  We consider the problem of reasoning and planning with incomplete knowledge
and deterministic actions. We introduce a knowledge representation scheme
called PSIPLAN that can effectively represent incompleteness of an agent's
knowledge while allowing for sound, complete and tractable entailment in
domains where the set of all objects is either unknown or infinite. We present
a procedure for state update resulting from taking an action in PSIPLAN that is
correct, complete and has only polynomial complexity. State update is performed
without considering the set of all possible worlds corresponding to the
knowledge state. As a result, planning with PSIPLAN is done without direct
manipulation of possible worlds. PSIPLAN representation underlies the PSIPOP
planning algorithm that handles quantified goals with or without exceptions
that no other domain independent planner has been shown to achieve. PSIPLAN has
been implemented in Common Lisp and used in an application on planning in a
collaborative interface.
