On the lattice structure of quantum logic
On the lattice structure of quantum logic
复制标题
论量子逻辑的晶格结构
DOI：
10.1017/s0004972700042210
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发表时间：
1969
影响因子：
0.7
通讯作者：
P. D. Finch
中科院分区：
文献类型：
--
作者：
P. D. Finch
弱逻辑结构被定义为一组布尔命题逻辑，其中可以定义否定和蕴涵的公共运算。弱逻辑结构的布尔成分的集合并是一个命题逻辑，它是一个正补偏序集，其中正补被解释为否定，偏序被解释为蕴涵。证明了如果在这个逻辑上定义一个具有某些似然性质的逻辑合取运算，那么这个逻辑就具有正交模格的结构。相反，如果逻辑是正交模格，则可以在其上定义合取运算。
A weak logical structure is defined as a set of boolean propositional logics in which one can define common operations of negation and implication. The set union of the boolean components of a weak logical structure is a logic of propositions which is an orthocomplemented poset, where orthocomplementation is interpreted as negation and the partial order as implication. It is shown that if one can define on this logic an operation of logical conjunction which has certain plausible properties, then the logic has the structure of an orthomodular lattice. Conversely, if the logic is an orthomodular lattice then the conjunction operation may be defined on it.