In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for bounded quantifiers that satisfies De Morgan's Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgan's Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgan's Laws.

在Birkhoff和von Neumann提出的量子逻辑中，德摩根定律在量子力学中的观测命题的投影值真值赋值中起着重要作用。Takeuti的量子集理论将这种分配扩展到了量子集宇宙上的所有集合理论陈述。然而，武体的量子集理论存在一个问题，即德摩根定律在通用有量词和存在有界量词之间不成立。在这里，我们通过引入满足De Morgan定律的有界量词的新真值分配来解决此问题。为了证明新分配的合理性，我们证明了转移原理，表明将真值分配给每个有界ZFC定理都有一个下限，该下限由换向器确定，投影值为可交换性，公式中的常量。我们研究最通用的真值分配类别，并为它们满足转移原理，满足德摩根定律以及同时满足这两个条件提供必要和充分的条件。对于具有多项式可定义的逻辑运算的分配类别，我们确定恰好36个满足转移原理的分配以及恰好6个既满足转移原理又符合De Morgan定律的分配。