Implicational quantum logic
Implicational quantum logic
复制标题
蕴涵量子逻辑
DOI：
10.1007/s10516-021-09614-y
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发表时间：
2022
期刊：
影响因子：
0.5
通讯作者：
Kenji Tokuo
中科院分区：
文献类型：
--
作者：
Kenji Tokuo
提出了正交模量子逻辑的一个非经典子系统。该系统采用两种基本运算：作为蕴涵的Sasaki钩子和作为连接的and-then运算。这些操作成功地满足了肯定前件和演绎定理。换句话说，它们在范畴论中形成了一个附加物。两种类型的语义提出了这种逻辑：一个代数和一个物理。代数语义处理正交模格，如在传统的量子逻辑。物理语义给出了一个程序，用于导出一系列是非实验的最后一段。
A non-classical subsystem of orthomodular quantum logic is proposed. This system employs two basic operations: the Sasaki hook as implication and theand-thenoperation as conjunction. These operations successfully satisfy modus ponens and the deduction theorem. In other words, they form an adjunction in terms of category theory. Two types of semantics are presented for this logic: one algebraic and one physical. The algebraic semantics deals with orthomodular lattices, as in traditional quantum logic. The physical semantics is given as a procedure for deriving a final segment of a series of yes-no experiments.