Discovering periodic patterns from historical information is a computationally hard problem due to the large amounts of historical data to be analyzed and due to a high complexity of the patterns. This work shows how the derivations rules for periodic patterns can be applied to discover complex patterns in case of logs of events. The paper defines a concept of periodic pattern and its validation in a workload trace created from the logs of events. A system of derivations rules that transforms periodic patterns into the logically equivalent ones is proposed. The paper presents a systematic approach based on the system of derivation rules to discovery of periodic patterns in logs of events.