  We reformulate Pratt's tableau decision procedure of checking satisfiability
of a set of formulas in PDL. Our formulation is simpler and more direct for
implementation. Extending the method we give the first EXPTIME (optimal)
tableau decision procedure not based on transformation for checking consistency
of an ABox w.r.t. a TBox in PDL (here, PDL is treated as a description logic).
We also prove the new result that the data complexity of the instance checking
problem in PDL is coNP-complete.
