Yichao Cao

Answering complex first-order logic queries on multi-modal knowledge graphs requires multi-hop reasoning over symbolic entities and fine-grained multi-modal elements. Existing geometric embedding methods represent logical operations and boundary uncertainty in continuous spaces. However, executing multi-hop deductions and global entity matching in such spaces necessitates dense floating-point operations, generating severe computational latency. To address these limitations, we propose Rough Cone Embedding Hashing (RCEH), a framework that introduces discrete hashing retrieval mechanisms into multi-modal logical reasoning. RCEH incorporates a cone-preserving hashing mask module that utilizes boolean sequences in Hamming space to retain the boundary features of rough cone representations and the inherent uncertainty of multi-modal entities. The framework subsequently applies cross-space cascade reasoning, which combines bitwise coarse filtering in discrete space with continuous space re-ranking to refine candidate entities and identify hidden sub-entity answers. Extensive experiments on large-scale datasets, including FB15k, FB15k-237, YAGO15k and DB15k, demonstrate that RCEH significantly reduces retrieval time while achieving state-of-the-art accuracy on multi-modal logical queries.