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In this paper, we consider classes of decision tables closed under removal ofattributes (columns) and changing of decisions attached to rows. For decisiontables from closed classes, we study lower bounds on the minimum cardinality ofreducts, which are minimal sets of attributes that allow us to recognize, for agiven row, the decision attached to it. We assume that the number of rows indecision 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, onlystandard lower bounds $\Omega (\log $ ${\rm cl}(T))$ on the minimum cardinalityof reducts for decision tables hold, where ${\rm cl}(T)$ is the number ofdecision classes in the table $T$. In another family, these bounds can beessentially tightened up to $\Omega ({\rm cl}(T)^{1/q})$ for some natural $q$.

Lower Bounds on Cardinality of Reducts for Decision Tables from Closed Classes