[Solved]: What is semantic closure?

Problem Detail: 

In the context of database theory, what does semantic closure mean (linguistically speaking, i.e. not the mathematical definition)

If X is the set of attributes of $F$, then the semantic closure $F^+$ of $F$ is defined as follows:
$F^+=\{$ Y $\rightarrow$ Z $\ |\ $ Y $\cup$ Z $\subseteq$ X $\wedge\ F \models$ Y $\rightarrow$ Z $\}$
$F \models $ Y $\rightarrow$ Z means that any database instance that satisfies every functional dependency of $F$ also satisfies Y $\rightarrow$ Z

Asked By : Oliver

Answered By : reinierpost

Generally speaking, the term closure is used when you have sets of items and some kind of operation that, given one or more items, can produce more such items. The closure of a set of items with respect to the operation is the set obtained by applying the operation on items in the set in whichever way possible, adding the resulting items to the set, and repeating this until no more items can be added (which may be infinitely often). The resulting set is the smallest set that includes the original set and is closed under the operation (in the sense that all possible applications of the operation on items in the set produce items that are also in the set).

Examples:

• the closure of {1} with respect to the operation add 2 is the set of odd natural numbers
• the closure of {1,3,5} with respect to the operation multiply is $\{3^n5^m \mid n, m \in I\!\!N\}$
• the transitive closure of the relation {(1,2), (2,4), (4,5)} is {(1,2), (1,4), (1,5), (2,4), (2,5), (4,5)} (the smallest transitive set that includes the original set)

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Question Source : http://cs.stackexchange.com/questions/11030