The　sparse　interactions　between　users　and　items　have　aggravated　the　difficulty　of　their　representations　in　recommender　systems.　Existing　methods　leverage　tags　to　alleviate　the　sparsity　problem　but　ignore　prevalent　logical　relations　among　items　and　tags　(e.g.,　membership,　hierarchy,　and　exclusion),　which　can　be　leveraged　to　enhance　the　accuracy　of　modeling　user　preferences　and　conducting　recommendations.　To　this　end,　we　propose　to　extract　logical　relations　among　item　tags　from　existing　tag　taxonomies　and　exploit　the　individual　strengths　of　the　Poincaré　and　the　Lorentz　models　in　hyperbolic　space　for　logical　relation　modeling　towards　enhanced　recommendations.　Moreover,　we　find　that　the　logical　relations　directly　extracted　from　existing　tag　taxonomies　can　be　inaccurate　and　coarse.　Therefore,　we　further　devise　innovative　consistency-based　and　granularity-based　weighting　mechanisms　based　on　user　behavior　patterns　for　data-driven　logical　relation　mining　that　can　be　jointly　optimized　along　with　recommendations　in　an　end-to-end　fashion.　Extensive　experiments　on　four　real-world　benchmark　datasets　show　drastic　performance　gains　brought　by　our　proposed　framework,　which　constantly　achieves　an　average　of　8.25%　improvement　over　state-of-the-art　competitors　regarding　both　Recall　and　NDCG　metrics.　Insightful　case　studies　further　demonstrate　that　our　automatically　refined　logical　relations　are　highly　accurate　and　interpretable.　　©　2024　IEEE.