2000 character limit reached
A New Connective in Natural Deduction, and its Application to Quantum Computing (2012.08994v6)
Published 16 Dec 2020 in cs.LO
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.