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arXiv · 2012.08994

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

Alejandro Díaz-Caro·Gilles Dowek
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Abstract

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 information-erasure, 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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Alejandro Díaz-Caro, Gilles Dowek. 2020-12-16. A New Connective in Natural Deduction, and its Application to Quantum Computing. https://doi.org/10.1016/j.tcs.2023.113840

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