Representing the Unknown in Specification Languages

During the operation of softwareontrolled physi al system, there are times when the values of environmental variables are not known by the ontrol software. To orre tly spe ify and reason about su h systems, a spe i ation language must allow variables to take a spe ial unde ned value that signi es that the value of the variable is unknown. Adding an unde ned value to the type system of a language, however, ompli ates the semanti s of the language be ause it auses many of the arithmeti operators to be ome partial fun tions. In this paper we dis uss di erent approa hes to managing unde ned values and present our approa h for the spe i ation language RSML e . We provide a loose semanti s that allows simulation/exe ution of in omplete models, and a tight semanti s, whi h, given a ompleted model, is used for ode-generation and stati analysis. To prevent misuse of unde ned values, we present a test that ensures that predi ates in RSML e annot evaluate to unde ned, and that variables annot impli itly take on unde ned values.