Appears in, AAAI-94 1

Omnipotence Without Omniscience:

Efficient Sensor Management for Planning

Keith Golden Oren Etzioni Daniel Weld*Department of Computer Science and Engineering

University of WashingtonSeattle, WA 98195

{kgolden, etzioni, weld}~cs.washington.edu

Abstract

Classical planners have traditionally made theclosed world assumption -facts absent fromthe planner's world model are false. Incomplete-information planners make the open world as-sumption -the truth value of a fact absent fromthe planner's model is unknown, and must besensed. The open world assumption leads to twodifficulties: (1) How can the planner determine thescope of a universally quantified goal? (2) Whenis a sensory action redundant, yielding informationalready known to the planner?This paper describes the fully-implemented XIIplanner, which solves both problems by represent-ing and reasoning about local closed world infor-mation (LCW). We report on experiments utilizingour UNIX softbot (software robot) which demon-strate that LCW can substantially improve the soft-bot 's performance by eliminating redundant infor-mation gathering.

IntroductionClassical planners (e.g., (Chapman 1987)) presupposecorrect and complete information about the world. Al-though recent work has sketched a number of algo-rithms for planning with incomplete information ( e.g.,(Ambros-Ingerson & Steel 1988; Olawsky & Gini 1990;Krebsbach, Olawsky, & Gini 1992; Peot & Smith 1992;Etzioni et al. 1992; Etzioni, Lesh, & Segal 1993;Genesereth & Nourbakhsh 1993)), substantial prob-lems remain before these planners can be applied toreal-world domains. Since the presence of incompleteinformation invalidates the Closed World Assumption,an agent cannot deduce that a fact is false based on itsabsence from the agent's world model. This leads totwo challenges:

.Satisfying Universally Quantified Goals: Goalsof the form "Move all widgets to the warehouse" or"Make all files in /tex write-protected" are com-mon in real-world domains. Classical planners suchas PRODIGY (Minton et al. 1989) or ucPop (Pen-berthy & Weld 1992) reduce universally quantifiedgoals to the set of ground instances of the goal, andsatisfy each instance in turn. But how can a plannercompute this set in the absence of complete infor-mation? How can the planner be certain that it hasmoved all the widgets or protected all the relevantfiles?

.A voiding Redundant Sensing: Should the plan-ner insert a sensory action ( e.g., scan with the cam-era, or the UNIX command Is) into its plan? Or isthe action redundant, yielding information alreadyknown to the planner? Since satisfying the precon-ditions of a sensory action can require arbitrary plan-ning, the cost of redundant sensing is potentially un-bounded and quite large in practice (see the Exper-imental Results section).

This paper reports on the fully-implemented XIIplanner 1 which addresses these challenges. We allow

incomplete information in the initial conditions, anduncertainty in the effects,2 but assume the informa-tion that is known is correct, and that there are noexogenous events. XII's planning algorithm is based onucPop (Penberthy & Weld 1992), but XII interleavesplanning and execution and, unlike UCPOP, does notmake the closed world assumption.

The next section introduces the central concept un-derlying XII'S operation: local closed world informa-tion (LCW). In the following section we describe howincorporating LCW in a planner enables it to solve uni-versally quantified goals in the presence of incompleteinformation. We then show how the same mechanismaddresses the problem of redundant information gath-oWe thank Denise Draper, Steve Hanks, Terrance

Goan, Nick Kushmerick, Neal Lesh, Rich Segal, and MikeWilliamson for helpful discussions. This research wasfunded in part by Office of N aval Research Grants 90-J-1904and 92-J-1946, and by National Science Foundation GrantsIRI-8957302, IRI-9211045, and IRI-9357772. Golden is sup-ported in part by a U niForum Research Award.

lXIl stands for "eXecution and IncompleteInformation."

2 All effects of operators must be specified, but XII sup-

ports a three-valued logic which allows us to specify a lim-ited form of uncertainty in the effects.

ering. The Experimental Results section demonstratesthe advantages of eliminating redundant sensing. Weconclude with a discussion of related and future work.

Local Closed World Information

Our agent's model of the world is represented as a setof ground literals stored in a database ~ .Since ~is incomplete, the closed world assumption is invalid -the agent cannot automatically infer that any sentenceabsent from ~ is false. Thus, the agent is forced torepresent false facts explicitly -as ~ sentences withthe truth value F .

In practice, many sensing actions return exhaustiveinformation which warrants limited or "local" closedworld information. For example, the UNIX Is -a com-mand lists all files in a given directory. After execut-ing Is -a, it is not enough for the agent to record thatpaper. tex and proofs. tex are in /tex because, in ad-dition, the agent knows that no other files are in thatdirectory. Note that the agent is not making a closedworld assumption. Rather, the agent has executed anaction that yields closed world information.

Although the agent now knows thatparent.dir(foo. /tex) is false, it is impractical forthe agent to store this information explicitly in ~ ,since there is an infinite number of such sentences. In-stead, the agent represents closed world informationexplicitly in a meta-Ievel database, DC, containing for-mulas of the form LCW( ) that record where the agenthas closed world information. LCW( ) means that forall variable substitutions 8, if the ground sentence 8is true in the world then 8 is represented in ~ .For instance, we represent the fact that ~ containsall the files in /tex with LCW(parent .dii:(f ./tex) )and that it contains the length of all such files with

LCW(parent.dir(f./tex)t\length(f.I».When asked whether an atomic sentence is true,

the agent first checks to see if is in ~ .If it is, thenthe agent returns the truth value (T or F) associatedwith the sentence. However, if It ~ then couldbe either F or U (unknown). To resolve this ambiguity,the agent checks whether DC entails LCW«1». If so, is F, otherwise it is u.

LCW U pdates

As the agent is informed of the changes to the externalworld -through its own actions or through the ac-tions of other agents -it can gain and lose LCW; these

.changes must be recorded ill DC. We assume here, andthroughout, the absence of hidden exogenous eventsthat invalidate XII's information. In other words, weassume that the rate of change in the world is slowerthan the rate at which XII plans and executes. This isthe standard assumption of correct information madeby most planners.3

When XII executes an action which ensures that~ contains all instances of that are true inthe world, XII adds a formula LCW( ) to Vc .For example, XII is given an axiom stating thateach file has a unique word count. Thus, exe-cuting the UNIX command wc paper. tex adds theformula LCW(word.count(paper.tex,c)) to Vc aswell as adding the actual length ( e. g. , word. count(paper.tex,42)) to ~. Since the LS operator (Fig-ure 1) has a universally quantified effect, executing 15-a /texyields LCW(parent.dir(!,/tex)).

It would be cumbersome if the author of each op-erator were forced to list its LCW effects. In fact, thisis unnecessary. XII automatically elaborates operatorschemata with LCW effects. For example, the followingeffects are automatically added to the LS operator:

LCW(parent.dir(!l, ?d))LCW(parent.dir(!2, ?d) A (filename 12, P2))LCW(parent.dir(!3, ?d) A (pathname !3, n2))

where the subscripted symbols indicate new uniquevariables, and ?d is a parameter that will be substi-tuted with a constant value at run-time. This com-pilation process takes time linear in the length of theoperator schemata and the number ofunique-value ax-ioms (Golden, Etzioni, & Weld 1994).

Observational effects ( e. g. , those of LS) can only cre-ate LCW, but causal effects can both create and destroyLCW.4 For example, deleting all files in /tex providescomplete information on the contents of the directoryregardless of what the agent knew previously. Com-pressing a file in /tex, on the other hand, makes thelength of the file unknown,5 thus invalidating previ-ously obtained LCW on the lengths of all files in thatdirectory.

The theory behind LCW is complex; (Etzioni, Golden,& Weld 1994) defines LCW formally, explains the con-nection to circumscription, and presents a set oftractable update rules for the case of conjunctive LCWformulas. In this paper, we show how to incorpo-rate conjunctive LCW into a least commitment plannerand argue that this addresses the challenges describedin the introduction: satisfying universally quantifiedgoals and avoiding redundant sensing.

U niv~rsally quantified goals

In this section we explain how XII utilizes LCW to satisfyuniversally quantified goals. Traditionally, plannersthat have dealt with goals of the form "Forall v of typet make Ll( v) true" have done so by expanding the goalinto a universally-ground, conjunctive goal called the~

tion. However, a discussion of this mechanism is beyondthe scope of this paper.

4XII operator schemata explicitly distinguish betweencausal effects (that change the state of the external world)and observational effects ( that only change the state of XII'Smodel) as explained in (Etzioni et al. 1992).

5This is written in the operator effects as(cause (length ?f ?1) U).

3In fact, the softbot relaxes this assumption by associ-ating expiration times with beliefs in ~ and 1JC and byrecovering from errors that result from incorrect informa-

(defoperator LS ((directory ?d) (path ?dp))(precond (and (satisfy (current.shell csh))

(satisfy (current.dir ?d))(satisfy (prote(;tion ?d readable) )(find-out (pathrLame ?d ?dp))))

(effect (forall ((file if) :in (parent.dir $ ?d))

(exists ((path !p) (name !n))(and (observe (parent.dir !f ?d))

(observe (pathname !f !p))(observe (filename !f !n))))))

(interface (execute-unix-commcLnd (ools -a") )(sense-func (!f !n !p) (ls-sense ?dp))))

Figure 1: UNIX operator. The XII LS operator lists all files in the current directory. The last two lines specifythe information needed to interface to UNIX. The first of these says to output the string "la -a" to the UNIXshell. The second says to use the function la-aenae to translate the output of the shell into a set of bindings forthe variables !f, !n and !p.

For completeness, XII also considers combinations ofthese mechanisms to solve a single 'v' goal, via a tech-nique called partitioning; see (Golden, Etzioni, & Weld1994) for details.6 In the remainder of this section weexplain these two mechanisms in more detail.

Protecting V links

In the simplest case, XII can use a universally quan-tified effect to directly support a universally quanti-fied goal. However, 'v' goals, like ordinary goals, canget clobbered by subgoal interactions; to avoid this,XII uses an extension of the causal link (McAllester& Rosenblitt 1991) mechanism to protect 'v' goals. A

causal link is a triple, written Ap~Ac, where G is agoal, Ap is the step that produces G and Ac is the stepthat consumes G. We refer to G as the label of the link.When XII supports a 'v' goal directly ( i. e. , without ex-panding into the universal base) it creates a link whoselabel, G, is a universally quantified formula (instead ofthe traditional literal); we call such links "'v' links." Ingeneral, a link is threatened when some other step, At ,has an effect that possibly interferes with G and Atcan possibly be executed between Ap and Ac. For nor-mal links, interference is defined as having an effectthat unifies with -,G. Such an effect also threatens a 'v'link, but 'v' links are additionally threatened by effectsthat possibly add an object to the quantifier's universeof discourse. For example, if XII adds a chmod g+r *step to achieve the goal of having all files in a directorygroup readable, the link would be threatened by a stepwhich moved a new file (possibly unreadable) into thedirectory. Threats to 'v' links can be handled using thesame techniques used to resolve ordinary threats: de-

universal base (Weld 1994). The universal base of sucha formula equals the conjunction ~ll\. ..1\~n in whichthe ~iS correspond to each possible interpretation of~(v) under the universe of discourse, {Gl, ..., Gn}, i.e.the possible objects of type t (Genesereth & Nilsson1987, p. 10). In each ~i, all references to v havebeen replaced with the constant Gi. For example, sup-pose that pf denotes the type corresponding to the filesin the directory /papers and that there are two suchfiles: Gl = a.dviand G2 = b.dvi. Then the universalbase of "Forall f of type pf make printed(J) true" is

printed(a.dvi)l\printed(b.dvi).A classical planner can satisfy 'v' goals by subgoal-

ing to achieve the universal base, but this strategyrelies on the closed world assumption. Only by as-suming that all members of the universe of discourseare known ( i. e. , represented in the model) can one beconfident that the universal base is equivalent to the 'v'goal. Since the presence of incomplete information in-validates the closed world assumption, the XII planneruses two new mechanisms for satisfying 'v' goals:

1. Sometimes it is possible to directly support J 'v' goalwith a 'v' effect, without expanding the universalbase. For example, given the goal of having all filesin a directory group readable, XII can simply executechmod g+r *; it doesn't need to know which files (ifany) are in the directory.

2. Alternatively, XII can subgoal on obtaining LCW onthe type i of each universal variable Vi in the goal.Once XII has LCW«1>i), the universe of discourse forVi is completely represented in its world model. Atthis point XII generates the universal base and sub-goals on achieving it. Note that this strategy differsfrom the classical case since it involves interleavedplanning and execution. Given the goal of printingall files in /papers, XII would plan and execute an Is-a command, then plan to print each file it found,and finally execute that plan.

6Note also that the classical universal base mechanismrequires that a type's universe be static and finite. XIIcorrectly handles dynamic universes. Furthermore, XII'spolicy of linking to V effects handles infinite universes, butthis is not of practical import.

motion, promotion, and confrontation.7 Additionally,the following rule applies.

/papers. If XII now adds a step which has the actioncompress myfile.txt, then the new step threatensthe link, since compress has the effect of making thelength of myfile .txt unknown.

.Shrinking LCW: Given a link with conditionLCW(P(x)I\Q(x)I\...I\Z(x» and threat causingP(foo) to be unknown (or true), XII can protectthe link by sub goaling to achieve -,Q(foo)V ...V-,Z(foo)8 at the time that the link's con-sumer is executed. For example, compress-

ing myf ile .txt threatens the link Ap~Ac de-scribed above, because if myf ile .txt is in direc-tory /papers, then the lengths of all the filesin /papers are no longer known. However, ifparent. dir(myfile .txt ./papers) is false then thethreat goes away.

Domain Growth We say that At threatens Ap~Acwith domain growth if G = LCW(Pl I\ ...I\ Pn), Atpossibly comes between Ap and Ac, and At containsan effect that makes R true, for some R that unifieswith some Pi. For the example above in which the

link Ap~Ac protects LCW on the length of every filein /papers, addition of a step which moved a new fileinto /papers would result in a domain-growth threat,since the agent might not know the length of the newfile. Such threats can be resolved by the following.

.Shrinking LCW (described above): If XII has LCWon the lengths of all postscript files in /tex, thenmoving a file into /tex threatens LCW. However, ifthe file isn't a postscript file, LCW is not lost.

.Enlarging LCW: Given a link with conditionLCW(P (x) I\Q (x) I\ ...I\Z (x) ) and threat causingP(foo) to be true, XII can protect the link by sub-goaling to achieve LCW(Q(foo)1\ ...I\Z(foo) ) at thetime that the link's consumer is executed. For ex-ample, moving a new file xii.tex into directory

/papers threatens the link Ap~Ac described above,because the length of xii. tex may be unknown.The threat can be resolved by observing the lengthof xii. tex.

Note that an effect which makes some Pi false doesnot pose a threat to the link! This corresponds to anaction that moves a file out of /papers -it's not aproblem because one still knows the lengths of all thefiles that remain.

Discussion

Given the new ways of resolving goals and threats, howmuch larger is the XII search space than that ofucpop?XII has an additional type of open condition: the LCWgoal. Since LCW goals, being conjunctive, can be solvedusing a combination of LCW effects, this would seem

8 N ote the difference between shrinking and protecting

a V link. U nlike the V link case, shrinking does not have adisjunct corresponding to S(foo).

to result in a large branching factor. In practice, thisis not the case, because LCW goals tend to be short.In XII, V goals can be solved by two additional mech-anisms: V links and partitioning. The addition of Vlinks increases the branching factor, but often resultsin shorter plans, and thus less search. Partitioning,in the worst case, has a branching factor equal to thenumber of predicates in the domain theory, but in prac-tice, XII partitions only on predicates that could po-tentially be useful. The number of such predicates istypically small. Nonetheless, partitioning can stillbe expensive, and search control heuristics that limitpartitioning are useful.

XII also adds three new ways of resolving threats;none of them apply to the standard causal links sup-ported by ucPOP, so the branching factor for threatsto these links is unchanged. For the new links sup-ported by XII, the branching factor for threat resolu-tion is increased by at most k, where k is the numberof conjuncts in the LCW condition or in the universe ofthe V condition. Presently, k ~ 3 in all of our UNIXoperators.

The question of completeness for XII is difficult to an-swer, because the notion of completeness is ill-definedin an environment that involves execution. Giventhe existence of irreversible actions, such as rm, vis-iting part of the search space may make a previouslysolvable goal unsolvable. For example, the dilemmaposed in Stockton's classic story "The lady, or thetiger?" (Stockton 1888) is solvable; opening the correctdoor will result in winning the game. However, theprotagonist cannot determine what is behind a doorwithout first opening it, and opening the wrong doormeans losing the game (and his life). By the formaldefinition of completeness, a complete planner mustproduce a plan guaranteed to win the game, since sucha plan exists, but clearly such a guarantee is impos-sible. In future work, we hope to define a notion ofcompleteness that is meaningful in such domains, andprove that XII conforms to that definition.

Redundant Information GatheringThe problem of redundant information gathering isbest illustrated by a simple example. Suppose thatwe ask a softbot to find an Alaska Airlines flight fromSeattle to San Francisco, cheaper than $80. The soft-bot can contact travel agents and airlines, which arelisted in various telephone directories ( cf (Levy, Sagiv,& Srivastava 1994)). In general, the separate informa-tion sources will contain overlapping information. Agiven travel agent might provide information on alldomestic flights within a given price range, while anairline will provide information on all flights it offers.Suppose that the softbot has contacted Alaska Airlinesand failed to find a fare less that $80. Unless it knowsthat contacting Alaska directly provides exhaustive in-formation on Alaska flights, it will be forced to back-track and pursue its other options. To make mattersworse, a travel agency might be listed in multiple di-

9We cannot simply associate exactly one sensory actionwith each goal, a priori, because the agent may fail to sat-isfy that action's preconditions -in which case trying adifferent sensory action is warranted.

loSince XII can subsequently lose LCW due to information

each problem the softbot benefited from the informa-tion gained in solving the previous problems.

Maintaining DC introduced less than 15% overheadper plan explored, and reduced the number of plans ex-plored substantially. In addition, the plans producedwere often considerably shorter, since redundant sens-ing steps were eliminated. Without LCW, the softbotperformed 16 redundant Is operations, and 6 redun-dant pwds in a "typical" file search. With LCW, onthe other hand, the softbot performed no redundantsensing. Furthermore, when faced with unachievablegoals, the softbot with LCW inference was able to failquickly; however, without LCW it conducted a massivesearch, executing many redundant sensing operationsin a forlorn hope of observing something that wouldsatisfy the goal. While much more experimentation isnecessary, these experiments suggest that local closedworld reasoning, as implemented in XII, has the po-tential to substantially improve performance in a real-world domain.

.Post hoc pruning: XII may gain LCW( G) af-ter A is computed (so option pruning did not ap-ply) but considerably before any of the steps in Aare about to be executed (so execution pruning isnot yet applicable). This occurs when executingan action yields LCW(G), or when a binding con-straint is asserted that oonstrains one or more ofthe variables in G. For instance, XII may not haveLCW(parent .dir(f .d) ) , but once d is instantiatedto, say, /tex, LCW(parent .dir(f ./tex) ) can resultin significant pruning.

In concert, these pruning techniques are surprisinglypowerful, as demonstrated in the next section.

Experimental Results

The reader might question whether redundant sensingis as common as we suggest, or wonder whether thecost of utilizing the LCW machinery outweighs the ben-efit from pruning XII'S search space. To address suchconcerns, and to empirically evaluate our LCW imple-mentation, we plugged XII into the UNIX softbot (Et-zioni, Lesh, & Segal 1993), providing XII with oper-ator descriptions of standard UNIX commands, andenabling it to actually execute the commands by send-ing ( and receiving) strings from the UNIX shell. Wegave the softbot a sequence of goals and measured itsperformance with and without LCW. Table 1 quantifiesthe impact of the LCW mechanism on the softbot's be-havior. We found that our LCW machinery yielded asignificant performance gain for the softbot.

In this experiment, the softbot's goals consisted ofsimple file searches ( e.g., find a file with word countgreater than 5000, containing the string "theorem,"etc. ) and relocations. The actions executed in the testsinclude mv (which can destroy LCW), observational ac-tions such as ls .wc and grep, and more. Each exper-iment was started with ~ and Vc initialized empty,but they were not purged between problems; so for

loss or domain growth (described in the previous section),it has to record this pruning decision and recompute theoptions for G if LCW(G) is lost. Doing this in an efficientbut sound manner is complex -see (Golden, Etzioni, &Weld 1994) for the details.

Related workXII is based on the UCPOP algorithm (Penberthy& Weld 1992). The algorithm we used for inter-leaving planning and execution closely follows IPEM,by Ambros-Ingerson and Steel (Ambros-Ingerson &Steel 1988). Our action language borrows both fromADL (Pednault 1986) and UWL (Etzioni et al. 1992).

Our research on LCW has its roots in the SOCRATESplanner, where the problem of redundant informa-tion gathering was initially discovered (Etzioni & Lesh1993). Like XII, SOCRATES utilized the UNIX do-main as its testbed, supported the UWL representa-tion, and interleaved planning with execution. In ad-dition, SOCRATES supported a restricted representa-tion of LCW, which enabled it to avoid redundant in-formation gathering in many cases. Our advancesover SOCRATES include the ability to satisfy universallyquantified goals, and the machinery for automaticallygenerating LCW effects and for detecting threats to LCWlinks.

Genesereth and Nourbakhsh (Genesereth & Nour-bakhsh 1993) share our goal of avoiding redundant in-formation gathering, but do so using radically differentmechanisms, and in the context of state--space search.

They derive completeness-preserving rules for pruningthe search as well as rules for terminating planning andbeginning execution. However, they do not have no-tions that correspond to LCW, a database like 'VC, orour threat resolution techniques.

Other researchers have investigated alternative ap-proaches for planning with incomplete information(see (Olawsky & Gini 1990) for a nice taxonomy).Contingent planners (Warren 1976; Schoppers 1987;Peot & Smith 1992) seek to exhaustively enumeratealternative courses of action; while this strategy is ap-propriate in critical domains with irreversible actions,the exponential increase in planning time is daunt-ing. Decision theory provides an elegant frameworkfor computing the value of information; however, al-though work in this direction is promising, many chal-lenges remain (Wellman 1993). Our approach sacrificesthe elegance of a probabilistic framework to achieve acomplete implementation able to tackle practical prob-lems.

Conclusion

This paper describes the fully-implemented XII plannerwhich uses local closed world information (LCW) to han-dle universally quantified goals and to avoid the prob-lem of redundant sensing. Our technical innovationsinclude the LCW machinery ( effects, goals, and noveltechniques for resolving threats to LCW links) and theLCW-based pruning techniques which solve the problemof redundant information gathering. As demonstratedin Table 1, the savings engendered by LCW can be quitelarge in the UNIX domain. Although our experiments,and illustrative examples, are drawn from the UNIXdomain, we emphasize that the notion of LCW, and thetechniques introduced in XII, are domain independent.In future work, we plan to measure the costs and bene-fits ofLCW in other domains, and to remove the assump-tion of correct information made by the XII planner .

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