动态的逻辑&逻辑的动态性;一些范例
Logic of Dynamics & Dynamics of Logic; Some Paradigm Examples
摘要：
本文综述了动态量子逻辑的一些最新发展，并概述了它的显式结构--与其他动态逻辑的一些类比和对比。摘要：“（静态）运算量子逻辑的发展”指出，经典的布尔结构过于僵化，无法描述量子系统的实际和潜在性质。另一方面，操作量子逻辑的直觉主义观点，通过重新考虑描述量子系统行为所需的原始命题，特别是鉴于量子测量的非确定性所产生的突现析取性，引导我们在逻辑上结合动力学的方向。对“直觉量子逻辑”的进一步阐述出现了“动态操作量子逻辑”，这使我们能够表达动态推理，因为我们可以捕捉实际属性如何传播，包括它们的时间因果结构，并为进化或提交测量的系统提供统一的逻辑描述。这种设置表明，即使是静态的操作量子逻辑也有一个隐藏的动态成分，即所谓的格结构的“正交模性”。针对动态操作量子逻辑的Quantale语义，我们描述了与（非）交换线性逻辑的Quantale语义的一些不同点。
英文摘要：
This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static) operational quantum logic" points out that classical boolean structures are too rigid to describe the actual and potential properties of quantum systems. On the other hand, an intuitionistic perspective on operational quantum logic, guides us in the direction of incorporating dynamics logically by reconsidering the primitive propositions required to describe the behavior of a quantum system, in particular in view of the emergent disjunctivity due to the non-determinism of quantum measurements. A further elaboration on "intuitionistic quantum logic" emerges into a "dynamic operational quantum logic", which allows us to express dynamic reasoning in the sense that we can capture how actual properties propagate, including their temporal causal structure, and provides a unified logical description of systems which evolve or which are submitted to measurements. This setting reveals that even static operational quantum logic bears a hidden dynamic ingredient in terms of what is called "the orthomodularity" of the lattice-structure. Focusing on the quantale semantics for dynamic operational quantum logic, we delineate some points of difference with the existing quantale semantics for (non)-commutative linear logic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
