  We work primarily with the Kripke frame consisting of two-dimensional
Minkowski spacetime with the irreflexive accessibility relation 'can reach with
a slower-than-light signal'. We show that in the basic temporal language, the
set of validities over this frame is decidable. We then refine this to
PSPACE-complete. In both cases the same result for the corresponding reflexive
frame follows immediately. With a little more work we obtain
PSPACE-completeness for the validities of the Halpern-Shoham logic of intervals
on the real line with two different combinations of modalities.
