This paper introduces a new approach for discovering rules in data in the environment with noise and incompleteness. The central idea is to substitute "Generalization Distribution Table (GDT)" for the ``version space'' defined by Mitchell. The GDT is a table in which the probabilistic relationships between concepts and instances over discrete domains are represented. Using a GDT as a hypothesis search space, the uncertainty of a rule, which includes the prediction for unseen instances, can be explicitly represented in the strength of this rule; noisy data, missing data, and data change can be handled effectively; and biases for rule generation can be selected.