归纳推理和归纳进程

分析了归纳推理与演绎推理的区别, 给出了归纳推理的形式化规则,定义了重构和归纳进程(序列)的概念.同时还给出了一个产生归纳序列的归纳过程模式,并证明:若已知模型M的全体实例集合ε_M,则可以从任一给定的理论出发, 使用此归纳过程模式所产生的所有归纳序列都收敛于同一极限,这个极限就是模型M的全部真语句. 这说明了归纳推理规则的合理性.

Inductive Inference and Inductive Process

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.