Anomaly localization is a practical technology for improving industrial production line efficiency. Due to anomalies are manifold and hard to be collected, existing unsupervised researches are usually equipped with anomaly synthesis methods. However, most of them are biased towards structural defects synthesis while ignoring the underlying logical constraints. To fill the gap and boost anomaly localization performance, we propose an edge manipulation based anomaly synthesis framework, named LogicAL, that produces photo-realistic both logical and structural anomalies. We introduce a logical anomaly generation strategy that is adept at breaking logical constraints and a structural anomaly generation strategy that complements to the structural defects synthesis. We further improve the anomaly localization performance by introducing edge reconstruction into the network structure. Extensive experiments on the challenge MVTecLOCO, MVTecAD, VisA and MADsim datasets verify the advantage of proposed LogicAL on both logical and structural anomaly localization.