Extrapolating future events based on historical information in temporal knowledge graphs (TKGs) holds significant research value and practical applications. In this field, the methods currently utilized can be classified as either embedding-based or logical rule-based. Embedding-based methods depend on learned entity and relation embeddings for prediction, but they suffer from the lack of interpretability due to the opaque reasoning process. On the other hand, logical rule-based methods face scalability challenges as they heavily rely on predefined logical rules. To overcome these limitations, we propose a hybrid model that combines embedding-based and logical rule-based methods to capture deep causal logic. Our model, called the Inductive Reasoning Model based on Interpretable Logical Rule (ILR-IR), aims to provide interpretable insights while effectively predicting future events in TKGs. ILR-IR delves into historical information, extracting valuable insights from logical rules embedded within relations and interaction preferences between entities. By considering both logical rules and interaction preferences, ILR-IR offers a comprehensive perspective for predicting future events. In addition, we propose the incorporation of a one-class augmented matching loss during optimization, which serves to enhance performance of the model during training. We evaluate ILR-IR on multiple datasets, including ICEWS14, ICEWS0515, and ICEWS18. Experimental results demonstrate that ILR-IR outperforms state-of-the-art baselines, showcasing its superior performance in TKG extrapolation reasoning. Moreover, ILR-IR demonstrates remarkable generalization capabilities, even when applied to related datasets that share a common relation vocabulary. This suggests that our proposed model exhibits robust zero-shot reasoning abilities. For interested parties, we have made our code publicly available at https://github.com/mxadorable/ILR-IR.