Compositional zero-shot learning (CZSL) aims to recognize unseen attribute-object compositions by learning the primitive concepts (i.e., attribute and object) from the training set. While recent works achieve impressive results in CZSL by leveraging large vision-language models like CLIP, they ignore the rich semantic relationships between primitive concepts and their compositions. In this work, we propose LOGICZSL, a novel logic-induced learning framework to explicitly model the semantic relationships. Our logic-induced learning framework formulates the relational knowledge constructed from large language models as a set of logic rules, and grounds them onto the training data. Our logic-induced losses are complementary to the widely used CZSL losses, therefore can be employed to inject the semantic information into any existing CZSL methods. Extensive experimental results show that our method brings significant performance improvements across diverse datasets (i.e., CGQA, UT-Zappos50K, MIT-States) with strong CLIP-based methods and settings (i.e., Close World, Open World). Codes will be publicly released.