We propose meaning-preserving translations between La, L, and Lsb (three modal logics in full agreement with branching bisimulation), thus proving that they all have the same expressivity. The translations can be implemented and have potential applications in the automated analysis of reactive systems. In this work the main difficulty is that La uses both forward and backward modalities, whereas Lu and Lab only have forward modalities. The technique we developed to cope with this, is an adaptation in a branching-time framework of the methods underlying Gabbay’s separation theorem for PTL (Gabbay, 1987). This technique is powerful and has been applied successfully to related problems.
['François Laroussinie', 'Sophie Pinchinat', 'Philippe Schnoebelen']
Translations between modal logics of reactive systems