A logic for the stepwise development of reactive systems

D↓is a new dynamic logic combining regular modalities with the binder constructor typical of hybrid logic, which provides a smooth framework for the stepwise development of reactive systems. Actually, the logic is able to capture system properties at different levels of abstraction, from high-level safety and liveness requirements, to constructive specifications representing concrete processes. The paper discusses its semantics, given in terms of reachable transition systems with initial states, its expressive power and a proof system. The methodological framework is in debt to the landmark work of D.Sannella and A.Tarlecki, instantiating the generic concepts of constructor and abstractor implementations by standard operators on reactive components, e.g. relabelling and parallel composition, as constructors, and bisimulation for abstraction.This work was funded by ERDF European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT – Portuguese Foundation for Science and Technology – within projects POCI-01-0145-FEDER-016692 (DaLí – Dynamic logics for cyber-physical systems: towards contract based design) and UID/MAT/04106/2013 at CIDMA. Further support was given by the project SmartEGOV, NORTE-01-0145-FEDER000037, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the EFDR. The first author is also supported by a FCT individual grant SFRH/BPD/103004/201