This paper introduces Petri nets (Peterson 1981) into the vexed question of lexical semantic representation. We argue that Petri nets can offer new insights into the organization of lexical meaning. Petri nets can furthermore be translated directly into linear logic, thus ensuring compatibility with the glue logic semantic construction already defined within LFG (Dalrymple 1999). The potential usefulness of Petri nets is demonstrated with respect to light verbs in Urdu.