Logical anomalies are violations of predefined constraints on object quantity, spatial layout, and compositional relationships in industrial images. While prior work largely treats anomaly detection as a binary decision, such formulations cannot indicate which logical rule is broken and therefore offer limited value for quality assurance. We introduce Logical Anomaly Classification (LAC), a task that unifies anomaly detection and fine-grained violation classification in a single inference step. To tackle LAC, we propose LogiCls, a vision-language framework that decomposes complex logical constraints into a sequence of verifiable subqueries. We further present a data-centric instruction synthesis pipeline that generates chain-of-thought (CoT) supervision for these subqueries, coupling precise grounding annotations with diverse image-text augmentations to adapt vision language models (VLMs) to logic-sensitive reasoning. Training is stabilized by a difficulty-aware resampling strategy that emphasizes challenging subqueries and long tail constraint types. Extensive experiments demonstrate that LogiCls delivers robust, interpretable, and accurate industrial logical anomaly classification, providing both the predicted violation categories and their evidence trails.