  We present the first direct tableau decision procedure with the ExpTime
complexity for HPDL (Hybrid Propositional Dynamic Logic). It checks whether a
given ABox (a finite set of assertions) in HPDL is satisfiable. Technically, it
combines global caching with checking fulfillment of eventualities and dealing
with nominals. Our procedure contains enough details for direct implementation
and has been implemented for the TGC2 (Tableaux with Global Caching) system. As
HPDL can be used as a description logic for representing and reasoning about
terminological knowledge, our procedure is useful for practical applications.
