Despite advances in unsupervised log anomaly detection, current models require dataset-specific training, causing costly procedures, limited scalability, and performance bottlenecks. Furthermore, numerous models lack cognitive reasoning abilities, limiting their transferability to similar systems. Additionally, these models often encounter the **“identical shortcut”** predicament, erroneously predicting normal classes when confronted with rare anomaly logs due to reconstruction errors. To address these issues, we propose **MLAD**, a novel **M**ulti-system **L**og **A**nomaly **D**etection model incorporating semantic relational reasoning. Specifically, we extract cross-system semantic patterns and encode them as high-dimensional learnable vectors. Subsequently, we revamp attention formulas to discern keyword significance and model the overall distribution through vector space diffusion. Lastly, we employ a Gaussian mixture model to highlight rare word uncertainty, optimizing the vector space with maximum expectation. Experiments on real-world datasets demonstrate the superiority of MLAD.