Software for safety critical systems must deal with the hazards identified by safety analysis. This paper investigates, how the results of one safety analysis technique, fault trees, are interpreted as software safety requirements to be used in the program design process. We propose that fault tree analysis and program development use the same system model. This model is formalized in a real-time, interval logic, based on a conventional dynamic systems model with state evolving over time. Fault trees are interpreted as temporal formulas, and it is shown how such formulas can be used for deriving safety requirements for software components.