Machine learning in real-world situations sometimes starts from an initial collection of training instances; learning then proceeds off and on as new training instances come intermittently. The idea of two-phase learning has then been proposed here for effectively solving the learning problems in which training instances come in this two-stage way. Four two-phase learning algorithms based on the learning method PRISM have also been proposed for inducing rules from training instances. These alternatives form a spectrum, showing achievement of the requirement of PRISM (keeping down the number of irrelevant attributes) heavily dependent on the spent computational cost. The suitable alternative, as a trade-off between computational costs and achievement to the requirements, can then be chosen according to the request of the application domains.