Title: On the complexity of temporal logics over linear time
domains.

We investigate the
complexity of the satisfiability problem of
temporal logics with a finite set of modalities.

We show that the problem is in PSPACE over the following classes.

1.the class of countable linear orders.

2.the class of countable well-order.

3 the class of countable scattered linear orders.

4 the class of Dedekind complete countable linear orders.

5 the class of Dedekind complete countable scattered linear orders.

6  over the rationals.

7. over reals

8. and few more interesting classes with names which do not tell you much.