We propose a framework for the specification of infinite state systems based on Petri nets with distinguished may- and must-transitions (called modalities) which specify the allowed and the required behavior of refinements and hence of implementations. Formally, refinements are defined by relating the modal language specifications generated by two modal Petri nets according to the refinement relation for modal language specifications. We show that this refinement relation is decidable if the underlying modal Petri nets are weakly deterministic. We also show that the membership problem for the class of weakly deterministic modal Petri nets is decidable. As an important application of our approach we consider I/O-Petri nets which are obtained by asynchronous composition and thus exhibit inherently an infinite behavior.