Integrating Temporal Logics

In this paper, we study the predicative semantics of different temporal logics and the relationships between them. We use a notation called generic composition to simplify the manipulation of predicates. The modalities of possibility and necessity become generic composition and its inverse of converse respectively. The relationships between different temporal logics are also characterised as such modalities. Formal reasoning is carried out at the level of predicative semantics and supported by the higher-level laws of generic composition and its inverse. Various temporal domains are unified under a notion called resource cumulation. Temporal logics based on these temporal domains can be readily defined, and their axioms identified. The formalism provides a framework in which human experience about system development can be formalised as refinement laws. The approach is demonstrated in the transformation from Duration Calculus to Temporal Logic of Actions. A number of common design patterns are studied. The refinement laws identified are then applied to the case study of water pump controlling.