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Metaphors involving motion and forces are a source of inspiration for understanding tonal music and tonal harmonies since ancient times. Starting with the rise of quantum cognition, the modern interactional conception of forces as developed in gauge theory has recently entered the field of theoretical musicology. We develop a gauge model of tonal attraction based on SU(2) symmetry. This model comprises two earlier attempts, the phase model grounded on U(1) gauge symmetry, and the spatial deformation model derived from SO(2) gauge symmetry. In the neutral, force-free case both submodels agree and generate the same predictions as a simple qubit approach. However, there are several differences in the force-driven case. It is claimed that the deformation model gives a proper description of static tonal attraction. The full model combines the deformation model with the phase model through SU(2) gauge symmetry and unifies static and dynamic tonal attraction. [ABSTRACT FROM AUTHOR]

How well does a given pitch fit into a tonal scale or tonal key, let it be a major or minor key? A similar question can be asked regarding chords and tonal regions. Structural and probabilistic approaches in computational music theory have tried to give systematic answers to the problem of tonal attraction. We will discuss two previous models of tonal attraction, one based on tonal hierarchies and the other based on interval cycles. To overcome the shortcomings of these models, both methodologically and empirically, I propose a new kind of models relying on insights of the new research field of quantum cognition. I will argue that the quantum approach integrates the insights from both group theory and quantum probability theory. In this way, it achieves a deeper understanding of the cognitive nature of tonal music, especially concerning the nature of musical expectations (Leonhard Meyer) and a better understanding of the affective meaning of music. [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]

The author comments on the paper "Abstractions and Idealisations: The Construction of Modern Linguistics," by Martin Stokhof and Michiel van Lambalgen. It discusses the way modern linguistics constructs its proper objects, the scientific criteria for characterizing its success or failure and the role of naturalism. He argues that a broader view of modern linguistics calls for a reconsideration of the role of abstraction and idealization. Some aspects deemed essential for constituting the generativist approach including innateness hypothesis, explicit inaccessible rule view and distinction between competence and performance are proposed. He opposes the suggestion that physics make exclusive use of abstraction and that abstraction is the only useful research tool within a naturalist setting.

Abstract: We propose a formalization of C.G. Jung’s theory of personality using a four-dimensional Hilbert-space for the representation of two qubits. The first qubit relates to Jung’s four psychological functions: Thinking, Feeling, Sensing and iNtuition, which are represented by two groups of projection operators, {T, F} and {S, N}. The operators in each group are commuting but operators of different groups are not. The second qubit represents Jung’s two perspectives of extraversion and introversion. It is shown that this system gives a natural explanation of the 16 psychological types that are defined in the Jungian tradition. Further, the system accounts for the restriction posed by Jung concerning the possible combination of psychological functions and perspectives. The empirical consequences of the present theory are discussed, and the results of a pilot study are reported with the aim to check some basic predictions of the theory. In addition, it is shown why the present praxis of personality diagnostics based on classical statistics is insufficient. [Copyright &y& Elsevier]

We propose a way in which Pothos & Busemeyer (P&B) could strengthen their position. Taking a dynamic stance, we consider cognitive tests as functions that transfer a given input state into the state after testing. Under very general conditions, it can be shown that testable properties in cognition form an orthomodular lattice. Gleason's theorem then yields the conceptual necessity of quantum probabilities (QP). [ABSTRACT FROM AUTHOR]