依赖保留可阻止在第二范式（$2NF$）处停止
Dependency Preservation May Prevent Stopping at $2NF$
AI总结：
该研究指出，函数依赖集可能导致数据库无法精确处于第二范式，需直接从第一范式规范化到第三范式，或接受中间形式，为此用FD-图刻画了相关现象。
摘要：
传统上，人们认为关系数据库可以逐步规范化，从不规范化的表集合依次转换为第一范式（$1NF$）的表，再到第二范式（$2NF$）、第三范式（$3NF$），最后（可能）到巴斯-科德范式（$BCNF$）。特别是，将$1NF$的表转换为$2NF$表集合所应用的规则似乎过于直接，不会带来任何困难。虽然从理论上普遍认为，数据库的规范化程度越高就“越好”，但实际应用表明情况并非总是如此——在某些情况下，若将数据库保留在较低的范式级别，而不牺牲较高范式的任何优势，数据库性能可能会提升。人们曾理所当然地认为，规范化过程可以在达到任意范式后停止，无需继续到下一个更高的范式。然而，我们证明，根据函数依赖集的不同，可能无法“精确地”（后续将解释该方式）处于$2NF$。在这些情况下，必须要么将从$1NF$到$3NF$的规范化作为不可分解的操作执行，要么接受一种介于$2NF$和$3NF$之间的规范化形式。为了清晰呈现并简洁刻画该现象，我们将函数依赖建模为一种特定类型的有向超图——FD-图。展示该现象所需的最小设置仅需要一个复合键，以及两条部分重叠的传递依赖链，这可被绘制为一个特定的子超图。因此，包含该子超图的FD-图表明其对应的数据库无法精确地处于$2NF$。
英文摘要：
Traditionally, it was accepted that a relational database can be normalized step-by-step, from a set of un-normalized tables to tables in $1NF$, then to $2NF$, then to $3NF$, then (possibly) to $BCNF$. In particular, the rule applied to a table in $1NF$ in order to transform it to a set of tables in $2NF$ seems to be too straightforward to pose any difficulty. While it is a common belief to consider, theoretically, a database to be 'better' the higher it is normalized, practical usage advocates that this may not always be true -- in some cases a database performance may increase if left in a lower normal form, without sacrificing any of the advantages of a higher normal form. It was taken for granted that a normalization process can be stopped after reaching any normal form, without proceeding to the next higher one. However, we show that, depending on the set of functional dependencies, it may be impossible to be `precisely' (in a manner to be explained in the sequel) in $2NF$. One must, in these cases, either perform the normalization from $1NF$ to $3NF$ as an indecomposable move, or settle for a normalization between $2NF$ and $3NF$. For a clear presentation and a concise characterization of the phenomena, we model the functional dependencies as a (particular type of) directed hyper-graph -- an FD-graph. The minimal setup to exhibit the phenomena requires a single composite key, and two partially overlapping chains of transitive dependencies. This can be sketched as a specific sub-hyper-graph. Thus, an FD-graph containing that sub-hyper-graph indicates that its corresponding database cannot be precisely in $2NF$.
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