Recommender systems filter contents/items valuable to users by inferring preferences from user features and historical behaviors. Mainstream approaches follow the learning-to-rank paradigm, which focus on discovering and modeling item topics (e.g., categories), and capturing user preferences on these topics based on historical interactions. However, this paradigm often neglects the modeling of user characteristics and their social roles, which are logical confounders influencing the correlated interest and user preference transition. To bridge this gap, we introduce the user role identification task and the behavioral logic modeling task that aim to explicitly model user roles and learn the logical relations between item topics and user social roles. We show that it is possible to explicitly solve these tasks through an efficient integration framework of Large Language Model (LLM) and recommendation systems, for which we propose TagCF. On the one hand, TagCF exploits the (Multi-modal) LLM's world knowledge and logic inference ability to extract realistic tag-based virtual logic graphs that reveal dynamic and expressive knowledge of users, refining our understanding of user behaviors. On the other hand, TagCF presents empirically effective integration modules that take advantage of the extracted tag-logic information, augmenting the recommendation performance. We conduct both online experiments and offline experiments with industrial and public datasets as verification of TagCF's effectiveness, and we empirically show that the user role modeling strategy is potentially a better choice than the modeling of item topics. Additionally, we provide evidence that the extracted logic graphs are empirically a general and transferable knowledge that can benefit a wide range of recommendation tasks. Our code is available in https://github.com/Code2Q/TagCF.