标题： 经典逻辑与量子逻辑的多模型及共同格模型 显示英文标题

标题： Classical and Quantum Logics with Multiple and a Common Lattice Models

摘要： 我们研究了一种适当的命题量子逻辑，并证明它有多个不相交的格模型，其中只有一个是以希尔伯特（量子）空间为基础的 orthomodular 格（代数）。我们给出了经典逻辑的一个等价证明，结果发现它有不相交的分配格和非分配 ortholattice 作为其模型。特别是，我们证明了经典逻辑和量子逻辑相对于这些格都是可靠且完全的。我们还表明存在一个共同的非 orthomodular 格，它是经典逻辑和量子逻辑的模型。用技术术语来说，这使我们能够在一个数字（标准、两子集、0-1 位）计算机和一个非数字（比如说，六个子集）计算机上运行相同的经典逻辑（具有适当的芯片和电路）。对于量子逻辑，同样的六个元素的公共格可以作为评估较大格模型方程或逻辑定理的有效基准。 显示英文摘要

摘要： We consider a proper propositional quantum logic and show that it has multiple disjoint lattice models, only one of which is an orthomodular lattice (algebra) underlying Hilbert (quantum) space. We give an equivalent proof for the classical logic which turns out to have disjoint distributive and non-distributive ortholattices as its models. In particular, we prove that both classical and quantum logics are sound and complete with respect to each of these lattices. We also show that there is one common non-orthomodular lattice that is a model of both quantum and classical logics. In technical terms, that enables us to run the same classical logic on both a digital (standard, two subset, 0-1 bit) computer and on a non-digital (say, a six subset) computer (with appropriate chips and circuits). With quantum logic, the same six element common lattice can serve us as a benchmark for an efficient evaluation of equations of bigger lattice models or theorems of the logic.