Logic and Decision-Theoretic Methods for Planning under Uncertainty

not assume how or in what context the represented knowledge will be used (Hayes 1977). Simply stated, logical inferences based on valid logical statements never result in invalid conclusions. The consistency of firstorder logic is appealing, but it comes at a cost: All knowledge must be stated categorically; no possible occurrences or partially achievable goals can exist. This consistency property prevents the use of first-order logic to represent and solve problems of planning under uncertainty, which inherently involve incomplete, uncertain, and inconsistent information. In response to this limitation, several researchers have devised augmented logical systems that allow a proposition to be assigned a truth value that signifies the proposition is consistent with the existing set of facts (true by default) even though these propositions have neither been proved nor disproved (for example, Reiter 1980). Because these default assumptions can be withdrawn based on new information, it is conceivable that new information will cause a retraction of an assertion and, therefore, a reduction in the number of provable logical statements about a particular problem. Thus, in contrast to firstorder logic, the number of statements provable from a set of default assumptions does not necessarily grow monotonically with the addition of new information. Thus, these systems are called nonmonotonic logics. To represent and solve a planning problem using a nonmonotonic logic, a system builder must acquire the relevant beliefs and assertions from an lanning consists of devising a course of action that conforms as well as possible to a set of goals. A planner attempts to determine the optimal action in a particular problem-solving situation. We are interested in automating decision support for a particular set of planning problems distinguished by the following characteristics: (1) the current situation is not known with certainty; (2) the consequences of action are not known with certainty; and (3) the goals of the planning process are conflicting and, therefore, are not completely satisfiable. We refer to problems of this type as planning under uncertainty. Because these planning tasks entail uncertainty and tradeoffs, a purely deductive process (such as state space search [Fikes and Nilsson 1971] or skeletal plan refinement [Friedland and Iwasaki 1985]) is difficult to employ to select the optimal plan (Langlotz et al. 1987). In the course of our investigation of viable alternative planning methodologies, we evaluated the applicability of two theoretical approaches: nonmonotonic logics and decision theory. In this article, we establish a simple correspondence between the two theories, describe how each theory applies to the planning task, and offer several suggestions based on the strengths and limitations of the two approaches.