三值量子逻辑进路探析

量子测量实验显示部分经典逻辑规则在量子世界中失效。标准量子逻辑进路通过特有的希尔伯特空间的格运算揭示出一种内在于微观物理学理论的概念框架结构,也即量子力学测量命题的正交补模或弱模格,解释了经典分配律的失效,它在形式化方面十分完美,但在解释方面产生了一些概念混乱。在标准量子逻辑进路之外,赖欣巴赫通过引入"不确定"的第三真值独立地提出一种不同的量子逻辑模型来解释量子实在的特征,不是分配律而是排中律失效,但是他的三值量子逻辑由于缺乏标准量子逻辑的上述优点而被认为与量子力学的概率空间所要求的潜在逻辑有很少联系。本文尝试引入一种新的三值逻辑模型来说明量子实在,它有以下优点:(1)满足卢卡西维茨创立三值逻辑的最初语义学假定;(2)克服赖欣巴赫三值量子逻辑的缺陷;(3)澄清标准量子逻辑遭遇的概念混乱;(4)充分地保留经典逻辑规则,特别是标准量子逻辑主张放弃的分配律。

Exploring the Approaches to Three-valued Quantum Logic

Quantum measurement experiment indicates that some classical logical rules fail in quantum world.Standard Quantum Logic approach reveals a structure inherited in conceptual framework of microphysical theories,namely the orthocomplementary modular or weakly modular lattice of quantum mechanical measurement propositions through the special Hilbert Space operation.It explains why classical law of distributivity fails and has a perfect formulation,but it also leads to some conceptual troubles about interpretive issues.In addition to the standard quantum logic,Reichenbach independently proposes a different quantum logic model to interpret the characteristics of quantum reality by introducing a third logic value ＂indeterminate＂.According to his quantum logic theory, it is that the law of excluded middle fails,not the law of distributivity.However,Reichenbach＇s three-valued quantum logic is considered as a logic which has little to do with the underlying logic required for quantum mechanical probability space because of the lack of advantages of standard quantum logic.This paper tries to introduce a new three-valued logic model to interpret quantum reality,which has the following merits： （1） satisfying the initial semantic assumptions of Lukasiewicz＇s three-valued logic;（2） overcoming the shortcomings of Reichenbach＇s three-valued quantum logic;（3） clarifying the conceptual troubles faced by standard quantum logic;（4） retaining the classical logical rules as many as possible especially including the law of distributivity given up by standard quantum logic.