Learning Management Systems (LMS) can generate log files that can give some insight of the way students face the proposed learning activities. Analyzing such logs, either from the perspective of the course materials or from the students' behaviour point of view is a necessity for teachers in order to modify and improve the proposed courses. In this paper we apply process mining techniques to analyze such logs. We are interested in studying the students' use of the learning resources, the students' fitness with respect to the planned assignments and the relationship between the students' behaviour and their final marks, for instance. A log analysis system has been implemented based on a Linear Temporal Logic (LTL) model checking tool and a set of general patterns making easier querying about students' behavioral aspects is proposed. The utility of the system is shown by means of the analysis of Moodle logs corresponding to a course related to Computer Science.