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Article Dans Une Revue Theoretical Computer Science Année : 2023

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

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We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue that these connectives model the informationerasure, the non-reversibility, and the non-determinism that occur, among other places, in quantum measurement. We introduce an intuitionistic propositional logic with a non-harmonious logical connective sup and two interstitial rules, and show that the proof language of this logic forms the core of a quantum programming language.
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hal-04398691 , version 1 (16-01-2024)

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Alejandro Díaz-Caro, Gilles Dowek. A New Connective in Natural Deduction, and its Application to Quantum Computing. Theoretical Computer Science, 2023, 957, pp.113840. ⟨10.1016/j.tcs.2023.113840⟩. ⟨hal-04398691⟩
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