From Durational Specifications to TLA Designs of Timed Automata

Different temporal logics tend to emphasise different aspects of a hybrid system. In this paper, we study the predicative interpretation of Duration Calculus (DC) and Temporal Logic of Actions (TLA) and the link between them. A notation called generic composition is used to simplify the manipulation of predicates. The modalities of possibility and necessity become generic composition and its inverse of converse respectively. The transformation between different temporal logics is also characterised as such modalities. The formalism provides a framework in which human experience about hybrid system development can be formalised as refinement laws. A high-level durational specification can be decomposed to two durational specifications driven by an automaton. In such a stepwise design process, durational features are reduced while automaton features increase gradually. The application of the technique is demonstrated in the case study of the gas burner problem.