We investigate an unsuspected connection between logical connectives with non-harmonious deduction rules, such as Prior's tonk, and quantum computing. We argue these 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 logical connective sup that has non-harmonious deduction rules and also with two interstitial rules, and show that the proof language of this logic forms the core of a quantum programming language.
翻译:我们调查了逻辑连接与非和谐的扣减规则(如Prior's tomnk)和量子计算(decondiction)之间的一种未预料的联系。 我们论证了在量子测量中出现的信息侵蚀、不可逆性和非确定性等关联模式。 我们引入了一种逻辑推论和逻辑连接的逻辑,它具有非和谐的扣减规则,还有两种互通规则,并表明这种逻辑的证明语言构成了量子编程语言的核心。