Syntactically correct process models are not necessarily meaningful or represent processes that are feasible to execute. Specifically, when executed, the modeled processes might not be guaranteed to reach their goals. We propose that assigning ontological semantics to process modeling constructs can result in more meaningful models. Furthermore, the ontological semantics can impose constraints on the allowed process models which in turn can provide rules for developing process models. In particular, such models can be designed to be valid in the senses that the process can accomplish its goal when executed. We demonstrate this approach for Petri Net based process models.