论文标题
量子测量的子结构逻辑
A substructural logic for quantum measurements
论文作者
论文摘要
本文介绍了一个非常有限的交换和削弱规则的序列逻辑。关于Quantic系统的测量序列，这是合理的。提供了声音和完整的语义。语义结构包括一个二进制关系，该关系表达元素之间的正交性并实现了将投影操作推广到希尔伯特空间中的操作的定义。该语言具有统一的结缔组织，一种否定和两个双二元连接，它们既不是交换性的，也不是联想性的连接。这为量子测量提供了逻辑，其证明理论在美学上令人愉悦。
This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic structures include a binary relation that expresses orthogonality between elements and enables the definition of an operation that generalizes the projection operation in Hilbert spaces. The language has a unitary connective, a sort of negation, and two dual binary connectives that are neither commutative nor associative, sorts of conjunction and disjunction. This provides a logic for quantum measurements whose proof theory is aesthetically pleasing.
