Some logical conundrums for decision-theoretic contingency planning

Abstract
There are two general approaches to handling contingencies in decision-theoretic planning. State-space planners reason globally, building a map of the parts of the world relevant to the planning problem, and then attempt to distill a plan out of the map. POCL planners reason locally, attempting to build the plan up from local relationships. A planning problem is constructed that humans find trivial, but no state-space planner can solve. This motivates an investigation of decision-theoretic POCL contingency planners. Existing POCL contingency planners attempt to generalize the results of classical POCL contingency planning. However, this paper argues that the nature of contingency planning changes dramatically in decision-theoretic contexts, and results from classical contingency planning are of little relevance. In particular, in classical planning contingencies can only be attached to conditional forks, but in most uses of contingencies in decision-theoretic planning they are attached to single branches of the plan rather than to conditional forks. A criterion of adequacy for contingency planners is formulated, following from ordinary completeness, and it is shown that existing decision-theoretic POCL contingency planners do not satisfy it. Some tentative suggestions are made regarding how to construct a planner that does satisfy the adequacy condition.
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