Boolean networks are widely used model to represent gene interactions and global dynam-ical behavior of gene regulatory networks. To understand the memory effect involved in some interactions between biological components, it is necessary to include delayed influences in the model. In this paper, we present a logical method to learn such models from sequences of gene expression data. This method analyzes each sequence one by one to iteratively construct a Boolean network that captures the dynamics of these observations. To illustrate the merits of this approach, we apply it to learning real data from bioinformatic literature. Using data from the yeast cell cycle, we give experimental results and show the scalability of the method. We show empirically that using this method we can handle millions of observations and successfully capture delayed influences of Boolean networks.