Intuitionistic Linear Temporal Logics

We consider intuitionistic variants of linear temporal logic with `next', `until' and `release' based on expanding posets: partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic which we denote $\iltl$, and by imposing additional constraints we obtain the logics $\itlb$ of persistent posets and $\itlht$ of here-and-there temporal logic, both of which have been considered in the literature. We prove that $\iltl$ has the effective finite model property and hence is decidable, while $\itlb$ does not have the finite model property. We also introduce notions of bounded bisimulations for these logics and use them to show that the `until' and `release' operators are not definable in terms of each other, even over the class of persistent posets.