Embedding time granularity in a logical specification language for synchronous real-time systems

Formal methods have proved to be highly beneficial in the requirements specification phase of software production and are particularly valuable in the development of real-time applications (the most critical software systems). Unfortunately, most common specification languages are inadequate for real-time applications because they lack a quantitative representation of time. In this paper, we define a logical language to specify the temporal constraints of the wide-ranging class of real-time systems whose components have dynamic behaviours regulated by very different time constants. We motivate the need for allowing the consistent treatment of different time scales in formal specifications of these systems with the purpose of enhancing the naturalness and practical usability of the notation. The logical specification language is based on a revised version of the specification language TRIO. We first present the features of the basic logical language; then, we semantically and axiomatically define its granularity extension in a topological logic framework. Finally, we show some examples of its application.