Bisimulations for intuitionistic temporal logics

We introduce bisimulations for the logic ITL with ◯ (‘next’), U (‘until’) and R (‘release’), an intuitionistic temporal logic based on structures (W,≼, S), where ≼ is used to interpret intuitionistic implication and S is a ≼-monotone function used to interpret the temporal modalities. Our main results are that ◇ (‘eventually’), which is definable in terms of U , cannot be defined in terms of ◯ and ◻, and similarly that ◻ (‘henceforth’), definable in terms of R, cannot be defined in terms of ◯ and U , even over the smaller class of here-and-there models.