Blocks World (BW) is one of the most popular model domains in AI. In this paper, we model a state of BW by a nite collection of nite chains, and call the theory of all these structures BW theory. We present seven simple axioms and prove that their consequences are precisely BW theory. We present a simple decision procedure for the theory which can be implemented in exponential space, and prove that every decision procedure (even if nondeterministic) for the theory must take at least exponential

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... time. We characterize both the de nable predicates in the theory and its nonstandard models.