database - 反单调性和单调性约束是什么意思？

Question

我在网上查看了这个答案，我得到的是对它们的相似定义。这是我发现的:

Monotone constraints possess the following property. If an itemset S violates a monotone constraint C, then any of its subsets also violates C. Equivalently, all supersets of an itemset satisfying a monotone constraint C also satisfy C (i.e., C is upward closed). Monotone

Anti-monotone constraints possess the following nice property. If an itemset S satisfies an anti-monotone constraint C, then all of its subsets also satisfy C (i.e., C is downward closed). Equivalently, any superset of an itemset violating an anti-monotone constraint C also violates C. Anti-monotone

引用链接中的定义:

A constraint C is monotone if and only if for all itemsets S and S′: if S ⊇ S′ and S violates C, then S′ violates C.

A constraint C is anti-monotone if and only if for all itemsets S and S′: if S ⊇ S′and S satisfies C, then S′ satisfies C.

谁能给我解释一下它们之间有什么区别？最好有例子。

Answer 1

根据第一个定义，如果 S 违反 C，则它的超集可能不会也违反 C，但子集必须...如果 S 满足 C，则超集它的一部分必须也满足 C 但一个子集可能不。

第二个定义是相反的...如果 S 违反 C，它的超集必须也违反 C 但子集可能不会...并且如果 S 满足 C，它的超集可能不也满足 C，但子集必须。