问题
Suppose we have a table with 3 columns A,B and C
A B C
---------------
1 2 3
2 4 5
4 6 7
n 5 n
Here 'n' means null.
Can we say that A -> B and A -> C? I know the definition of functional dependencies but I'm just confused in the case of null values.
回答1:
If null is considered a value, then the answer is yes. A -> B, C holds in the given data. However, to be a value imposes certain requirements. All operators applicable to the domain (e.g. integers) like equality, addition, less than, and so on, must be well-defined in the presence of nulls.
If null is not a value, then the answer is more complicated. Functional dependencies, strictly speaking, apply to relations. If a table represents a relation, then we can refer to functional dependencies in the table. However, a symbol that represents the absence of a value is metadata, not data. It allows multiple union-incompatible relations to be represented by a single table. In this case, we can't apply the concept of functional dependency to the table since it's not clear which relation we're talking about.
Further confusing things, SQL DBMSs don't handle nulls consistently. In some cases, they're handled like values, in others like the absence of values. If you want to understand and describe a table logically, the best option is to decompose it into a set of null-free relations, and then to analyze each of those parts independently.
In the case of your example table, we run into a problem if null isn't a value. The last row has no unique identifier (it can't be B:4 since another row has B:4 as well) and we can't determine anything from a lack of information. The example can't be decomposed into a set of relations without discarding that row.
If we change the last row to have B:5 instead, then we decompose it into two relations: R1 = {(A:1, B:2, C:3), (A:2, B:4, C:5), (A:4, B:6, C:7)} and R2 = {(B:2), (B:4), (B:6), (B:5)}. We can say A -> B, C holds in R1 but not in R2.
来源：https://stackoverflow.com/questions/46956259/functional-dependencies-in-case-of-nulls