Specifying deadlines with continuous time using deontic and temporal logic

This paper considers the notion of deadlines in the context of continuous (dense) time. It shows that obligations and actions are essential elements in the specification of deadlines. These notions can be relatively easily combined when a discrete temporal framework is used. Once a dense time is introduced, however, several problems appear. They cannot be solved with the same framework and definitions as are used for discrete time. In the new framework a branching dense temporal framework is the basis for specifying both actions and obligations. Finally, all the types of deadlines defined for the discrete temporal framework can also be defined for continuous time. The formalisms are important for enforcing commitments in electronic commerce.