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. (shrink)

Degrees of belief; Dempster's rule of combination; Simple and separable support functions; The weights of evidence; Compatible frames of discernment; Support functions; The discernment of evidence; Quasi support functions; Consonance; Statistical evidence; The dual nature of probable reasoning.

This book is a fascinating and accessible summary of Roger Penrose's current thinking on those areas of physics in which he feels there are major...

_Figure 1. Dendrites and cell bodies of schematic neurons connected by dendritic-dendritic gap junctions form a laterally connected input_ _layer (“dendritic web”) within a neurocomputational architecture. Dendritic web dynamics are temporally coupled to gamma synchrony_ _EEG, and correspond with integration phases of “integrate and fire” cycles. Axonal firings provide input to, and output from, integration_ _phases (only one input, and three output axons are shown). Cell bodies/soma contain nuclei shown as black circles; microtubule networks_ _pervade the cytoplasm. According to the (...) Orch OR theory, gamma EEG-synchronized integration phases include quantum computations in_ _microtubule networks which culminate with conscious moments. Insert closeup shows a gap junction through which microtubule quantum_ _states entangle among different neurons, enabling macroscopic quantum states in dendritic webs extending throughout cortex and other_ _brain regions._. (shrink)

Takes students and researchers on a tour through some of the deepest ideas of maths, computer science and physics.

Question order effects are commonly observed in self-report measures of judgment and attitude. This article develops a quantum question order model (the QQ model) to account for four types of question order effects observed in literature. First, the postulates of the QQ model are presented. Second, an a priori, parameter-free, and precise prediction, called the QQ equality, is derived from these mathematical principles, and six empirical data sets are used to test the prediction. Third, a new index is derived from (...) the model to measure similarity between questions. Fourth, we show that in contrast to the QQ model, Bayesian and Markov models do not generally satisfy the QQ equality and thus cannot account for the reported empirical data that support this equality. Finally, we describe the conditions under which order effects are predicted to occur, and we review a broader range of findings that are encompassed by these very same quantum principles. We conclude that quantum probability theory, initially invented to explain order effects on measurements in physics, appears to be a powerful natural explanation for order effects of self-report measures in social and behavioral sciences, too. (shrink)

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. (shrink)