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.

翻译：本文提出了一种具有严格受限交换规则和弱化规则的矢列子结构逻辑。该逻辑对于量子系统的测量序列具有可靠性，并给出了完备的语义模型。语义结构包含一个表示元素间正交性的二元关系，由此可定义出将希尔伯特空间投影运算泛化的操作。语言系统包含一个酉联结词（一种否定算子）以及两个既非交换亦非结合的二元对偶联结词（合取与析取算子）。这为量子测量提供了证明论结构简洁优美的逻辑体系。