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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)


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.

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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.

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