Abstract: This paper analyzes the difference between inductive inference and deductive inference, presents a formal logic framework for inductive inference, and defines the concepts of reconstruction and inductive sequence. In addition, it gives an inductive procedure to generate inductive sequences. It proves that for a model M, if the set ε_M of all its instances is known, then starts with any theory, all inductive sequences generated by the procedure will converge to the same limit, i.e., the set of all true sentences of model M. Therefore, it justifies the inductive rules.