A calculus of durations

Abstract

The purpose of the calculus of durations is to reason about designs and requirements for time-critical systems, without explicit mention of absolute time. Its distinctive feature is reasoning about integrals of the durations of different states within any given interval. The first section introduces the running example, of leakage in a gas burner. The second section defines and axiomatises the proposed calculus as an extension of interval temporal logic. The third section applies it to the problem described in the introduction. The fourth section briefly surveys alternative calculi.