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The state context property formalism: from concept theory to the semantics of music

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Abstract

Quantum cognition is an emergent area of research that applies quantum structures in cognitive situations where traditional approaches are problematic. Independently from quantum cognition, quantum approaches for the semantics of music interpretation and improvisation have been proposed in the context of quantum computational logic and standard quantum mechanics, respectively. These frameworks overcome the non-contextual and compositional approaches to the semantics of music. In this paper, we analyze the quantum approach to the semantics of music from the perspective of quantum cognition. We first introduce an operational framework, inspired by the Brussels–Geneva approach to the foundations of quantum theory, named state context property (SCoP) formalism, that has been applied in quantum cognition to model concepts. Next, we show that the quantum approaches to the semantics of music can be operationalized in SCoP. In particular, we apply the SCoP definitions of ‘orthogonal property’ and ‘experiment-context’ to operationalize the notions of ‘vague meaning’ and ‘interpretation’, and to characterize the structural differences between the semantics of music interpretation and improvisation.

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Notes

  1. For example, quantum cognition is not based upon the assumption of quantum processes in the brain.

  2. The function \(\nu \) can be extended to graded evaluations. For simplicity, we present \(\nu \) in its binary form.

  3. For example, the language of standard quantum mechanics is used for physical systems and teaching, quantum-logic is used in logic, quantum-information is used in computer science and some areas of physics, the C\(*\)-algebra formulation is used in mathematical physics, etc.

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Acknowledgments

I would like to thank Maria Luisa Dalla Chiara for pointing out and facilitating relevant material during the development of this paper, and to the two anonymous reviewers for insightful comments.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Kelowna, BC, Canada

    Tomas Veloz

  2. Insituto de Filosofía y Ciencias de la Complejidad, Los Alerces, 3024, Nuñoa, Chile

    Tomas Veloz & Pablo Razeto

  3. Center Leo Apostel for Interdisciplinary Studies, Brussels Free University, 1050, Brussels, Belgium

    Tomas Veloz

  4. Universidad Diego Portales, Vicerrectoría Académica, Manuel Rodríguez Sur 415, Santiago, Chile

    Pablo Razeto

Authors
  1. Tomas Veloz
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  2. Pablo Razeto
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Correspondence to Tomas Veloz.

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The authors declare that they have no conflict of interest.

Additional information

Communicated by M.L. Dalla Chiara, R. Giuntini, E. Negri and S. Smets.

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Veloz, T., Razeto, P. The state context property formalism: from concept theory to the semantics of music. Soft Comput 21, 1505–1513 (2017). https://doi.org/10.1007/s00500-015-1914-z

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