We introduce a sequent system which is Gentzen algebraisable with orthomodular lattices as equivalent algebraic semantics, and therefore can be viewed as a calculus for orthomodular quantum logic. Its sequents are pairs of non-associative structures, formed via a structural connective whose algebraic interpretation is the Sasaki product on the left-hand side and its De Morgan dual on the right-hand side. It is a substructural calculus, because some of the standard structural sequent rules are restricted—by lifting all such restrictions, one recovers a calculus for classical logic.

中文翻译：

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正交模量子逻辑的子结构根岑微积分

我们引入了一个序列系统，它可以用正交模格进行 Gentzen 代数作为等效代数语义，因此可以被视为正交模量子逻辑的微积分。它的序列是一对非关联结构，通过结构连接词形成，其代数解释是左侧的 Sasaki 积 及其 De Morgan双在右侧。它是一种子结构微积分，因为一些标准结构顺序规则受到限制——通过解除所有这些限制，人们可以恢复经典逻辑的微积分。< /span>