Obligations and dense time for specifying deadlines

We consider the notion of deadlines in the context of dense time. We show that obligations and actions are essential elements for the specification of deadlines. These notions can be relatively easily combined when a discrete temporal framework is used. However, we show that once a dense time is introduced, several problems appear. In solving these problems we cannot use the same framework and definitions as used for the discrete time. In the new framework we use a branching dense temporal framework as a basis to specify both actions and obligations. Finally we show that all types of deadlines that were defined for the discrete temporal framework can also be defined for dense time