PSIPOP: Planning with Sensing over Partially Closed Worlds

We present a new partial order planner called PSIPOP, which builds on SNLP. We drop the closed world assumption, add sensing actions, add a class of propositions about the agent’s knowledge, and add a class of universally quantified propositions. This latter class of propositions, which we call C-forms, distinguishes this research. C-forms represent partially closed worlds, such as "Block A is clear", or "x.ps is the only postscript file in directory/rex." We present our theory of planning with sensing and show how partial order planning is performed using C-forms. Noteworthy are the facts that lack of information iscan be represented precisely and all quantified reasoning has polynomial complexity. Thus, in finite domains where the maximum plan length is bounded, PSIPOP is NPcomplete. Several researchers have examined planning with sensing in an open world, where the agent must take action both to acquire knowledge and to change the world (e.g., (Peot & Smith 1992; Etzioni et al. 1992; Krebsbach, Olawsky, & Gini 1992; Scherl & Levesque 1997; Golden 1998)). But how does the agent represent a partially closed world (PCW)-i.e., the fact that either (A) it knows everything about a particular question, or (B) it knows precisely what it does not know about that question. For example, how does it represent that "(1) a.ps and b.ps are the only postscript files in directory ~rex" (an example of A) or that "(2) c.ps is in /home and d.ps may or may not be in /home, but there are no other postscript files in /home!’ (an example of B). Such representations are needed for numerous actions as: ̄ preconditions: E.g., when removing a directory in Unix, the directory must be emptyJ ̄ effects of sensing new information: E.g., when performing a Unix "Is", one learns something about all 1 Note that the blocks world trick of using Clear(x) when a block has nothing on it does not easily generalize ifa block can have numerous blocks on top of it. files, namely, those in the the directory and those not in it. In contrast, SADL (Golden & Weld 1996) uses conditional effects to represent the effects of sensing. Some works (e.g., (Scherl & Levesque 1997)) first-order logic (FOL), which easily represents PCWs but which appears to preclude practical planning algorithms due to the undecidability of entailment in FOL. The other works build upon the partial order planning (POP) work of SNLP (McAllester & Rosenblitt 1991) and yield NP-complete planning algorithms when there are a finite number of ground atoms and where the maximum plan length is bounded (Erol, Nau, & Subrahmanian 1992). While NP-complete problems are still intractable in general, applications of stochastic search to propositional satisfiability have made solving many such problems considerably more plausible (Kautz & Selman 1996; Kautz, McAllester, & Selman 1996). Closely related are locally closed worlds (LCWs) (Golden, Etzioni, & Weld 1994; Etzioni, Golden, Weld 1997), which are used in the PUCCINI planner (Golden 1998) and others. LCWs allow the agent to represent that it knows everything about a given conjunction of atoms. For example, LCW(PS(x) In(x,/tex)) states that the agent knows about all x’s that are postscript files and that are in the directory /rex. Coupled with a set of ground atoms that represent all the positive knowledge the agent possesses, the agent can easily determine whether any given file is a postscript file in/tex: test whether or not it is in the set of atoms. However, the LCW framework cannot represent example 2 from above because the agent does not know about all postscript files in/home--i.e., it does not know whether or not d.ps is in/home. In other words, it can represent locally closed world but not what we call partially closed worlds. This weakness can easily be overcome by the use of exceptions--i.e., represent that the agent knows about all postscript files in/home except for d.ps. However, From: AAAI Technical Report SS-99-07. Compilation copyright © 1999, AAAI (www.aaai.org). All rights reserved. (Etzioni, Golden, & Weld 1997) does not take this approach and furthermore suggests that such a representation leads to intractable reasoning when planning. We take this approach. Beginning with the expressive power of the LCW framework, we introduce what we call C-forms and add the use of exceptions. Example 1 from above is represented as follows. I In(a.ps, /tex) A In(b.ps, /tex)A sl = PS(x) v In(x, /tex) = a.ps)^ -,i x b.ps) The last proposition above is a C-form that represents all clauses of the form -,PS(x) V -~In(x,/tex) for all x except for -~PS(a.ps) V -~In(a.ps, ~rex) and -~PS(b.ps) V -,In(b.ps,/tex). From this, we can easily determine if a given file, say y, is a postscript file in /tex by determining whether $1 ~ PS(y)AIn(y, /tex). Example 2 from above is represented as follows. $2 = -,PS(x) V -,In(x, /home) -~(x c. ps)A -,(x = d.ps) $2 is similar to $1 except that, from it, we cannot conclude anything about d.ps. In this paper we present PSIPOP, a partial order planner that plans to act and to gather information, and that reasons over an open world that can have partially closed worlds represented with atoms and Cforms.