In　personalized　recommendations,　users　often　express　complex　logical　requirements,　involving　the　intersection　of　multiple　preferences　over　heterogeneous　graphs　containing　users,　items,　and　external　knowledge.　Existing　methods　for　mining　logical　relations　face　challenges　in　scalability　and　often　overlook　the　semantics　of　relations,　which　are　essential　for　uncovering　higher-order　connections　and　addressing　incomplete　relations　within　the　graph.　To　tackle　these　challenges,　we　propose　RelRec,　a　novel　approach　that　leverages　large　language　models　(LLMs)　to　mine　logical　relations　and　satisfy　users＇　logical　requirements　in　personalized　recommendation　tasks.　Specifically,　the　framework　begins　with　the　extraction　of　user-driven　logical　relations,　followed　by　a　rule-based　logical　relation　mining　module　that　integrates　both　semantic　and　structural　information　using　the　capabilities　of　LLMs.　By　uncovering　higher-order　logical　relations,　our　approach　effectively　refines　the　heterogeneous　graph　for　reasoning　capacity　and　recommendation　accuracy.　Extensive　experiments　on　real-world　datasets　demonstrate　that　RelRec　significantly　outperforms　existing　methods.　©　2025　Copyright　held　by　the　owner/author(s).　Publication　rights　licensed　to　ACM.