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

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

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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Correspondence to Alejandro Díaz-Caro .

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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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