Abstract
The Timed Interval Calculus, a timed-trace formalism based on set theory, is introduced. It is extended with an induction law and a unit for concatenation, which facilitates the proof of properties over trace histories. The effectiveness of the extended Timed Interval Calculus is demonstrated via a benchmark case study, the mine pump. Specifically, a safety property relating to the operation of a mine shaft is proved, based on an implementation of the mine pump and assumptions about the environment of the mine.
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