In this paper, we consider classes of decision tables closed under removal of attributes (columns) and changing of decisions attached to rows. For decision tables from closed classes, we study lower bounds on the minimum cardinality of reducts, which are minimal sets of attributes that allow us to recognize, for a given row, the decision attached to it. We assume that the number of rows in decision tables from the closed class is not bounded from above by a constant. We divide the set of such closed classes into two families. In one family, only standard lower bounds $\Omega (\log $ ${\rm cl}(T))$ on the minimum cardinality of reducts for decision tables hold, where ${\rm cl}(T)$ is the number of decision classes in the table $T$. In another family, these bounds can be essentially tightened up to $\Omega ({\rm cl}(T)^{1/q})$ for some natural $q$.

翻译：本文考虑在删除属性（列）和修改行对应决策这两种操作下封闭的决策表类。针对封闭类中的决策表，我们研究约简（即能够识别给定行对应决策的最小属性集合）的最小基数下界。假设封闭类中决策表的行数不受常数上界约束，我们将此类封闭类划分为两个族。其中一个族仅能获得决策表约简最小基数的标准下界 $\Omega (\log {\rm cl}(T))$，其中 ${\rm cl}(T)$ 表示表 $T$ 中的决策类数量；另一个族中，对于某个自然数 $q$，该下界可实质上收紧至 $\Omega ({\rm cl}(T)^{1/q})$。