planning in complex worlds via mixed-initiative interaction

Planning in Complex Worlds via Mixed-Initiative Interaction

James F. Allen, George M. Ferguson and Len K. SchubertDept. of Computer Science

University of RochesterRochester, NY 14627

(james, ferguson, schubert)@cs.rochester.edu

AbstractThis paper presents an overview of research at Rochesteraddressing problems in developing large-scale plans incomplex worlds. The work can be divided into threegeneral areas. We address representational issues bydeveloping new representations of actions and plans thatincrease the expressiveness of plan representations,especially in dealing with external events and interactingoverlapping actions. We address efficiency issues bydeveloping a set of temporal reasoning algorithms forthe efficient handling of very large-scale temporaldatabases. And finally, we address the problem ofdeveloping plans in the real world by defining a modelof mixed-initiative planning using an interactivedialogue-based model of plan management. By viewingthe human as an essential part of the planning process,we dramatically change the problems that are importantfor the ultimate successful application of planningtechnology.

1. IntroductionIn command and control situations and logistics planning, ahuman planner faces several difficult problems. First, there isa surplus of data, only a small amount of which is actuallyrelevant to the current task. In fact, what data is relevantcannot be determined in advance and only becomes clear asthe situation and the plan develop. Second, the plans beingconsidered are large and complex, and it is beyond humancapabilities to manage all the details effectively. Automatedplanning systems are better able in principle to handle thescale, but are hard to apply because of the under-specifiedinitial situations, and the fact that many planning decisionsare made on an intuitive basis that cannot be effectivelyquantified. As a result, neither the human or the computercan effectively solve such planning problems in isolation.

This problem motivates the three research areas whichhave been the focus of the work at Rochester.

1. Mixed-initiative planning systems, where the computeracts as a collaborating assistant to the human. Bycooperating, the human-computer "teum" is able to dealwith problems that neither could handle easily alone.

2. Plan representation formalisms that go beyond theassumptions underlying most planning formalisms and

handle such complexities as external events andinteracting overlapping actions.

3. Efficient algorithms for handling large-scale problems,especially in dealing with large-scale temporal databases,and in developing heuristics for speeding up traditional"well-founded" planners.

Mixed Initiative PlanningTo explore mixed-initiative planning, we designed and builta prototype system, TRAINS-95, that helps a manager solverouting problems in a simple transportation domain. Themanager is presented with a map displaying cities and railconnections between them. The system generates randomproblems that require planning routes for a set of engines to aset of destinations. Various environmental factors can ariseduring the interaction, which the manager and system mustthen plan to accommodate.

Our goal was a robust, modular, multi-modal, mixed-initiative planning assistant. By "robustness" we mean thatno matter what occurs during the interaction, the system notonly doesn’t crash, but does something to indicate itsunderstanding of the manager’s intentions and its ownattempts to further the plan. By "modular" we are takingseriously the idea that there are, or will be shortly, a varietyof knowledge sources, reasoning agents, and display enginesavailable as resources that the system can employ. Examplesinclude weather information, news feeds, map servers, and soon, as well as "off-the-shelf" technology such as speechrecognizers and generators. By "multi-modal" we mean thatthere are a multitude of ways of communicating betweenhumans and computers, include speech input and output,written text, and graphical displays such as maps, charts,forms, and the like, for both input and output. By treating allmodalities as linguistic, that is, as a form of language, weobtain a powerful unifying model of the interaction as a formof dialogue.

Finally, by "mixed-initiative" we mean that both thesystem and the human are on roughly equal ground asparticipants in the dialogue. This is not to say that they areequals, since clearly they are good at different things. But in atruly mixed-initiative system, both participants can do whatthey do best. The human typically has knowledge of thehigh-level goals and means of achieving them, while ofcourse, the computer is good at managing the multitude of

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From: ARPI 1996 Proceedings. Copyright © 1996, AAAI (www.aaai.org). All rights reserved.

low-level details that go into such plans. As well, in realisticsituations, the human may be guided by’ principles that aredifficult or impossible to quantify precisely, making itimpossible to fully automate the task and replace them. Evenif this were possible in principle, the resulting master-slavestyle of communication would hardly be natural and probablywouldn’t be very efficient.

Representing Time, Action and Plans

Most traditional representations of action and plans use astate-based approach that builds in strong assumptions aboutthe nature of action and the world (the so-called STRIPSassumptions). These require that action definitionscompletely describe how the action changes the world, andallows only a single action to be performed at a time.

Our work focused on using an expressive temporal logicto generalize this model and develop models of actions,events and plans to support reasoning in complex worlds.There were five key points that we felt were essential forsuch a representation.

1. actions and events take time. While some events may beinstantaneous, most occur over an interval of timeduring which other events and actions may also occur.

2. the relationship between actions and their effects iscomplex. Some effects become true at the end of theaction, but others become true at the beginning and stillothers may be true during the action and not true after.

3. actions and events may interact in complex ways whenthey overlap, including the production of additionaleffects (syncrgy) and partial or full interference.

4. externally caused change may occur no matter what theagent plans. The planner must be able to reason aboutpossible external events so as to construct reliable plans.

5. knowledge of the world and the possible actions isincomplete in most applications. Virtually no plan isthus foolproof and can only be made on the basis ofcertain assumptions, which should be made explicit.

We developed a representation (Allen & Ferguson, 1995) thatis significantly more expressive and more natural thanprevious approaches along these criteria.

We also developed a new approach to the frame problemcalled explanation closure (Schubert, 1993) that can be usedboth with more traditional representations and with theinterval temporal logic. Explanation closure makes theassumptions underlying the frame problem explicit, leadingto a much richer representation than possible using theSTRIPS assumption or non-monotonic models thatminimize change.

Reasoning about large-scale problems

No matter what plan representation is used, it is clear thatefficient temporal reasoning will be an essential part of anysystem dealing with complex planning problems. Early inthe project, we performed an evaluation of six existingtemporal reasoning systems on constructed databasesreflecting movement in the TRAINS world (Yampratoom

Allen, 1993). These databases ranged from a few hundredtemporal elements up to 60,000. We found that theexpressive interval-based temporal reasoners could not handledatabases of more than a few hundred times effectively, andcompletely collapsed around 500 temporal elements. The lessexpressive point-based reasoners fared better, but those thatused data structures encoding a completely connected set ofconstraints eventually became unusable on the databasesinvolving tens of thousand elements. The most promisingapproaches were the systems that did not construct acomplete constraint graph, such as Schubert’s TimeGraphsystem.

These results motivated further development both toimprove the performance of reasoners over the "time pointalgebra" (relations using <, <=, =, =1=) and to developefficient methods for handling more expressiverepresentations allowing disjunctions.

Another problem in dealing with large-scale problems isthe search efficiency of traditional planners. We concentratedon "well- founded" planning methods, such as UCPOP, thatarc sound and complete and have other desirable propertiesand developed a set of methods for improving theperformance of such systems by an order of magnitude. Thetechniques range from modifying the search strategy toinclude necessary actions first, to preprocessing methods thatrestricts that set of values that a variable can take.

The remainder of this paper describes these results in moredetail. We discuss mixed-initiative planning and theTRAINS-95 system in section 2, our work on therepresentation of actions, events, and plans in section 3, ourwork on efficient large-scale temporal reasoning in section 4,and our work on improving the efficiency’ of well-foundedplanning algorithms in section 5. While problems remain,our results make a significant contribution to the goal ofbuilding mixed-initiative systems for constructing large-scale, realistically complicated, plans.

2. The TRAINS-95 SystemThe TRAINS-95 system was built to demonstrate thefeasibility and usefulness of dialogue-based models of mixed-initiative planning. The system, which runs in near real-time~ and supports speech, keyboard and a map display’. Thekey insights motivating this work were:

I. that the dialogue should provide the context required forsuccessful interaction independent of input modality; and

2. that the plan reasoning requirements of mixed-initiativesystems differ markedly from the specifications oftraditional planners.

The domain reasoner in TRAINS-95 maintains a knowledgebase describing the state of the world and provides planningand plan recognition services to the dialogue modules. Forthe simple route-planning domain, of course, it would beeasy to build a perfect reasoner that solved the problems assoon as the manager had stated their goals. However, it isunlikely that wc will ever be able to build such a reasoner for

’ on an Ultrasparc with 190 Meg of memory.

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a realistic domain. We therefore deliberately weakened theTRAINS-95 domain reasoner so to force the manager tointeract in order to overcome its shortcomings. The routeplanner can therefore only plan route segments less than fourhops long, and for those it chooses a random path. Theknowledge base maintains an accurate view of the map, andallows various "natural" events such as bad weather or trackmaintenance to arise during the interaction. These also forceinteraction in order to revise plans to take account of them.

The domain reasoning in TRAINS-95 is incremental andincorporates aspects of both planning and plan recognition ina tightly-coupled way. For example, the domain reasonermay be asked to incorporate a new constraint on an existingplan, e.g., that it go via a particular city. The domainreasoner must first recognize how that constraint fits into theplan (a task shared with the dialogue modules, for example indetermining which route is being modified). It then adds theconstraint to the plan, possibly removing other softerconstraints (such as to try an avoid cities known to becongested). It must then plan a new route satisfying thecurrent constraints, preferably one that makes the smallestpossible change to the plan already under consideration.

Although it’s doing planning, a mixed-initiative planningsystem isn’t doing what we might recognize as "traditional"planning, that is, constructing a sequence of operators from afully-specified initial situation to a stated goal. In fact, in aninformal analysis of one hour of human-human problem-solving dialogues (part of a larger eight hour study (Heemanand Allen, 1995), we found that a relatively small percentageof the utterances, 23%, dealt with explicitly adding orrefining actions in the plan. In fact, we found the followingdifferent forms of interaction:

Evaluation/comparison of options 25%Suggesting courses of action 23%Establishing world state 13%Clarifying/confirming communication 13%Discussing problem solving strategy 10%Summarizing courses of action 10%Identifying problems/alternatives 7%

Note the importance of being able to explicitly evaluate andcompare options, even between humans of roughly equalability. In human-computer interactions, we would expectthis number to increase, as the computer can perform moreand larger analyses. Similar conclusions about the nature ofinteractive planning are presented in Ferguson (1995) andPollack (1992).

In Ferguson et al (1996), we discuss why mixed-initiativeplanning seems to involve so little traditional planning. Themain points focus on the fact that the initial situation, thegoals, and the evaluation criteria for plans are all impracticalto specify in complex domains, and this information is onlyacquired incrementally during the interaction. The upshot ofthis is that even if we had implemented a "perfect" routeplanner for the simple TRAINS-95 domain, we would stillneed all the other components of the system. If the goal is anatural, interactive planning assistant, the solution will notbe found in traditional planning. The question becomes how

Figure 1: The initial scenario

to incorporate traditional systems within the context of arobust, mixed-initiative system.

We have developed a model of the mixed-initiativeplanning process from analysis of the TRAINS dialogues andimplemented a simple version of it in TRAINS-95. Thismodel consists of four steps:A. Focus: Identify the goal/subgoal under consideration.B. Gather Constraints: Collect constraints on the solution,

selecting resources, gathering background information,and adding preferences.

C. Instantiate Solution: As soon as a solution can begenerated efficiently, one is generated.

D. Criticize, Correct or Accept: If the instantiation iscriticized and modifications are suggested, the processcontinues at step (B). If the solution appears acceptablethen we continue at step (A) by selecting a new focus.

At first glance, this model seems quite similar to the expand-criticize cycle found in hierarchical planners since Sacerdoti(1977). The significant difference is in step (C). Rather pursuing a least commitment strategy and incremental top-down refinement, we "leap" to a solution as soon aspossible. In TRAINS-95, solutions are generated by adomain-specific specialist program rather than by traditionalsearch-based planning. We expect this will be typical in allpractical applications of planning systems in the future. Youmight call this a "look then leap" strategy rather than thetraditional "wait and see" strategy used in least-commitmentplanning.

To support this model of mixed-initiative planning, wehave developed a four layer architecture that generalizes theTRAINS-95 system architecture. The discourse levelmaintains information important for reference identificationand for speech act interpretation and generation. While criticalto the overall system, the other levels are more centrallyconcerned with the planning process.

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The problem solving level maintains meta-leveiinformation about the problem solving tasks, similar to theproblem solving level actions described by Litman and Allen(1987) and Lambert and Carberry (1991). Actions at level are problem solving actions such as "solve goaldirectly," "decompose goal into subproblems," "resolveresource conflict," and so on. This level supports processessuch as identifying the task desired (e.g., distinguishingbetween an elaboration of the plan for the current goal andshifting to another goal). It does this by maintaining anabstract tree of goals and information on which part of theproblem is currently in focus. It also supports the process ofdetermining the scope of problem solving actions such ascancellations and modifications. Finally, it supportsdiscussion of the problem solving strategy to be used, andcan maintain ordering constraints on when certain problemsolving tasks should be performed.

When more sophisticated domain-level reasoning isrequired, we rely on the services of a set of domain reasotwrs.The abstract plan representation level manages the interfacebetween the mixed-initiative system and these variousdomain specialists, matching open issues with reasoners andcoordinating the responses. These reasoners might be, forexample, a scheduler or an internet agent that can retrieveinformation. The key to integrating such components is theability to specify and reason about their capabilities. That is,the abstract plan reasoner needs to be able to reason aboutwhich domain reasoners might be suitable for what tasks,and interpret their results. This is complicated by the desireto use existing components "off the shelf" as much aspossible. The TRAINS system uses KQML (Finin et al1994) to anticipate future integration efforts.

We have been concerned from the outset with theevaluation of our work, that is, how to know if we aremaking progress. This has traditionally been a problem forinteractive systems and planners. Our current system hasbuilt into it a simple set of task-related metrics that arcrecorded for each interaction. As we refine those metrics, wecan explore whether particular strategies are better than othersat getting the task done, or whether the presence of certaincomponents helps or hinders performance. Our firstevaluation of the system is reported in Allen et al (1996),where we show that most people can use the TRAINSsystem to solve 3-route problems with virtually no training.

The TRAINS-95 system is a concrete first step towards amixed-initiative planning assistant. We have demonstratedthe feasibility of the diaioguc-based approach to interactiveplanning, and have developed a substantial infrastructure forfuture research. More information on the TRAINS-95system can be found in Ferguson et al (1996) and Alien et (1996), and from our web site at URLhttp://www.cs.rochcster.cdu/rcseareh/trains/.

3. Representing Action and PlansA significant part of this project has focused on exploringcommon sense reasoning in the context of reasoning about

actions and plans. The goal of the research is theories thataccount for human abilities to reason and communicate abouttheir plans and actions, and systems based on those theoriesthat can interact with people in a natural manner.

Wc are interested in common sense theories. In particular,this means that techniques we develop must represent theworld in a manner that is "natural" for people, which we taketo mean that they can be described and discussed in naturallanguage. Taking language descriptions seriously imposesquite strict breadth requirements on the theories. Of course,any theory must idealize certain aspects of the problem, andany computer program necessarily has its limits. Butoversimplification is a problem that has led AI research downseveral unpromising (and worse, misleading) paths.

Reasoning about actions and plans has always been a coreissue in artificial intelligence research. Indeed, the underlyingquestions of causality, intention, and physical intuitions havea rich intellectual history in fields ranging from philosophyto physics, although this history has not always beenappreciated by researchers in AI. Our research addressed twomain thrusts that span this spectrum.

The first was an exploration of the representation ofactions in order to support natural, common sense reasoning.Traditional models of action in AI have been extremely weak,unable to represent such things as simultaneous actions oractions with durations. Of course, such phenomena areubiquitous in realistic environments, and arise in any naturaldescription of a scenario. Building on work by Allen (1984),we reexamined the foundations of Interval Temporal Logicand its use in formalizing realistic domains naturally(Fcrguson 1992, Allen and Ferguson 1994). in this work revisit the logical foundations of temporal logic, reexaminingsome of the very fundamental properties of the logic anddiscussing alternatives. Although quite technical, many ofthe points have clear natural analogs in terms of distinctionsthat people make in reasoning about action and time. Wethen move one to consider actions and causality, andintroduce events as an important part of the ontology. Eventsconsist of something happening, as opposed to actions thatare specific things that agents can do in the world, some ofwhich result in events occurring. The connection betweenactions and events is context-dependent--an action doesn’t¯ always have the same effect.

One classical difficulty that besets planning (andreasoning about action in general) in any reasonably complexworld is the Frame Problem, i.e., the problem of succinctlycharacterizing and efficiently inferring what doesn’t changewhen actions arc performed. Schubert (1990) proposed method of dealing simply with the Frame Problem (in non-probabilistic worlds) called Explatu2tion Closure (EC). Thismethod allows efficient, monotonic inference of non changewhen considering a set of actions to be taken. During thisproject we explored this theory’s potential and limitations forreasoning about actions and change. Using a fairly standardsituation calculus representation, we tested it on the suite ofproblems collected by Sandewall (1992) for the purpose examining thc properties of various non monotonic

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approaches. We found that EC in combination with simple"action closure" (AC) axioms (stating that certain actionswere the only ones taken within a certain setting) allowedsimple and direct solution of all of Sandewall’s problems,except for one probabilistic problem (a version ofMcCarthy’s "potato in the tailpipe" problem). A prohability-logic solution was proposed for this last problem, and it isexpected that EC/AC methods can be generalized toprobabilistic worlds. This work was reported as acontribution to a special issue of J. Logic and Computationon Actions and Processes (Schubert, 1994).

We also then explored the use of explanation closure withour Interval Temporal Logic representation. We found is wellsuited for solving the Sandewall test suite problems again,and in handling a wide range of problems involving externalevents and simultaneous actions (Allen and Ferguson, 1994).

Another aspect of our work in this areas was concernedwith formal models of planning, or more generally,reasoning about plans. This obviously builds on the work onrepresenting and reasoning about action, since plansfundamentally involve action. However, when we considerthe many cognitive tasks that people perform with plans,especially in mixed-initiative planning, it becomes clear thatplans involve more than just sequences of actions, contraryto the more-or-less standard approaches seen in AI planningformalisms.

Our early work on mixed-initiative planning (Fergusonand Allen 1993a, Ferguson and Allen 1993b), looked atapproaches to plan reasoning that unified these tasks.Previous work on the various plan reasoning tasks hadgenerally been disjoint, to the extent that the planning andplan recognition communities had little in common. Whenwe started to take seriously the interactive nature of mixed-initiative planning, we saw that plan communication was thecrucial task (Ferguson and Allen 1994). Informal statisticsgathered from work on the TRAINS system (described insection 2) showed that many of the utterances were concernedwith keeping the conversation going: confirming, rejecting,clarifying, etc. A relatively low proportion of the utteranceswere doing what might be recognizable as "AI planning,"namely generating sequences of actions to satisfy a goal. Wetherefore proposed a formalism for representing plans whichtreats them as arguments in a formal system of defeasiblereasoning. This style of non monotonic reasoning is similarto the theory formation approach described above. Inargumentation (now called "computational dialectics"),arguments can be put forth in support some conclusion,drawing on the facts at hand, as well as cases from previousexperience, and so on. These arguments can be defeated byother arguments that attack their premises, and these attackscan be defeated, and so on, until a conclusion is establishedthat cannot be defeated. There are a variety of interestingtechnical details about argumentation as a form of inference(it is clearly non monotonic, and in very interesting ways).But the main attraction of the model is its apparentsimilarity with the communicative "give-and-rake"we seeduring mixed-initiative planning.

Ferguson’s dissertation (Ferguson 1995) goes into moredetail regarding argument-based reasoning, and looks atformalizing plans more concretely as arguments. That is, itis clear that we can allow arguments to be built from aknowledge base that contains the definitions of actions andevents, causal rules, and so on. But what does it buy us? Tobegin with, the fact that arguments make explicit theassumptions they depend on allows us to connect them to anunderlying logic of action and time. It also describes how theexplanation closure approach used effectively in therepresentation of action plays a role in the formalization ofplans as arguments. Finally, it looks at recasting someexisting planning formalisms, despite their weakexpressivity, within the argument system approach, andshow how some of the techniques and heuristics usedtraditionally appear as properties of the argument system.

4. Temporal Reasoning SystemsThe overall direction of our work in temporal reasoningduring this project has been develop theoretical foundationsand practical tools for scalable temporal reasoning andplanning, keeping in mind the eventual needs in atransportation planning domain like TRAINS.

The results can be divided into theoretical development andpractical implementation of extremely efficient methods forthe "time point algebra" (relations using <, <=, =, =/=) andtheoretical complexity analysis of disjunctive temporalrelations, and development of efficient methods for handlingsuch disjunctions

Scalable temporal reasoning

The starting point for this work was the TimeGraph 1system. In experiments conducted by Yampratoom and Allen(1993), this system showed promise of being able outperform all other existing temporal reasoning systems onlarge-scale TRAINS-world problems, involving qualitativetime ordering information as well as numerical timeconstraints. The system uses a DAG representation of timepoint relations, with a superimposed metagraph structure thatpartitions the DAG into "time chains". Inference of implicittime-point relations is often near constant-time. Someweaknesses of TimeGraph I were the dependence of efficiencyon the order in which temporal information is supplied, andinability to handle inequations of form x =/= y for timepoints x, y. Also its reasoning is incomplete in the presenceof numeric constraints.

Our first work was aimed initially at adding inequations toa qualitative time graph, i.e., one without numericalinformation. (This means extending the convex point "algebrato the full point algebra.) Our theoretical analysis uncovereda serious flaw in the proof of a lemma by van Beek andCohen (1990), which is crucial to designing completeinference methods for time-point-algebra networks. We wereable to formulate a completely new (and conceptuallysimpler) proof of the lemma (Gerevini and Schubert, 1993b,1995a), thus providing a sound basis for system-building.

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We further formulated efficient new algorithms for the"bottleneck" problem of explicitly deriving relations of formx < y that are implicit in sets of relations of forms x .~ y, w~Z.

We then proceeded to implement a new system,TimeGraph !I, which improved on TimeGraph 1 in severalrespects: it builds a near-optimal TimeGraph structure for agiven set of temporal relations in linear time and space, alsochecking for consistency; it handles the full time-pointalgebra (but not numerical constraints), and it uses improveddata structures and algorithms for graph construction and forinference, achieving a speed up of about a factor of 2 (forinference) over TimeGraph I. Furthermore, theimplementation of the new algorithm for deriving implicitrelations of form x < y was shown experimentally to beorders of magnitude more efficient than the "minimal labels"algorithm that had been employed by van Beck (1992). our knowledge, TimeGraph II significantly outperforms allother comparable temporal reasoning systems. A theoreticaldescription of TimeGraph II and experimental results aredescribed in Gerevini and Schubert (1993a) (see also Gereviniand Schubert 1995b). Descriptions of the usc of TimeGraph and II as temporal reasoning tools are given in Gerevini et al.(1993), and more fully (as conference paper and as expanded journal version) in Gerevini et al. (1994,5). version of TimeGraph II described there also includesmethods for handling disjunctions (described below), and available via anonymous ftp to cs.rochester.edu, files tg-ii-1.tar.gz and tg-ii.readme in the directorypub/packages/knowledge-tools.

Disjunctive temporal relationsThe greatest source of computational complexity inqualitative temporal reasoning comes from disjunctiveconstraints such as (x < y)V(w <= z). since such constraintsgive rise to a combinatorial explosion in the pairwiseorderings of time points that have to be considered inlooking for a consistent solution. Yet such constraints arevery important in planning and scheduling, since it is oftennecessary to ensure disjointness of intervals corresponding toevents that must be scheduled in series (e.g., because theydemand a common resource), or exclusion of a point eventfrom the interval between two other events (e.g.. where oneof these events establishes a preconditions for the other, andinsertion of the third event would "clobber" theprecondition). These cases give rise to 3-point instances ofdisjunctive constraints, such as (x < ymin)V(x > ymax).

Surprisingly, the complexity of such "point-intervalexclusion" relations, as well as interval-interval exclusion,was not well understood, despite some relevant results ondisiunctive relations on pairs of intervals by Golumbic andShamir (1992), among others. This motivated a systematictheoretical investigation of point-based temporaldisjointness, building on Golumbic and Shamir’s work. Weinvestigated the complexity of consistency-testing andsolution-finding for .56 possible 3-point and g-point relations(allowing for strictness and non strictness of various ordering

relations involved), and found that in the majority of casesthese problems are NP-complete. The few polynomial casesare not very useful. (For instance, sets of interval- intervalexclusion relations are trivially consistent when all orderingrelations are non strict, merely because all given points canbe consistently collapsed into a single time point). Thestrongest NP-completeness result concerns sets of very weakpoint-interval exclusion relations, of form "x is strictlybefore or strictly after the interval formed by y,z, where y =/=z (but it is unspecified whether y < z or z < y)". Preliminaryresults are reported in Gerevini and Schubert (1993b) and thecomplete analysis is in Oerevini and Schubert (1994b).

These NP-completeness results led naturally to the nextresearch issue: are there practical ways to deal with large setsof temporal relations that include disjunctions, despite theworst-case intractability of consistency testing (etc.) for suchproblems? Our interest was in complete methods, as opposedto polynomial-time but incomplete methods such as pathconsistency. The methods we developed were again based onTimeGraph structures, augmented with arbitrary sets ofbinary disjunctions of form (x < y)v(w < z). consistency-testing and solution-finding methods consist of aset of polynomial-time preprocessing techniques, followed bya form of intelligent backtrack search. As an example of apreprocessing step applied to (x < y)v(w < z), the disjunct < y) can be tested very quickly in the TimeGraph for truth orfalsity. If it is true, the disjunction can be dropped; if it isfalse, the disjunct can be dropped. Of course in general therelations comprising the TimeGraph need not decide the truthor falsity of a disjunct, and search may be needed to determinewhich disjunet (if an),) can consistently be made true.

Our very efficient preprocessing techniques turned out tohave the interesting property that they are sufficient bythemselves to determine consistency for Nebel andBuerckert’s ORD-Horn algebra (Nebel and Buerckert, 1993),the maximal tractable sub algebra of Allen’s interval algebraIA (among those sub algebras that include all the pointizableinterval relations). Furthermore, our intelligent backtrackingtechnique also turned out to be practically efficient, runningin approximately quadratic time on average (relative to thenumber of given temporal relations, including disjunctiveones). These theoretical and experimental results are reportedin Gerevini and Schubert (1994a, 1995b).

In summary, our temporal reasoning work has led tocomplete, theoretically sound methods for qualitativereasoning about large sets of temporal relations that areextremely efficient in practice, allowing for fast inference ofimplicit relations, consistency testing, and solution-finding.Future work includes the design of methods that work wellincrementally, i.e., when temporal relations may be added atan)’ time: integration of qualitative relations relations withquantitative bounds (as in TimeGraph I, but withcompleteness guarantees): and generalization of disjunctivereasoning to handle a greater variety of disjunctions. Withcertain additions (including some ternary and quarticdisjunctions) our methods would properly subsume IA.whereas at present they neither subsumes IA nor are

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subsumed by it. However, our techniques as they stand andTimeGraph 1[ seem well-suited to many problems, includingthe sorts of planning problems that provided our motivation.

$ Improving the effectiveness of "well-founded" planning

While there are some practically oriented planning systemssuch as SIPE (Wilkins, 1988) and O-Plan (Dalton et at.,1994) that could be applied to problems of modest size, thesesystems are quite complex, become ineffectual for largeproblems, and are logically incomplete and theoreticallyrather opaque. An ideal planner would be one that is simpleand "well-founded" (i.e., theoretically transparent, sound andcomplete), and scales up well to large problems. At present,however, well-founded planners such as UCPOP (Penberthyand Weld, 1992) are unable to solve any but trivially smallproblems. Our goal has been to find ways of acceleratingsuch planners so as to bring them closer to practicalusefulness.

Besides being applicable to the frame problem,Explanation Closure can also be used to infer actions thatmust be taken in any solution to a problem. Gerevini andSchubert explored the possibility of using such models toguide planners like UCPOP. It turned out that such plannersare easily modified to emphasize addition of necessaryactions, a strategy we term "zero commitment". As ithappens, implementing zero-commitment in UCPOP doesnot require any technique as logically general as EC and AC,since UCPOP has a built-in STRIPS assumption, i.e., anyproperties that are not explicitly declared to change in thedefinition of an action in fact remain unchanged when thataction is instantiated. Thus, it was possible to experimentwith the zero commitment strategy with only minormodifications to UCPOP; all that is required is a change toUCPOPs strategy for selecting "open conditions" (goals stillto be established) so as to favor goals that can only beachieved.by a unique action instance. Other goals arescheduled on a LIFO basis, and we term the resultingstrategy ZLIFO.

ZLIFO turned out to be extremely effective, especiallywhen combined with a modification of UCPOP’s default A*strategy for selecting a plan to work on. The "mistake" inthe default plan-selection strategy is to include a termreflecting the number of potential "clobbering" interactionsbetween effects of actions and protected conditions (causallinks). By eliminating or diminishing this term, we obtainedlarge performance improvements in a wide spectrum of testproblems from the UCPOP test suite, among others.Together, the new goal-selection and plan-selection strategiesgave order of magnitude speedups, for all problems that weredifficult for UCPOP to begin with. The hardest problemsshowed the greatest speedups (e.g., from several minutes ofCPU time to a fraction of a second, with similarimprovements in number of plans generated/explored), Theanalysis and experiments are reported in Schubert andGerevini (1995).

Finally, the most recent work on improving well-fi)undedplanning is concerned with the potential benefits ofpreprocessing operator and domain descriptions. The idea isto extract information that can be used to radically reduce thenumber of actions and states that need to be considered duringplanning. This holds great promise for making well-foundedplanning practical.

Our first effort in this direction was based on theobservation that UCPOP generates many impossible actionswhen it performs goal regression, i.e., actions with parametervalues that cannot possibly be instantiated, starting in thegiven initial conditions. We developed a prcprocessingtechnique to calculate parameter domains (sets of constants)for all operators, based on "forward" propagation ofconstants. The idea is to match the initial conditions to alloperator preconditions and thus associate potential valueswith some parameters in some operator preconditions. Forthose operators that had ALL preconditions matched, thepotential values of the same parameter occurring in differentpreconditions can be intersected, and the effects of theoperator can again be matched to operator preconditions,passing on the intersected value sets of the parameters; etc.At the end all operator parameters have associated domains.What makes the algorithm nontrivial is the allowance inUCPOP for conditional effects in operator definitions, whichmay or may not lead to actual effects in particular uses of theoperator.

A theoretical analysis of this technique showed that itruns in low-order polynomial time (in terms of the combinedsize of the operator specifications and the initial/goal statespecifications). Our implementation gave negligible runningtimes (relative to planning cost). We then modified UCPOPso that it eliminates actions with impossible parametervalues (as determined by the precalculated domains), and alsoso that it eliminates apparent threats that would requireimpossible parameter values to be actualized. Ourexperimental tests concentrated on some of the harderproblems from the UCPOP suite and on TRAINS worldproblems of the type actually used for some of the simplestTRAINS-91/93 dialogues. Typical specdups of a factor of 10were obtained (beyond those obtained by our goal and planselection strategies), bringing some simple problems withinthe realm of feasibility for UCPOP that previously could notbe solved at all. A paper on this work has been accepted forconference presentation (Gerevini and Schubert, 1996).

In summary, our work on improving well-foundedplanning has led to order-of-magnitude speedups in state-of-the-art partial order planners, and further work should be ableto make such planning practical. Current work on apreprocessing technique that infers state constraints fromoperator structure and initial conditions promises to provideanother powerful means for cutting down search duringplanning. Another important future task is to modify ourefficient temporal reasoning methods for use in planning. Itshould be possible to eliminate much of the searching inplanning by using a TimcGraph-likc reasoner to quickly findtemporally consistent scenarios.

Allen 59


ReferencesJ.F. Allen (1983), "Maintaining knowledge about temporalintervals", Comm.. ACM 26(1), pp. 832-843.James F. Allen, 1984. Towards a general theo~" of actionand time, Artificial Intelligence, 23:123-- 154.James F. Allen and G. Ferguson, 1994. Actions and eventsin interval temporal logic, Journal of Logic andComputation, 4(5):531--579.James F. Allen, L. K. Schubert, G. Ferguson, P. Heeman,C. H. Hwang, T. Kato, M. Light, N. G. Martin, B. W.Miller, M. Poesio, D. R. Traum. 1995. The TRAINSProject: A case study in building a conversational planningagent," Journal of Experimental and Theoretical AI, 7:7--48James F. Allen, G. Ferguson, B. Miller, and E. Ringger,1995. Spoken Dialogue and Interactive Planning, Prec.ARPA Spoken Language Technology Workshop, Austin,TX, Morgan Kaufmann.J. Dalton, B. Drabble, and A. Tate. 1994. The O-Planconstraint , in 13th Workshop of the UK Planning SpecialInterest Group, Glasgow, UK.George Ferguson, 1995. Knowledge Representation andReasoning for Mixed-Initiative Planning. Ph.D. Thesis, TR562, Dept. of Computer Science, Univ. Rochester, NY.George Ferguson, J. Allen, and B. Miller, 1996. TRAINS-95: Towards a Mixed-Initiative Planning Assistant. to appearin Prec. Third Conference on Artificial Intelligence PlanningSystems (AIPS-96), Edinburgh, Scotland, May, 1996.George Ferguson and J. F. Allen. 1994. Arguing AboutPlans: Plan Representation and Reasoning for Mixed-Initiative Planning, Second Conf. or, Artificial IntelligencePlanning Systems ( AI PS- 94 ), Morgan Kaufmann.George Ferguson and J. F. Allen. 1993. Cooperative PlanReasoning for Dialogue Systems. AAAi Fall Symposiumon Human-Computer Collaboration, Raleigh, NC.George Ferguson and James F. Allen. 1993. Generic PlanRecognition for Dialogue Systems, ARPA Workshop onHuman Language Technology, Morgan Kaufmann.George Ferguson, 1992. Explicit Representation of Events.Actions and Plans for Assumption-Based Plan Reasoning,TR 428, Dept. of Computer Science, University ofRochester, Rochester, NY.A. Gerevini, L.K. Schubert, and S. Schaeffer. 1993.Temporal reasoning in Timegraph l-II. SIGART Bulletin 4(3), pp. 21-2.5.A. Gerevini and L.K. Schubert. 1993a. Efficient temporalreasoning through timegraphs, Prec. of the 13th Int. JointConf. on Artificial Intelligence ( IJCAI-93), pp. 648-654.A. Gerevini and L.K. Schubert. 1993b. Complexity oftemporal reasoning with disjunctions of inequalities.Workshop on Spatial and Temporal Reasoning, IJCAI-93.A. Gerevini and L.K. Schubert. 1994a. An efficient methodfor managing disjunctions in qualitative temporal reasoning.Prec. of the 4th h~t. Conf. on Principles of KnowledgeRepresentation and Reasoning (KR’94), pp. 214-225.A. Gerevini and L.K. Schubert. 1994b. On point-basedtemporal disjointness, Artificial Intelligence 70, 347-361A. Gerevini and L.K. Schubert. 1995a. On computing theminimal labels in time point algebra networks,

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minimal labels in time point algebra networks,Computational Intelligence I 1 (3), pp. 443-448.A. Gerevini, L.K. Schubert, and S. Schaeffer. 1995d. Thetemporal reasoning tools Timegraph l-II, Int. J. of ArtificialIntelligence Tools 4 ( 1 and 2), pp. 281-299.A. Gerevini and L.K. Schubert. 1996. Precomputation ofparameter domains as an aid to planning, 3rd Int. Conf. onPlanning Systems (AIPS-96), Edinburgh.M. Golumbic and R. Shamir. 1992. Algorithms andcomplexity for reasoning about time, Prec. AAAI-92.C.H. Hwang and I,.K. Schubert. 199. EL: A formal, yetnatural, comprehensive knowledge representation, Prec.AAAI-93, Washington, D.C., pp. 676-682.S.A. Miller and L.K. Schubert. 1990. Time revisited,Computational Intelligence 6, 2, pp. 108-118, May 1990.B. Nebel and HJ. Buereker. 1993. Reasoning about temporalrelations: a maximal tractable subclass of Allen’s interval¯ algebra, J. ACM, to appear.J.S. Penberthy and D.S. Weld. 1992. UCPOP: A sound,complete partial order planner for ADL. Prec. of the 3rd Int.Conf. on Knowledge Representation and Reasoning ( KR’92 ),Boston, MA, Morgan-Kaufmann, pp. 103-114.E. Sandewall. 1992. Features and Fluents, to appear.Available as report LiTH-IDA-R-92-30, Dept. of Computerand Information Science, Linkoeping University, Sweden.L.K. Schubert. 1990. Monotonic solution of the frameproblem in the situation calculus, in H. Kyburg, R. Loui andG. Carlson (eds.), Knowledge Representation and DefeasibleReasoning, Kluwer, Dortrecht, pp. 23-67.L.K. Schubert. 1994. Explanation closure, action closure,and the Sandewall test suite for reasoning about change, J. ofLogic and Computation 4(5), pp. 679-799.Lenhart K. Schubert, 1992. Explanation Closure. ActionClosure. and the Sandewall Test Suite for Reasoning aboutChange, TR 440, Department of Computer Science,University of Rochester, Rochester, NY, October, 1992.L.K. Schubert and A. Gerevini. 1995. Accelerating partialorder planners by improving plan and goal choices, Prec. ofthe 7th Int. Conf. on Tools with A! (ICTAI’95) pp. 442-450.David R. Tmum, L. K. Schubert, M. Poesio, N. G. Martin,M. Light, C. H. Hwang, P. Heeman, G. Ferguson, and J. F.Allen, 1996. Knowledge Representation in the TRAINS-93Conversation System", to appear, International Journal ofExpert SystemsP. van Beek. 1992. Reasoning about qualitative temporalinformation. Artificial Intelligence 58(!-3), pp. 297-321.P. van Beck and R. Cohen. 1990. Exact and approximatereasoning about temporal relations. Computationalh~telligence 6, pp. 132-144.D.E. Wilkins. 1988. Practical Planning: Extending theClassical AI Planning Paradigm. Morgan Kaufmann, SanMateo, CA.F~I Yampratoom and James Allen, 1993. Performance ofTemporal Reasoning Systems, SIGART Bulletin 4(3).

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planning in complex worlds via mixed-initiative interaction

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