In this paper, the qualitative and quantitative semantics for rules in data tables are investigated from a logical viewpoint. In modern data analysis, knowledge can be discovered from data tables and is usually represented by some rules. However, the knowledge is useful for a human user only when he can understand the meaning of the rules. This is called the interpretability problem of intelligent data analysis. The solution of the problem depends on the selection of the rule representation language. A good representation language should have clear semantics so that a rule can be effectively validated with respect to the given data tables. In this regard, logic is one of the best choices. Starting from reviewing the decision logic for data tables, we subsequently generalize it to fuzzy and possibilistic decision logics. The rules are then viewed as the implications between well-formed formulas of these logics and their semantics with respect to precise or uncertain data tables are presented. The validity, support, and confidence of a rule are also rigorously defined in the framework.