【摘要】 分配律在经典逻辑推理机制中具有核心地位。量子逻辑不再具有经典逻辑中的分配律,从而也失去了经典逻辑推理机制,因此量子逻辑是否可称为逻辑备受人们质疑。指出了希尔伯特空间闭子空间刻画量子逻辑的不足,并深层次地分析了经典逻辑推理机制的内涵,利用正交模律取代经典逻辑中的分配律,可以实现量子逻辑的推理能力。最后,通过范畴理论中伴随函子的概念重新审视逻辑推理机制,使经典逻辑推理机制推广到更广泛的逻辑领域中。更多还原

【Abstract】 It is well known that the distributive law plays a core role in deduction mechanism of classical logic.However,distributive law is abandoned in quantum logic,so that the classic deduction mechanism disappears from quantum,which spontaneously arises the debate whether the quantum logic can be called"logic"?In this paper,we introduced the defects of using closed subspaces of Hilbert space to describe quantum logic and deeply analyzed the deduction mechanism in classical logic.Further,the deduction mechanism can be established in quantum logic by using the orthomodular law instead of distributive law.In particular,the deduction mechanism can be renewed with adjunctions in category,which is a generalization of deduction mechanism in classical logic.更多还原