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This paper presents a novel framework, named Global-Local Correspondence Framework (GLCF), for visual anomaly detection with logical constraints. Visual anomaly detection has become an active research area in various real-world applications, such as industrial anomaly detection and medical disease diagnosis. However, most existing methods focus on identifying local structural degeneration anomalies and often fail to detect high-level functional anomalies that involve logical constraints. To address this issue, we propose a two-branch approach that consists of a local branch for detecting structural anomalies and a global branch for detecting logical anomalies. To facilitate local-global feature correspondence, we introduce a novel semantic bottleneck enabled by the visual Transformer. Moreover, we develop feature estimation networks for each branch separately to detect anomalies. Our proposed framework is validated using various benchmarks, including industrial datasets, Mvtec AD, Mvtec Loco AD, and the Retinal-OCT medical dataset. Experimental results show that our method outperforms existing methods, particularly in detecting logical anomalies.