The discovery of process models out of system traces is an interesting problem that has received significant attention in the last years. In this work, a theory for the derivation of a Petri net from a set of traces is presented. The method is based on the theory of abstract interpretation, which has been applied successfully in other areas. The principal application of the theory presented is Process Mining, an area that tries to incorporate the use of formal models both in the design and use of information systems.