Predicting drug-drug interaction (DDI) plays a crucial role in drug recommendation and discovery. However, wet lab methods are prohibitively expensive and time-consuming due to drug interactions. In recent years, deep learning methods have gained widespread use in drug reasoning. Although these methods have demonstrated effectiveness, they can only predict the interaction between a drug pair and do not contain any other information. However, DDI is greatly affected by various other biomedical factors (such as the dose of the drug). As a result, it is challenging to apply them to more complex and meaningful reasoning tasks. Therefore, this study regards DDI as a link prediction problem on knowledge graphs and proposes a DDI prediction model based on Cross-Transformer and Graph Convolutional Networks (GCN) in first-order logical query form, TransFOL. In the model, a biomedical query graph is first built to learn the embedding representation. Subsequently, an enhancement module is designed to aggregate the semantics of entities and relations. Cross-Transformer is used for encoding to obtain semantic information between nodes, and GCN is used to gather neighbour information further and predict inference results. To evaluate the performance of TransFOL on common DDI tasks, we conduct experiments on two benchmark datasets. The experimental results indicate that our model outperforms state-of-the-art methods on traditional DDI tasks. Additionally, we introduce different biomedical information in the other two experiments to make the settings more realistic. Experimental results verify the strong drug reasoning ability and generalization of TransFOL in complex settings. Data and code are available at https://github.com/Cheng0829/TransFOL.