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A New Connective in Natural Deduction, and Its Application to Quantum Computing

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Theoretical Aspects of Computing – ICTAC 2021 (ICTAC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12819))

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Abstract

We investigate an unsuspected connection between non-harmonious logical connectives, such as Prior’s tonk, and quantum computing. We argue that non-harmonious connectives model the information erasure, the non-reversibility, and the non-determinism that occur, among other places, in quantum measurement. We introduce a propositional logic with a non-harmonious connective sup and show that its proof language forms the core of a quantum programming language.

Founded by STIC-AmSud 21STIC10, ECOS-Sud A17C03, and the IRP SINFIN.

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Acknowledgements

The authors want to thank Jean-Baptiste Joinet, Dale Miller, Alberto Naibo, and Alex Tsokurov for useful discussions.

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Authors and Affiliations

  1. DCyT, Universidad Nacional de Quilmes, Bernal, Argentina

    Alejandro Díaz-Caro

  2. ICC, CONICET–Universidad de Buenos Aires, Buenos Aires, Argentina

    Alejandro Díaz-Caro

  3. Inria, ENS Paris-Saclay, Gif-sur-Yvette, France

    Gilles Dowek

Authors
  1. Alejandro Díaz-Caro
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  2. Gilles Dowek
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Corresponding author

Correspondence to Alejandro Díaz-Caro .

Editor information

Editors and Affiliations

  1. Nazarbayev University, Nur-Sultan, Kazakhstan

    Antonio Cerone

  2. Department of Informatics, University of Oslo, Oslo, Norway

    Peter Csaba Ölveczky

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Díaz-Caro, A., Dowek, G. (2021). A New Connective in Natural Deduction, and Its Application to Quantum Computing. In: Cerone, A., Ölveczky, P.C. (eds) Theoretical Aspects of Computing – ICTAC 2021. ICTAC 2021. Lecture Notes in Computer Science(), vol 12819. Springer, Cham. https://doi.org/10.1007/978-3-030-85315-0_11

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  • DOI: https://doi.org/10.1007/978-3-030-85315-0_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-85314-3

  • Online ISBN: 978-3-030-85315-0

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