A logical framework on Machine Learning by Rule Generation (MLRG) from tables with non-deterministic information is proposed, and its prototype system in SQL is implemented. In MLRG, the certain rules defined in Rough Non-deterministic Information Analysis (RNIA) are obtained at first, and each uncertain attribute value is estimated so as to cause the certain rules as many as possible, because the certain rules show us the most reliable information. This strategy is similar to the maximum likelihood estimation in statistics. By repeating this process, a standard table and the rules in its table are learned (or estimated) from a given table with non-deterministic information. Even though it will be hard to know the actual unknown values, MLRG will give a plausible estimation value. © Springer International Publishing AG 2017.