By focusing on two specific formalisms, viz. Box Algebra and Interval Temporal Logic, we extend the recently introduced translation of Petri nets into behaviourally equivalent logic formulas. We remove restrictions concerning the way in which the control flow of a concurrent system is modelled, and allow for a fully general synchronisation operator. Crucially, we strengthen the notion of equivalence between a Petri net and the corresponding logic formula, by proving such an equivalence at the level of transition based executions of Petri nets, rather than just by considering their labels.