We propose four axiomatic systems for intuitionistic linear temporal logic
and show that each of these systems is sound for a class of structures based
either on Kripke frames or on dynamic topological systems. Our topological
semantics features a new interpretation for the `henceforth' modality that is a
natural intuitionistic variant of the classical one. Using the soundness
results, we show that the four logics obtained from the axiomatic systems are
distinct. Finally, we show that when the language is restricted to the
`henceforth'-free fragment, the set of valid formulas for the relational and
topological semantics coincide