Planning with Incomplete Knowledge and Limited Quanti

We present a new method for partial order planning in the STRIPS/SNLP style. Our contribution centers on how we drop the closed world assumption while adding a useful class of universally quantiied propositions to the representation of states and actions. These quan-tiied expressions allow expression of partially closed worlds , such as \block A has no other block on it", or \F is the only Tex le in directory D." In addition, we argue informally that the time complexity of our algorithm is no worse than traditional partial order planners that make the closed world assumption. STRIPS-style planning (Fikes & Nilsson 1971) is de-cidable only if we restrict the language to nitely many ground terms (Erol, Nau, & Subrahmanian 1992). STRIPS-style planning becomes NP-complete only when we bound the length of the plan being sought (Gupta & Nau 1991). Thus, planning is intractable in the general case. However, thanks to recent advances in applying stochastic search to propositional satissa-bility problems (SAT) (Selman, Levesque, & Mitchell 1992) and planning problems (Kautz & Selman 1996), much larger classes of NP-complete planning problems can now be solved. Moreover, recent work demonstrates that studying partial order planning (POP) can lead to good encodings of planning problems for eventual use by stochastic search algorithms (Kautz, McAllester, & Selman 1996). Our long term research goal is to make planning more realistic by discarding some of the simpliica-tions of the STRIPS-style planning while still remaining in the class of NP complete problems. 1 Specii-cally, in this paper, we investigate a method for dropping the closed world assumption (CWA) in the context of SNLP-style (McAllester & Rosenblitt 1991) partial order planning (e. A common approach when dropping the CWA retains much of the structure of STRIPS-style planners but reconsiders the set of propositions associated with each state of the world. Instead of being a complete description 1 Therefore, in large part, we agree with the strategy proposed by Ginsberg (Ginsberg 1996). of each state, the set of propositions is considered to be a subset. Thus, with each state we have a set of beliefs that are assumed to be true but incomplete (e. 2 The above approach for dropping the CWA is eeec-tive but limited in its expressive power if there is no quantiication. For example, you can represent a state where the agent knows that directory D has Tex les F and G in it, but you …