Natural language understanding is a challenging problem that covers a wide range of tasks. While previous methods generally train each task separately, we consider combining the cross-task features to enhance the task performance. In this paper, we incorporate the logic information with the help of the Natural Language Inference (NLI) task to the Story Cloze Test (SCT). Previous work on SCT considered various semantic information, such as sentiment and topic, but lack the logic information between sentences which is an essential element of stories. Thus we propose to extract the logic information during the course of the story to improve the understanding of the whole story. The logic information is modeled with the help of the NLI task. Experimental results prove the strength of the logic information.