We propose an interpretable model to uncover the behavioral patterns of human movements by analyzing their trajectories. Our approach is based on the belief that human actions are driven by intentions and are influenced by environmental factors such as spatial relationships with surrounding objects. To model this, we use a set of spatial-temporal logic rules that include intention variables as principles. These rules are automatically discovered and used to capture the dynamics of human actions. To learn the model parameters and rule content, we design an EM learning algorithm that treats the unknown rule content as a latent variable. In the E-step, we evaluate the posterior over the latent rule content, and in the M-step, we optimize the rule generator and model parameters by maximizing the expected log-likelihood. Our model has wide-ranging applications in areas such as sports analytics, robotics, and autonomous cars. We demonstrate the model's superior interpretability and prediction performance on both pedestrian and NBA basketball player datasets, achieving promising results.