provides a generalized geometric approach to similarity and can address several of Tversky's main findings. Similarity is modeled as quantum probability, so that asymmetries emerge as order effects, and the triangle equality violations and the diagnosticity effect can be related to the context-dependent properties of quantum probability. We so demonstrate the promise of the quantum approach for similarity and discuss the implications for representation theory in general. [ABSTRACT FROM AUTHOR]

The idea that choices can have a constructive effect has received a great deal of empirical support. The act of choosing appears to influence subsequent preferences for the options available. Recent research has proposed a cognitive model based on quantum probability (QP), which suggests that whether or not a participant provides an affective evaluation for a positively or negatively valenced stimulus can also be constructive and so, for example, influence the affective evaluation of a second oppositely valenced stimulus. However, there are some outstanding methodological questions in relation to this previous research. This paper reports the results of three experiments designed to resolve these questions. Experiment 1, using a binary response format, provides partial support for the interaction predicted by the QP model; and Experiment 2, which controls for the length of time participants have to respond, fully supports the QP model. Finally, Experiment 3 sought to determine whether the key effect can generalize beyond affective judgements about visual stimuli. Using judgements about the trustworthiness of well-known people, the predictions of the QP model were confirmed. Together, these three experiments provide further support for the QP model of the constructive effect of simple evaluations. [ABSTRACT FROM AUTHOR]

All mental representations change with time. A baseline intuition is that mental representations have specific values at different time points, which may be more or less accessible, depending on noise, forgetting processes, etc. We present a radical alternative, motivated by recent research using the mathematics from quantum theory for cognitive modelling. Such cognitive models raise the possibility that certain possibilities or events may be incompatible, so that perfect knowledge of one necessitates uncertainty for the others. In the context of time-dependence, in physics, this issue is explored with the so-called temporal Bell (TB) or Leggett–Garg inequalities. We consider in detail the theoretical and empirical challenges involved in exploring the TB inequalities in the context of cognitive systems. One interesting conclusion is that we believe the study of the TB inequalities to be empirically more constrained in psychology than in physics. Specifically, we show how the TB inequalities, as applied to cognitive systems, can be derived from two simple assumptions: cognitive realism and cognitive completeness. We discuss possible implications of putative violations of the TB inequalities for cognitive models and our understanding of time in cognition in general. Overall, this paper provides a surprising, novel direction in relation to how time should be conceptualized in cognition. [ABSTRACT FROM AUTHOR]