Psiplan: Planning with -forms over Partially Closed Worlds

We have developed a new partial order planner called PSIPLAN for open world planning, where the agent does not have complete information about the world and must take actions both to acquire knowledge and to change the world. Incompleteness of the agent's knowledge means that it cannot use the Closed World Assumption (CWA) in the representation of the state and must rely on a diierent method for representing large quantities of negative information. We drop the closed world assumption, and add a class of universally quantiied propositions. This latter class of propositions, which we call-forms, distinguishes this research. The most comprehensive of all practical solutions to the problem of planning in open worlds is the PUCCINI planner Gol98]. It uses what are called Locally Closed Worlds or LCWs EGW97] to represent parts of the world of which the agent has complete knowledge. For example, LCW(P S(x) ^ In(x; =tex)) states that the agent knows all x's that are postscript les in directory =tex. But there are drawbacks. The LCW logic is incomplete and, in some cases, discards information due to limits on its expressive power. Moreover, any planner that uses it is necessarily incomplete, even if the planner does no sensing. We use-forms to represent parts of the world of which the agent has complete knowledge. Given a domain of objects,-forms represent sets of ground clauses obtained by instantiating a clause of negated literals, called its main part. For example 1 = f:P (x; y) j :(x = A) ^ :(x = B; y = C)g represents ground clauses obtained by all possible instantiations of :P (x; y) except those in which x = A or x = B; y = C. The logical interpretation of a-form is a universally quantiied proposition. For example , 1 above is equivalent to the formula 8x; y : :P (x; y) _ (x = A) _ (x = B; y = C). Given this logical interpretation, we deene entailment between-forms in a usual way. We have developed inference methods between-forms, which are sound and complete and have polynomial complexity in the number of propositions, the maximum size of any clause in a-form, and the maximum number of variables used in a-form. Contrary to the LCW representation, the state representation which uses-forms never needs to discard information after an action is performed. Moreover, our partial order planner that uses-forms is complete when it does …