Collaborative Plans for Complex Group

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Citation Grosz, Barbara J. and Sarit Kraus. 1996. Collaborative Plans for Complex Group Action. Artificial Intelligence 86(2): 269-357.

Published Version http://dx.doi.org/10.1016/0004-3702(95)00103-4

Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:2562070

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Collab orative Plans for Complex Group Action

Barbara J Grosz

Division of Applied Sciences

Harvard University

Cambridge MA USA

groszeecsharvardedu

Sarit Kraus

Department of Mathematics and Computer Science

Bar Ilan University

Ramat Gan Israel

saritcsbiuacil and

Institute for Advanced Computer Studies

University of Maryland College Park MD

Note This article app ears in Articial Intel ligence

This pap er is an extension of our pap er in IJCAI Grosz and Kraus We thank Joyce Friedman for

many thoughtprovoking questions and Karen Lo chbaum for the same and for helpful comments on many drafts We

also thank Michael Bratman David Israel and Martha Pollack for comments on earlier versions and the anonymous

reviewers for their helpful suggestions and illuminati ng comments This researchwas initiated when the rst author

was a Harold Perlman Visiting Professor Hebrew University Jerusalem Partial supp ort for the rst author was

provided by U S WEST Advanced Technologies The second author was supp orted in part by NSF GrantNumber

IRI and the Israeli Science Ministry grant No

Abstract

The original formulation of SharedPlans Grosz and Sidner a was develop ed to provide

a mo del of collab orative planning in whichitwas not necessary for one agenttohaveintentionsto

toward an act of a dierent agent Unlike other contemp oraneous approaches Searle this

formulation provided for two agents to co ordinate their activities without intro ducing any notion

of irreducible jointintentions However it only treated activities that directly decomp osed into

singleagent actions did not address the need for agents to commit to their joint activity and did

not adequately deal with agents having only partial knowledge of the way in whichtoperform

an action This pap er provides a revised and expanded version of SharedPlans that addresses

these shortcomings It also reformulates Pollacks denition of individual plans Pollack

to handle cases in which a single agent has only partial knowledge this reformulation meshes

with the denition of SharedPlans The new denitions also allow for contracting out certain

actions The formalization that results has the features required by Bratmans account of shared

co op erative activity Bratman and is more general than alternative accounts Levesque

Cohen and Nunes Sonenb erg et al i

Contents

Intro duction

Examples of Collab orative Plans

Overview of the Mo del

Supp orting Denitions and Notation

Recip e Notation Subsidiary Predicates and Functions

Basic Mo dal Op erators

Attitudes of Intention

Typ es of Intending

Mo dal Op erators for Attitudes of Intention

Axioms for Intention Op erators

MetaPredicates for the AbilitytoAct

Complex Actions for Planning

Individual Plans

Full Individual Plans

Partial Individual Plans

Capabilities to Perform Actions in Individual Plans

SharedPlans and Intendingthat

Denition of SharedPlan

Full SharedPlans

Intentionsthat in SharedPlans

P artial SharedPlans

Capabilities to Perform Actions in SharedPlans

An Example SharedPlan for Dinner

Implications of the Formalization

Comparison with Alternative Approaches

Conclusions and Future Work

A Abilities and Beliefs

A Pro of of Theorem T

BFormal Plan Denitions and Additional Intentionthat Axiom ii

List of Figures

Key comp onents of collab orative plans

Recip e tree and the other leaf no des are basiclevel actions



The denition of IntTo

Axiom to avoid conicting intentions

Intentions and b eliefs

Denition of CBA can bring ab out and CC can contract

Denition of CBAG can bring ab out group and CCG can contract group

Denition of GTD get to do

English description of the FIP full individual plan denition

FIP Core case

FIP Contractingout case

English description of the PIP partial individual plan denition

PIP Finding a recip e

PIP Core case

PIP Contractingout case

PIP Unreconciled case

Denition of SP SharedPlan

English description of the FSP full SharedPlan denition

FSP Core case singleagent action

FSP Core case multiagent action

Contracting in a FSP singleagent subactions

Contracting in a FSP multiagent subactions

Axioms for intendingthat

Helpfulb ehavior axiom for intendingthat

English description of the PSP partial SharedPlan denition

PSP Finding a recip e

PSP Core Case singleagentact

PSP Core Case multiagentact

PSP Unreconciled case

Beliefs and capabilities to p erform actions in FIP and the denition of BCBA b elieve

can bring ab out and related theorem

Beliefs and capabilities to p erform actions in PIP and the denition of WBCBA

weakly b elieve can bring ab out

Beliefs and capabilities to p erform actions in FSP and the denition of MBCBAG

mutuallyb elievedcanbri ngab outgroup

Beliefs and capabilities to p erform actions in PSP and the denition of WMBCBAG

weakly mutually b elieve can bring ab out group

Denition of Full Individual Plan

Denition of Partial Individual Plan

Denition of Full SharedPlan

FSPC Contracting in FSP

The p erformance of the contracting action in the contracting cases of FSP MP

Memb er of the group p erforms the contracting action SGPsubgroup p erforms the

contracting action

Denition of Partial SharedPlan iii

PSP Contractingout case singleagent

PSP Contractingout case multiagent

Another helpfulb ehavior axiom for intendingthat iv

Intro duction

Co op erative problem solving by teams comp osed of p eople and computers requires collab oration

and communication Collab oration is a sp ecial typ e of co ordinated activity one in which the par

ticipants work jointly with each other together p erforming a task or carrying out the activities

needed to satisfy a shared goal Because collab orative action comprises actions by dierent agents

collab orative planning and activityinvolvetheintentions of multiple agents As a result collab

orative plans cannot b e recast simply in terms of the plans of individual agents but require an

integrated treatment of the b eliefs and intentions of the dierentagents involved Furthermore the

collab orative planning pro cess is a renement pro cess a partial plan description is mo died over

the course of planning by the multiple agents involved in the collab oration Thus capabilities for

collab oration cannot b e patched on but must b e designed in from the start Searle Grosz

and Sidner a

In this pap er wepresent a formal mo del of collab orative plans that deals more completely with

collab oration than previous existing theories of actions plans and the plan recognition pro cess

This mo del grew out of an attempt to provide an adequate treatment of the collab orative b ehavior

exhibited in dialogues Grosz and Sidner The collab orative prop erty of dialogue aects

communication in all mo dalities and thus is a factor that must b e reckoned with in developing

more advanced systems for humancomputer communication regardless of the mo dality of commu

nication Communication and collab oration also playseveral imp ortant roles in multiagent action

First communication provides a means for working together to achieve shared ob jectiv es Bond and

Gasser Davis and Smith Durfee Conry et al Werner inter alia

most multiagent systems in which the agents need to co ordinate their activities incorp orate some

mechanism for agents to communicate Second manymultiagent situations require that agents

have an ability to plan and act collab oratively the avoidance of conicting actions is a necessary

part of such capabilities but is not sucient in itself Kraus and Wilkenfeld Zlotkin and

Rosenschein Gasser Kraus and Lehmann inter alia For example in some

cases agents must decide collectively on the approach they will take to acting ie the constituent

actions they will p erform and negotiate ab out resp onsibilities for p erforming the subsidiary ac

tions entailed The mo del presented here is intended to provide the basis for constructing computer

agents that are fully collab orativeaswell as to provide a framework for mo delling the intentional

comp onent of dialogue Grosz and Sidner Lo chbaum

The original formulation of the SharedPlan mo del of collab orative planning Grosz and Sidner

a extended Pollacks mental state mo del of plans Pollack c Pollack to the situa

tion in whichtwo agents together form a plan to p erform a complex action requiring contributing

activityby b oth agents Pollacks denition of the individual plan of an individual agenttodoan

action includes four constituent mental attitudes b elief that p erformance of certain actions

would entail p erformance of the constituted a recip e for b elief that the agent could

i i

p erform each of the intentions to do eachofthe anintention to do by doing the

i i

To dene SharedPlans Grosz and Sidner a mo died these comp onents to incorp orate

i

multiagent actions and asp ects of mental state needed for a pair of agents to co ordinate their ac

tivities eg mutual b elief In subsequentwork Lo chbaum Grosz and Sidner Lo chbaum

algorithms were provided for constructing and augmenting SharedPlans in the context of a

dialogue

Although this formulation overcame several problems with previous mo dels of plan recognition

for discourse eg the treatmentofintentions of one agenttoward another agents actions in appli

cations of sp eech act theory Allen and Perrault it had several problems that emerged when

we attempted to apply it to dialogue pro cessing and complex actions in multiagentenvironments

Lo chbaum Grosz and Sidner Lo chbaum First the original mo del presumed that

every multiagent action decomp osed directly into singleagent actions As a result the mo del did

not adequately provide for complex activities entailing joint activityatmultiple levels or for mesh

ing of individual plans for individual action with collab orative plans for joint action Second the

mo del did not account for the commitmentofanagent to the success of a collab orative partners



actions Third the agents who undertake the development of a collab orative plan often do not

know a complete recip e for accomplishing their joint action the mo del did not provide a sucient

means of describing the mental state of agents in this situation The notion of a partial SharedPlan

SharedPlan was intended to represent this kind of partialitybutwas never sp ecied in any detail

One or more of these limitations applies to alternative mo dels develop ed subsequently Levesque

Cohen and Nunes Jennings Jennings Sonenb erg et al The formulation

presented in this pap er overcomes each of these deciencies and thus provides a more complete and

accurate mo del than the original formulation and alternative approaches

Collab orative activitymust rest eventually on the actions of individual agents as a result the

collab orative plans of a group of agents must include as constituents the individual plans of group

memb ers These individual plans may b e more complex than those accounted for in Pollacks

formulation Pollack c Pollack in three w ays First Pollacks formulation presumed

that an agent had a complete recip e for the action it was p erforming whereas individual agents

as well as groups of agents may initially have only partial knowledge of how to p erform an action

one function collab orators may serveistoassistanagent in completing a partial recip e Second

Pollack considered only twotyp es of action relations generation Goldman and enablement

her formalization of simple plans uses only generation and the plans are named simple b ecause

of this limitation Balkanski describ es several additional action relations that arise in the

p erformance of complex tasks including sequential and parallel execution Third agents may

contract out to other agents some of the actions to b e done Weprovide an extended denition

of the plans of an individual agent that overcomes these limitations

Because the formal plan denitions are complex highly recursive and dep endent on several

new mo dal op erators in the next section weprovide informal descriptions of several examples that

motivate the denitions presented in the pap er We will refer to these examples throughout the

pap er to illustrate the range of collab orativebehavior the mo del is intended to cover and the wayin

which it do es so Section provides an overview of the formalization and its ma jor distinguishing

features Section presents auxiliary functions predicates and mo dal op erators that are used in the

plan denitions It includes a characterization of the dierentintentional attitudes that play a role

in collab orative planning followed by denitions and axioms for them It also provides denitions

of predicates used to mo del an agents ability to p erform an action given dierent degrees of partial

knowledge ab out how to p erform the action a prop erty that is essential to the plan denitions and

it describ es certain pro cesses that playcentral roles in expanding partial plans to more complete

ones Sections and provide the formal plan denitions Ateac hstagewe discuss those asp ects

of the resulting theory that address the deciencies describ ed ab ovetoprovide a more adequate

mo del of collab orative activity Section examines claims ab out collab oration made in the AI

The last clause of the original denition was intended to ensure this commitmentaswell as other prop erties

of co ordinated acting It sp ecied that the agent p erforming an action intended to do that action to contribute to

the p erformance of the group action See the reply Grosz and Sidner b for a discussion of replacing the BY

op erator used in the original denitions by Contributes and the pap er Lo chbaum Grosz and Sidner for a

denition of Contributes However this approach is inadequate in general It seemed to work only b ecause the

action decomp osition in the original pap er was single level ie the rst deciency describ ed ab ove In the current

pap er weprovide a more principled approach

and philosophical literatures and describ es the way they are accounted for within the framework

we present Section compares our formalization with alternative accounts The pap er concludes

with a description of several key problems for future research

Examples of Collab orativePlans

Our primary example comes from the co oking domain it is a collab oration of twoagents preparing

a meal together Although the problem of collab oratively making a meal may not b e an ideal

application for rob ots or other kinds of computer systems we use it throughout this pap er for

three reasons unlike tasks such as constructing space stations Ephrati and Rosenschein

or network management Lo chbaum Grosz and Sidner making a meal is an undertaking

for which almost all readers have rsthand knowledge and go o d intuitions this task contains

the essential elements of the typical collab orativetaskinwhich computer systems and rob ots in

particular may b e exp ected to participate limited resources including time constraints multiple

levels of action decomp osition a combination of group and individual activities partial knowl

edge on the part of each agent and the need for co ordination and negotiation previous work

on plan recognition using this domain provides a baseline for comparison Kautz Litman

and Allen Mapping from the co oking domain to repair and construction tasks in which

rob ots might more naturally participate is straightforward given the prop erties of the application

Other applications to humancomputer collab oration eg network maintenance mayinvolve lit

tle ob ject construction but more extensive use of exchange actions Lo chbaum

though information actions are quite prevalent in the meals domain as well Still other applications

eg co ordination of search and rescue missions will fall somewhere b etween the construction and

informationcentered tasks

e In particular we will consider the collab orative planning that arises when twoagents whom w

call Kate and Dan agree to make dinner together They decide that Kate will make an app etizer

Dan will make lasagna for the main course and the two of them together will make the dessert

Thus Kate and Dan must each form one individual plan Kates for the app etizer and Dans for

the lasagna They need not know the complete details of each others individual plans but they

need to avoid conicts arising b etween these plans For example they cannot b oth use one pan

during the same time interval Thus as they develop their individual plans in cho osing howto

do actions and what resources to use they must consider p otential conicts with each other and

communicate if they detect a p ossible problem In addition Kate and Dan together must form a

shared collab orative plan for the dessert The particular details of how they will do this must b e

mutually known to b oth of them In forming their plans Kate and Dan mayinterleave planning

and acting hence at any stage of their activity their plans may b e only partial For example

Kate mayhave decided to makemushro om pus for the app etizer but not yet havechosen a recip e

for doing so Alternatively she mayhavechosen the recip e but not yet decided how she will do

some of the subtasks As we will show b elow providing for partial knowledge intro duces a number

of complexities into the formalization It is necessaryhowever to treat such partialitytohavea

realistic mo del

The second example we will use exemplies situations in which all that an agent knows ab out

how to p erform an action is how to nd a description of the wa y to do it Purchasers of construction

kits that include instructions are often in this situation We will consider the example of Kate buying

a bicycle that comes unassembled in a b ox accompanied by asetofassembly instructions The

plan denitions b elow treat the case of Kate forming a plan to build the bicycle given this level of

partial knowledge ab out how to do so They also cover the case of Kate and Dan forming a plan to

assemble the bicycle together Although analogous situations may arise in co oking eg knowing

only to lo ok in a co okb o ok for a recip e they are more naturally apparent in the constructionkit

example

Finallywe will use three examples to illustrate the use of contracting Both individual agents

and groups of agents may decide that the b est way to p erform an intended action is to contract out

one of the subsidiary actions Thus Kates plan for doing the mile maintenance on her car

might include contracting out changing the oil Likewise if Kate and Dan decide to renovate their

house they might decide to hire someone to redo the o ors In the meals example Kate and Dan

might decide to contract out making the dessert Dan mightcontract out some part of making the

lasagna or Kate mightcontract out part of making the app etizer Our mo del of plans provides for

all these cases

Overview of the Mo del

The mo del given in this pap er provides a sp ecication of the capabilities to act and mental attitudes

that individual agents must have to participate in collab orative activities with one another In

addition weprovide sp ecications of plans for individual action that are mo died from previous

accounts to t with plans for collab orative activity The sp ecications are normative and intended

to provide the basis for constructing agents that act rationally Russell and Norvig Although

our work has b een informed byananalysisofhuman collab orations Balkanski we do not

claim to have a complete descriptive accountofhuman collab orative b ehavior However the mo del

has b een used to explain a variety of naturallanguage dialogues Lo chbaum Lo chbaum

We adopt a mentalstate view of plans Bratman Pollack agents have plans when

they ha ve a particular set of intentions and b eliefs We distinguish individual plans that are formed

by individual agents from SharedPlans that are constructed by groups of collab orating agents

When agents have a SharedPlan to do a group action they have certain individual and mutual

b eliefs ab out how the action and its constituent subactions are to b e done Each agentmayhave

individual intentions and plans to p erform some of the subactions The agents also have individual

intentions toward the successful p erformance of their individual and group actions We distinguish

between complete plans plans in which the agentoragents have completely determined the way

in which they will p erform an action and partial plans

Our formalization uses a rstorder logic augmented with several mo dal op erators meta

predicates and action expressions To distinguish among the dierenttyp es of plans the for

malization denes ve metapredicates FIP for ful l individual plans PIP for partial individual

plans FSP for ful l SharedPlans PSP for partial SharedPlansand SP for SharedPlans of indenite

completeness These metapredicates are dened in Sections and using terminology develop ed

in Section Although the plan metapredicates make claims ab out the mental states of agents

they are not new mo dal op erators Rather each is dened in terms of inten tions and b eliefs of

the agents who have plans of the given typ e When PIP or FIP hold for an agent that agent has

the collection of intentions and b eliefs including b eliefs ab out connections among the intentions

sp ecied in the metapredicate denition When a group of agents has a SharedPlan ie SP and

PSP or FSP holds then memb ers of the group have the individual intentions and b eliefs given in

the denitions of these metapredicates



We classify these as metapredicates b ecause some of their arguments are prop ositions but they are not new

mo dal op erators Rather each metapredicate refers to a complex formula namely the combination of predications

in its denition

Tohave a collab orative plan for an action a group of agents must have

mutual b elief of a partial recip e

a individual intentions that the action b e done

b individual intentions that collab orators succeed in doing the identied constituent subactions

individual or collab orative plans for the subactions

Figure Key comp onents of collab orative plans

An interpretation for the logic is an extension of standard Kripke p ossible worlds semantics

in whicheach p ossible world is a temp oral structure The mo dal op erators for which accessibility

relations are required dened in Sections and include the b elief op erator op erators repre

senting commitment and four intentional attitudes and two op erators related to the p erformance of

actions Several structures for interpretation prop osed in researchonintentions and b elief Cohen

and Leveque Rao and George Konolige and Pollack Wo oldridge and Jennings

inter alia provide an appropriate base for this logic However the establishment of the full set

of constraints on accessibility relations required to prove soundness and completeness results with

resp ect to our axioms requires further study All of the metapredicates are dened in terms of the

mo dal op erators and standard rstorder predicates and functions Hence accessibility relations

are not needed for them

The formalization is not intended to b e directly implemented for example by a theorem proving

system Rather it is intended to b e used as a sp ecication for agent design In this role the mo del

constrains certain planning pro cesses eg to meet the axioms of intention and provides guidance

ab out the information that collab orating agents must establish for themselves and communicate

with one another The SharedPlan formalization has b een used in the design of a dialogue system

to provide the intentional context in which utterances are interpreted and pro duced Lo chbaum

Lo chbaum Jennings provides an instance of the use of a similar sp ecication

in agent design He mo died Cohen et als formalization Levesque Cohen and Nunes to

provide an explicit mo del of co op eration for use in the design of industrial multiagent systems

Jenningss implementation demonstrates the advantages of incorp orating explicit mo dels of the

intentions required for collab oration into agent design for situations in which agents have incomplete

information and op erate in dynamic environments with unpredictable events it also shows the

imp ortance of formalizations of collab oration in designing these mo dels

Figure lists key comp onents of the mental states of agents when they have a collab orative plan

to do a group action It provides a highlevel overview for the formalization given in this pap er

and a framework in which to describ e the overall collab orative planning pro cess weenvision This

list highlights three principal ways in which plans for group action dier from plans for individual

action First a collab orative plan to do an action requires that the group of agents agree on the

recip e they will use to p erform the action Item As a result agents must have pro cesses for

deciding which recip es to use and for combining their individual knowledge of recip es Second

agents must have commitments not only to their own individual actions but also to the actions

of the group as a whole Item a and to those of other agents Item b This need requires

intro duction of a dierenttyp e of intention from the usual concept of an agentintending to do an

action Third the plans for group activities mayhave as comp onents b oth the plans of individual

agents for constituent subactions and the plans of subgroups Item As a result groups must

ys of deciding on the agent or subgroup who will do the subactions havewa

Any realistic treatment of planned activitymust takeinto account the dynamic nature of plans

plans are develop ed over time Agents b egin with partial plans and extend them until they have

complete plans Because an agents b eliefs may b e faulty or the world maychange while the agentis

planning or is acting on the basis of a partial plan partial plans mayhave to b e revised To address

these needs the sp ecications given in this pap er provide for b oth individual and collab orative plans

to b e partial in a number of ways

As a result of the dynamic nature of plans at anygiven moment while the agents are developing

and carrying out a collab orative plan any of the comp onents in Figure may b e incomplete For

example the agents mayhave only a partial recip e for the action or they may not yet have

decided who will do certain constituent subactions and so mayhave no individual or collab orative

plans for those acts or an agentmaynothave determined whether p otential new intentions are

compatible with its current commitments and so can b e adopted As the agents reason individual ly

communicate with one another and obtain information from the environment p ortions of their

plans b ecome more complete If agents determine that the course of action they have adopted is

not working then a plan mayrevert to a more partial state For example if an agent is unable to

p erform an assigned subaction then the group may need to revise its recip e

ThusthelistinFigureisbestviewed schematically it has dierent instantiations at dierent

times Each instantiation provides a snapshot of the b eliefs and intentions collab orating agents have

at that time with resp ect to their collab orative activity The formalization must ensure that the

snapshots corresp onding to a given plan are co ordinated Several dierent pro cesses are entailed

in completing partial plans analogous to the transitions b etween snapshots including pro cesses

for identifying recip es reconciling intentions and group decision making

The ma jor fo cus in this pap er is on providing a sp ecication of the agents mental state that

is comprehensive in its treatment of partiality of b elief and intention and that handles complex

actions Although the plan denitions entail that the reasoning mechanisms individual agents uti

lize for extending partial plans have certain prop erties the pap er do es not provide a complete

sp ecication of these pro cesses or individual agentdesign Rather the mo del presumes a basic

design for individual agents that accommo dates resource constraints and the need to op erate in a

dynamic world such designs are prop osed in a variety of current planning architectures and formal

izations Russell and Wefald Bratman Israel and Pollack Shoham inter alia

In particular we assume that the agent design incorp orates capabilities for managing p ending

and adopted intentions including capabilities for deciding when to consider adopting an intention

cho osing among comp eting options scheduling and executing the intended actions and monitoring

their eects and the state of the world Bratman Israel and Pollack The denitions given

in this pap er entail certain constraints on each of these pro cesses but leave other options op en

We discuss ramications of those choices that aect collab oration as wedevelop the mo del

The formalization in this pap er is signicantly more complex than those in the original for

mulation of SharedPlans or in alternative mo dels The complexity derives from the interaction of

tly by providing for partiality and complex actions In particular complexity is increased signican

multiple levels of recip es to b e entailed in p erforming a complex action and by allowing agents to

have incomplete knowledge of the recip es to b e used at anylevel These features are essential for

designing rational agents that collab orate The complete treatmentwe give also distinguishes our

mo del from the alternatives as we discuss in Section

Bratman describ es three prop erties that must b e met to have shared co op erative activ

ity mutual resp onsiveness commitment to the joint activity and commitmenttomutual supp ort

In Section we demonstrate that agents that meet the sp ecications of our formalization will form

collab orative plans that have these prop erties Furthermore they will b e able to do so even in

situations in which their initial b eliefs ab out how to p erform actions are less complete and the

typ es of actions they p erform are more complex than those describ ed by Bratman In addition the

accountwe provide retains the broadly individualisti c tenor of Bratmans characterization

The formalization develop ed in this pap er do es not require any unreduced notion of joint in

tentions or weintentions Searle p A notion of collectiveintentionality presents

two p ossible diculties Either one must presupp ose some kind of group mental state or one must

explain howweintentions can b e realized in terms of the mental state of individuals The notion

of group mental state not only presents philosophical problems Searle but also app ears to

necessitate that any agents that mightwork together in a group b e designed together Searle

explains weintentions as attitudes held by all memb ers of a group toward a group action As

we discuss in Section our approach satises Searles conditions for collective action it do es so

using only constructs for individual intentions that are useful in situations other than collab orative

group action In Section we compare our approach with other computational accounts of group

action highlighting dierences in exibility and in the range of group activitycovered

Supp orting Denitions and Notation

This section of the pap er presents the op erators functions and predicates needed to formalize

individual and collab orative plans and describ es basic terminology and notation used throughout

the pap er Mo dal op erators are used to representvarious facets of the mental state of collab orating

agents Predicates and functions of rstorder logic are intro duced to represent particular prop erties

of actions and the contexts in which they are planned and p erformed Acttyp es are dened

to representtwo classes of actions that are central to planning The plan metapredicates we

intro duce are dened in terms of these predicates functions and acttyp es as well as the mo dal



op erators and metapredicates Several of the denitions incorp orate references to the plan meta

predicates dened later the informal descriptions of plantyp es given previously should suce for

understanding these references To assist the reader Table lists the constructs to b e used the

notation used for each category and the section in whicheach is rst dened

Recip e Notation Subsidiary Predicates and Functions

Actions are abstract complex entities that have asso ciated with them various prop erties suchas

action typ e agent time of p erformance and other ob jects involved in p erforming the action In

most cases we will use lowercase Greek letters eg to refer to actions We assume a set

of functions that can b e used to obtain the various prop erties asso ciated with the action eg a

function ty pe that can b e used to refer to the typ e of action However to simplify the presentation

weintro duce simpler notation to refer to action prop erties where p ossible For example we use

the term T to refer to the time prop erty of the action ie T is shorthand for time In

addition to refer to the complex pro cesses used byagents in planning we will use terms of the form

p p where denotes ty pe and the p are parameters that refer to sp ecic prop erties

 n i

of

Not all actions are realized byevents o ccurring in the world We distinguish b etween an



action an abstraction and its o ccurrence a concrete individual that realizes the action In



Many of the op erators and predicates include temp oral parameters Because the formalization do es not place

any sp ecial constraints on temp oral reasoning we do not prop ose the use of any sp ecic temp oral logic



Thus our actions are likePollacks b but use a representation that diers from her acttyp e agent time

triples Occurrences corresp ond to acts in Israel et als theory and dier from actions in a similar manner

Typ e Notation Meaning Section Figures

IntTo intendto

IntTh intendthat

Mo dal PotIntTo p otential intentionto

Op erators PotIntTh p otential intentionthat

Exec ability to p erform basic level actions

Commit commitment to basic level actions

Do p erformance of action

FIP full individual plan

Meta PIP partial individual plans

Predicates SP SharedPlans

Plans FSP full SharedPlans

PSP partial SharedPlans

Meta CBA can bring ab out

Predicates CBAG can bring ab out group

Ability

CONF actionsprop ositions conict

GTD get to do

Meta CC can contract

Predicates CCG group of agents can contract

subsidiary BCBA b elieve can bring ab out

MBCBAG mutually b elieve can bring ab out group

WBCBA weakly b elieve can bring ab out

WMBCBAG weakly mutually b elieve can bring ab out group

MP memb er of group p erforms action

SGP subgroup p erforms action

FSPC contracting in FSP

PSPC contracting in PSP

Acttyp es Select Rec agent selects extends recip e

for Select Rec GR group of agents selects extends recip e

Planning Elab orate Individual agent extends partial plan

Actions Elab orate Group group of agents extends partial SharedPlan

Predicates singleagent singleagent action

subsidiary multiagent group action

basiclevel basiclevel action

constr constraints of a context

Functions recip e recip es for action

cost cost of action

econ relativize cost for b enet comparison

Table Summary of notations

the formalization as develop ed so far wehave not needed to refer directly to o ccurrences and so

we do not intro duce a function from actions to o ccurrences However we do need to predicate

o ccurrence we use the op erator Do dened later in this section to do so

The function recip e asso ciates with each action a set of recip es for doing that action recip e

denotes the set of recip es for action As in previous work a recip e is a sp ecication of a group of

actions whichwe will denote as i n the doing of which under appropriate constraints

i

denoted as j m constitutes p erformance of Pollack Balkanski Lo chbaum

j

Grosz and Sidner The indices i and j are distinct for simplicity of exp osition we omit the

range sp ecications in the remainder of the pap er We assume eachagent has a library of recip es

for action typ es that it collects and up dates over time When planning to p erform a given action

agents use recip es for the action typ e to construct elements of recip e Agents libraries may

dier and the successful completion of a collab orative plan may require integrating recip es from

the libraries of dierent agents

In the denitions we use the metalanguage symbol R to denote a particular recip e That is

to make the denitions more readable we will write R f g to indicate that R is b eing used

i j

to refer to the set of subsidiary actions and constraints denoted by f g The subscript in this

i j

case identies the action for which this is a recip e To distinguish among alternative recip es for

j

the same action requires more cumb ersome notation eg R Because we do not need to make

such distinctions in this pap er wedonotintro duce the additional notation However in some

p

cases wemay need to refer to a partial p ossibly empty recip e for we will use R to denote such

p

g a partial recip e ie R f

i j

Recip es may include actions at dierent levels of abstraction and the parameters of an action

may b e incompletely sp ecied in a recip e either in the library or in a partial plan Thus a recip e

may include uninstantiated variables eg for the agent or time of an action and constraints on

these variables However for agents to have a complete plan the parameters must b e fully sp ecied



in a manner appropriate to the acttyp e Lo chbaum addresses this issue in the context of

using SharedPlans for discourse pro cessing

The subsidiary actions in the recip e for action whichwe will also refer to as subacts or

i

subactions of may either b e basiclevel actions or complex actions The predicate basiclevel

holds if is a basiclevel action We assume basiclevel actions are executable at will if appropriate

situational conditions hold and do not dene this further see Pollacks argument that this is a

reasonable assumption in a computational setting Pollack c Furthermore we assume that

agents b eliefs are correct with resp ect to whether actions are basic level or complex If an action

is basic level agents b elieve it is so if an agentbelieves an action is basic level it is

For those that are complex there will b e recip es R that include constituent subactions

i

i

The may similarly b e either basic level or complex Thus considering just decomp osition

iv iv

and not other constraints represented by the wehave the general situation pictured in Figure

j

in which the leaves of the tree are basiclevel actions We refer to this tree as the complete recip e

tree for and use this example for illustrative purp oses throughout the pap er

To treat contracting we will need also to refer to a mo died form of recip e tree The plan

denitions provide for contracting out of actions in b oth individual and SharedPlans For example

Dan in forming his individual plan for the main course may decide to sub contract to his son one of

the tasks required by the recip e he has chosen eg chopping the onions likewise while renovating

their house Kate and Dan may sub contract the job of renishing the o ors When contracting is

part of agents plans the recip e expansion changes to incorp orate contracting actions In essence a

piece of the complete recip e tree for is replaced by the recip e tree for the contracting action For

example if the agent plans to contract out by p erforming the contracting action then the part

j

of the recip e tree for below is replaced by a recip e tree for We will refer to this tree as the

j

extended recip e tree for a formal denition of extended recip e tree is given in App endix A

Complex actions are further distinguished dep ending on whether the agent of the action is an

individual or a group of agents The predicate singleagent holds if is a single agent action

and multiagent holds if the agentof is a group All basiclevel actions are singleagent

tormulti actions To simplify the sp ecications we assume that an action is either singleagen

agent but not b oth For example singing a solo is a single agent action whereas singing a duet



Precisely dening appropriate to the acttyp e raises a variety of complex issue as discussions in several pap ers

make clear Hobbs App elt and Kronfeld Morgenstern inter alia

h

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h

h

h

h

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h

h

h

h

  

 k

P

a

b

Q P

a

P D

a b

Q P

a

P

b

Q a P D

P

a b

Q P

a

b P D

Q

a

a

P

P

b

D

b

 

 

  

h m k  kn

X

h

h X H H

h

X

h

h X H H

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X

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h X H H

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kn kn   p

Figure Recip e tree and the other leaf no des are basiclevel actions



is necessarily a multiagent action Likewise a single agent co oking dinner alone eg Kates

co oking dinner by herself is a dierenttyp e of action from multiple agents co oking dinner together

eg Kate and Dan co oking dinner

The intended actions that play a role in individual and collab orative plans are always planned

and p erformed in some context Various op erators functions and predicates on actions as well

as the plans that are formed for doing them need to refer to this context We use the notation

C to refer to the context in which the action is b eing done Two constituents of the context

parameter C are relevant to this pap er First C includes a constraints comp onent that enco des

For example Kates individual plan to make the app etizer may constraints on the p erformance of

have the constraint of b eing done b efore a certain time or the constraint of not using a particular

pan The function constr maps eachcontext to its constraints comp onent constrC denotes the

constraints comp onent of the context C Second C includes a representation of the intentional

context in which G is doing For example if is b eing done as part of doing some higherlevel

action A ie is part of the recip e adopted in the plan to do A then C enco des this fact

eg using the Contributes relation Lo chbaum Grosz and Sidner alternatively the agent

mighthavechosen to do to satisfy some indep endent desire This constituentofC is constructed

recursively as an agentcho oses recip es and constructs plans for the actions in them We adopt the

notational of app ending actions in the subscript eg C tomake this fact evident

i

in the denitions that follow The plan by which is b eing done is also part of this constituent

formally the denitions require that each plan b e identied by a name

Basic Mo dal Op erators

We use two standard mo dal op erators for b elief Bel and MB for b elief and mutual b elief resp ec

tively they have their usual denitions Kraus and Lehmann inter alia In addition we

sp ecify several mo dal op erators that relate agents and actions Exec CommitandDo and the

intention op erators presented in the next section In this pap er Exec Commit and Do are treated

as primitive op erators their intended meanings are as follows

ExecG T represents the fact that agent G has the ability to p erform action at time

T under the constraints Exec applies only to basiclevel actions The signicant dierence

between this mo dal op erator and Pollacks predicate EXEC Pollack c Pollack are the

constraints

CommitG T T C represents the commitmentofagent G at time T to p erforming the ac

i i

tion at time T The last parameter C represents the context in which the agents commitment

is made Commit also applies only to basiclevel actions

DoG T holds when G do es action over time interval T under constraints G may

b e either a group of agents or a single agent If T is in the past then DoG T is true if G

did at time T

Attitudes of Intention

Typ es of Intending



The plan denitions require four dierentintention op erators Two of these IntTo and IntTh

representintentions that have b een adopted byanagent The other two PotIntTo and PotIntTh

are variations of the rst two that are used to represent potential intentions Potential intentions are

used to represent an agents mental state when it is considering adopting an intention but has not

yet delib erated ab out the interaction of that intention with the others it currently holds Potential

intentions motivate an agenttoweigh dierent p ossible courses of actions or options Bratman

Israel and Pollack They thus representintentions that an agentwould like to adopt but

to which it is not yet committed Potential intentions typically arise in the course of meansends

reasoning Attitudes of PotIntTo stem from an agents delib erations ab out how to do some ac

tion it is committed to p erforming PotIntThs derive from the need to ensure that collab orating

agents plans mesh correctly Bratman

IntTo and PotIntTo are used to representanagents intentions to do some action IntTh and

PotIntTh are used to representanagents intention that some prop osition hold In the denitions

that follow IntToGT T C represents agent Gs intention at time T to do action at time

i i

opT T C represents an agent Gs intention at time T T in the context C IntThGpr

i pr op pr op i

that a certain prop osition prop hold at time T in the context C C is the analogue for

pr op pr op pr op

prop ositions of C for actions

The commonalitybetween intentionsto and intentionsthat is that b oth commit an agent not to

adopt conicting intentions Werner and constrain replanning in case of failure Bratman

The signicant distinction b etween them is not in the typ es of ob jects each relates but

in their connection to meansends reasoning and in their dierent presumptions ab out an agents

ability to act in service of the intention

An IntTo commits an agent to meansends reasoning Bratman and at some p oint to

acting In contrast an IntTh do es not directly engender such b ehavior IntThs form the basis

for meshing subplans helping ones collab orator and co ordinating status up dates Bratman

Levesque Cohen and Nunes Searle all of whichplay an imp ortant role in collab orative

plans any of these functions may lead to the adoption of an IntToandthus indirectly to meansends

reasoning

An agent can only adopt an intentionto toward an action for which it is the agent In addition

the agentmust b elieve it will b e able to do the action at the appropriate time In this pap er

w e adopt the strong p osition that an agentmust b elieveitcan successful ly p erform any action it

intends to do As others have noted eg Pollack a p and others cited there this stance

is to o strong Although it is clear that the agentcannot believeitisincapable of succeeding it may

have doubts ab out the success of the intended action Bratman Thus our formalization

would b e b etter served by a probabilistic approach to the mo deling of ability but wehave not

identied a suitable computational mo del Such an approachwould enable us to replace atout

b elief Bratman pp with the more realistic requirement that an agents b elief in the

likeliho o d of success of its actions b e ab ove a certain threshold for the agent to b e able to intend

to p erform the act



Vermazen describ es the need to consider more than a single attitude of intention

IntToG T T C

i

N

basiclevel BelG ExecG T constrC T CommitG T T C

i i

basiclevel

aP R

N

a FIP P G T T R C

i

bP P T R

elab elab elab

b PIPP G T T C

i

Elab orate IndividualP G T T C T T R C b FIP P G

i i elab elab elab

elab

b IntToG Elab orate IndividualP G T T C T T C

i i elab

elab

Figure The denition of IntTo

The meansends reasoning and knowledge constraints on intentionsto lead to an asymmetry

between IntTo and IntTh Any prop osition pr opcanbeconverted to an action Achiev epr op

where Achiev e is a function that maps arbitrary prop ositions to generalized actions that have that

prop osition as an eect However an IntThGpropT T C do es not necessarily entail an

i pr op pr op

IntToGAchievepropT T C b ecause an agentmay b e unable to do meansends reason

i pr op pr op

ing ab out Achiev epr opormay b e incapable of carrying out any particular action that instantiates

the Achiev epr op

The dierences b etween the four typ es of intentional attitudes ma y b e illustrated with the dinner

example intro duced in Section Dan and Kates collab orative plan consists of Kate making an

app etizer Dan the main course and the two of them together making the dessert Thus their

plan to make dinner includes Kate having an intention to IntTomake the app etizer a b elief that

she will b e able to do so and an individual plan for doing so likewise it includes Dan having an

intention to IntTomake the main course a b elief that he can and an individual plan for doing

so in addition it includes their having a collab orative plan to make the dessert The plan for

making dinner will also include Dans intention that IntTh Kate b e able to make the app etizer

and Kates intention that IntTh Dan b e able to make the main course

If Kate has decided to makemushro om pus for the app etizer but not yet chosen a recip e for

doing so her individual plan will b e partial It will include an IntTo select or construct a recip e

for mushro om pus The identication of the recip e entails meansends reasoning As she do es this

meansends reasoning she will determine actions she needs to p erform to make the mushro om pus

and will adopt p otential intentions to PotIntTo p erform these actions The p otential intentions

will b ecome part of a delib eration pro cess Bratman Israel and Pollack and through that

pro cess may b ecome IntTos

Mo dal Op erators for Attitudes of Intention

The denition of IntTo is given in Figure The rst part of this denition Clause deals

with the case of an agentintending to do an action that is basic level Two standard constraints

Bratman are represented in this part of the denition that the agent b e committed to

doing the action and that the agent b elieve it can execute the action

tending to do an action that The second part of the denition addresses the case of an agentin

is complex Two issues arise each stemming from needing to generalize the constraints for basic

level actions First of what do es the commitment comp onentofintention consist in this case in

particular what other commitments do es it entail Second to what extentmust an agentknow

how to p erform the action and b elieve that it will b e able to do so



For the agent to p erform the intended action completely it must have a full recip e for the

action ie it must have recip es for all of the complex actions in the recip e for that it is doing

itself and for any complex contracting actions that it plans to use and must likewise have recip es

for any complex actions in these subsidiary recip es and so on recursively to basiclevel actions

In addition the agentmust haveintentionsto do all of the basiclevel actions in the full recip e

From the base case Clause the agentmust b elieve it will b e able to execute each of these

basiclevel actions and must b e committed to doing so This degree of knowledge and commitment

is to o restrictive for the initial adoption of an intentionto Such a restriction would prohibit partial

plans or incremental planning b oth of which are imp ortant to our approach

However the agentmust have at least some minimal commitment to the complex act Fur

thermore we argue this commitment is only meaningful if the agent has some minimal knowledge

ab out how to identify a recip e for the act either through construction or bychoice from several

options and a commitment to identify a recip e In addition the agentmust b elieve that the recip e

it will select is one it will b e able to execute These additional constraints followfromintentionsto

engendering meansends reasoning Bratman If an agentdoesnothave a recip e for and

furthermore has no idea at all ab out how to nd or construct a recip e then it cannot do any

meansends reasoning ab out

The denition separates its treatmentofanagentintending to do a complex action into two

parts We discuss the ma jor constraints imp osed byeach part here they derive from the plan de

nitions given in Section If the agent has a complete individual plan to do the action Clause a

then the strongest constraints describ ed ab ove are met Clause b covers the case in which the

agents knowledge of how to do the act and commitment are more partial The partial individual

plan in Clause b establishes minimally that the agent has chosen and is committed to some

way of identifying a recip e for Clause b represents the agents commitment to completing



this partial plan Clause b is entailed by Clause b as discussed in the next section we

include it explicitly to emphasize that this particular mo dalitymust hold of the agent ie that

the agent adopts an additional intentionto Although not formally required this clause is useful

when using the formalization in agent design

Although the constraints in Clause b might seem strong they are actually quite weak

Together they ensure only that the agent is committed to meaningful meansends reasoning ab out

First the partial plan of Clause b do es not require that the agenthave a recip e for

only that the agentknow some way of identifying such a recip e For example Kates recip e for

identifying a recip e for the app etizer might consist only of calling her mother or of lo oking in a

co okb o ok or of doing b oth and then deciding whether she wants to use any of those recip es or

her old favorite one or Kate mighthave a more metalevel recip e for nding a recip e one that

h of these three options to pursue Thus the consists of waiting until later and then deciding whic

constraint represented by this clause amounts to stipulating that the agent cannot b e at a complete

loss ab out how to nd a recip e nor can the agent b e uncommitted to selecting a complete recip e

eventually

Individual term in Clause b refers to general complex planning ac Second the Elab orate

tions for expanding partial plans see Section Although these actions may at some level refer

to recip es in the partial plan they do not dep end on them Thus the full plan in Clause b

amounts to a sp ecication that an agent b e committed to invoking one of its planning pro cedures



More precisely this requirement holds for the agent to p erform the action intentionall y the agent might acciden

tally p erform the action a situation not of concern here



The planname parameters in b and b are identical to ensure that the particular plan is completed

Substituting the weaker constraint of a partial individual plan for elab oration into Clause b

would lead to an innite regress The agents plan to elab orate the elab oration could b e partial

and so on innitely none of the intentions to elab orate would need to ground out in Clause a A

mo dication that stopp ed the recursion after a nite numb er of steps might seem a more reasonable

mo del For example wemight stop the recursion at the second step allowing the agenttohavea

partial plan for the elab oration but requiring a full plan for the elab oration of the elab oration But

to do this would require intro ducing a sp ecial stronger notion of intention and at no extra gain

By allowing the elab oration pro cess itself to b e quite general and include exploration of disjunctive

p ossibilities weachieve the same result

In this pap er we do not dene IntTh in terms of more basic constructs Instead we provide a



set of axiom schemas that sp ecify the ways in whichintendingto and intendingthat interact with

each other and with b elief Although we cannot provide a full set of axioms the central axioms

needed for our formalization are given in the next section additional axioms for intendingthat are

discussed in Section

The meals example illustrates many of the dierences in reasoning and reconciliation that are

engendered byintentionsto and intentionsthat Kates individual plan to make the app etizer leads

her to meansends reasoning ab out the way in whichtodoeach of the actions in the recip e including

reasoning ab out reducing each of the steps in the highlevel recip e eg a recip e like one that might

app ear in a co okb o ok to basiclevel actions The intentionsto do each of the actions entailed by

the recip e are her own and thus under the control of her reconciliation pro cesses In contrast if

she forms a collab orative plan with Dan to make the dessert then Dan will b e resp onsible for

some of the subactions say preparing the egg whites chopping nuts and whipping cream for a cake

icing Dan forms in tentionsto p erform each of these subsections Kate has intentionsthat he will

b e able to do them Kate can aid Dan by not presenting him with the need to reconcile additional

intentions eg not asking him to plant the vegetable garden at the same time by b eing helpful

eg discussing approaches to problems Dan encounters for example the egg whites not whipping

and by not doing things that interfere with his actions eg not using the mixer when he needs it

However she will not otherwise do any meansends reasoning ab out howtochop nuts or to whip



egg whites or cream Furthermore Dan will b e reconciling other intentions with intentions to

do the actions he is contributing to the dessertmaking His obligations and desires will determine

whether he watches the evening news or works on the cake

Axioms for Intention Op erators

In this section we presentseveral basic axioms relating intentions to one another and to b eliefs

These axioms further constrain the design of computer agents for rational action

A ma jor role intentions play in planning is to make the pro cess more tractable by constraining

agent delib eration Bratman Bratman Signicant fo cusing of attention results from

the constraint that an agent cannot hold two conicting intentions simultaneously The axiom

stating this constraint uses the metapredicate CONF CONF T T represents

situations in which a the p erformance of an action conicts with the p erformance of another

uing to hold or c action or b the p erformance of an action conicts with a prop osition contin



two prop ositions cannot hold simultaneously Thus CONF T T is true in the



All the axioms that are sp ecied in this pap er are actually axiom schemas

At least she will not necessarily do such reasoning She may b ecome involved if Dan needs help determining an

appropriate recip e Lo chbaum

The denition of CONF encompasses only conicts among prop ositions and the p erformance of singleagent

actions Conicts that arise from group actions are handled through the inclusion of intentionsthat IntTh prop o

A Bel G CONF T T constrC constrC T

i

fI ntT xG T T C IntTyG T T C

i i

IntTyG T T C I ntT xG T T C g

i i

may b e either an action if IntTxyIntTo or a prop osition if IntTxyIntTh

Figure Axiom schema to avoid conicting intentions



following three situations

and are actions for which G is the agent G s p erformance of under the constraints

conicts with its p erformance of under constraints This conict may arise either

b ecause the p erformance of one of the actions will bring ab out a situation in whichitis

no longer the case that the agent can p erform the other action formalized using the meta

predicate CBA dened in the next subsection or b ecause the constraints on the p erformance

of the two actions are in conict In either case this conict can b e formalized as

R R CBA G R T CBAG R T

is an action for which G is the agent is a prop osition Either Gs p erformance of will

cause not to hold or converselyif holds then G cannot p erform Formally

DoG T R CBAG R T

and are prop ositions which cannot simultaneously hold ie

Each of these conict situations may b e illustrated with the dinner making example Supp ose

that Dan and Kate have only one lasagna pan all lasagna recip es require using this pan and all

recip es for making spinach squares also require the pan There is a conict of the rst sort b etween

Dans making lasagna and Kates making spinach squares during the same time interval A conict

of the second sort arises b etween Dans making lasagna the action and Kates b eing able to make

spinach squares the prop osition The second typ e of conict also o ccurs b etween the prop osition

that Dan and Kate are making dinner at time T ie the prop osition DofDan K ategmake

dinnerT and Kates playing basketball at time T The third conict situation holds b etween

the pan b eing clean and empty and the lasagna ingredients b eing in the pan

As formalized by the axiom in Figure an agent cannot knowingly hold conicting intentions

neither conicts b etween intentions of the same typ e IntToorIntTh nor conicts b etween

an IntTo and an IntTh are allowed If an agent is unaware of ie do es not knowaboutan

existing conict this axiom do es not applyTwo prop erties of our formalizationthat agents may

have partial plans and that collab orating agents do not need to know the complete plans of their

tial unknown conicts We discuss the rationale for these prop erties partnersare sources of p oten

and the ramications for agent design in the intro duction to Section

Within the formalization we provide the need to checkintention conicts arises most prevalently

in the transitions needed to form complete plans from partial ones In particular the transition

pro cess includes an agent turning p otential intentions into actual intentions If the agent discovers

a conict b etween adopting a new intention as a fulledged intention and intentions it already

has it must reconcile b etween the comp eting intentions The reconciliation pro cess is part of the

sitions in the plan denitions



If is a prop osition then the set of constraints is empty likewise if is a prop osition then is empty

A Axiom If is a basiclevel action and G it intends to do

then G really intends to do

T T basiclevel Bel G IntToG T T C T IntToG T T C

i i i i

T Theorem T T FIPP G T T R C T IntToG T T C

p p p i

A Axiom Bel G IntThG pr op T T C T IntThG pr op T T C

i pr op pr op i i pr op pr op

A Axiom Bel G PotIntTxG T T C T PotIntTxG T T C

i i i pr op

where PotIntTx is equal to PotIntTo if is an action or PotIntTh if is a proposition

Figure Intentions and b eliefs

basic agent design presumed by this pap er as discussed in Section The pro cess of transforming

p otential intentions to actual intentions is part of the plan elab oration pro cess represented by the

acttyp e term Elab orate Individual which is describ ed in Section

In the dinner making example Kates individual plan for making the app etizer cannot pro duce

intentions that conict with her intention that Dan succeed in making lasagna For instance once

Kate knows that Dan intends to make lasagna for the main course she cannot intend to do an

action that would use their sole lasagna pan for example under the assumptions describ ed ab ove

she cannot intend to make spinach squares If p otential intentions lead to consideration of adopting

such conicting intentions the reconciliation pro cess will cause one intention to b e dropp ed as a

result some p ortion of the SharedPlan will b ecome or remain partial For example Kate might

initially consider making spinach squares for the app etizer but drop that p otential intention when

she realizes she cannot do so without conicting with Dans abilitytomake lasagna She might

then adopt a p otential intention to makemushro om pus instead

Figure gives the basic axioms relating b eliefs and intentions Axiom A stipulates that an

agent actually intends to do any basiclevel action that it b elieves it intends to do

Theorem T asserts that an agent has an intention to do the complex action whenever the

agent has a full individual plan to do This axiom follows in a straightforward manner from the

denition of FIP if the agent has intentions to do all of the basic level actions required for doing

and furthermore intends these actions in the context of a plan to do then it follows that the agent

intends to do However an agent do es not always haveanintention when it has a partial plan

In particular from the denition of IntTo if the agents plan is partial and it has not formed a

complete plan to elab orate the partial plan eg it has not reconciled the relevantintentions then

it will not yet haveanintention to do Furthermore an agentmighthave successfully reconciled

an intention to do but have only some and not all of the b eliefs required for a partial plan in

this case it do es not yet have a fulledged intention to do

Finally Axiom A stipulates that an agent actually intends that a prop osition holds if it

b elieves it so intends and Axiom A states that if an agent b elieves it has a p otential intention

then it really do es

MetaPredicates for the AbilitytoAct

To represent the knowledge agents haveabouttheirown and their collab orators abilities to p erform

actions in a plan weintro duce two related metapredicates the singleagent metapredicate CBA

can bring ab out and the multiagent metapredicate CBAG can bring ab out group Three

additional metapredicates are dened to treat contracting and the knowledge agents need to have

ab out their own and their contractors abilities The metapredicates CC can contract and

CCG group of agents can contract sp ecify the conditions under which agents can do an action

by contracting it out to other agents Contracting in turn dep ends on an agent b elieving that by

doing one action and thus bringing ab out a certain state of aairs it can get a dierent agentto

p erform another action the metapredicate GTD get to do is used to represent this state of

aairs

The metapredicates CBA and CBAG presupp ose an omniscient p ersp ective from which the

recip es for action and all its constituent acts are known eg the complete set of recip es for the

full recip e tree in Figure or if contracting is involved for the extended recip e tree is known

The plan denitions however use these metapredicates only within b elief or intention contexts

that existentially quantify the recip e Although CBA and CBAG are very strong the result of

emb edding them in b elief or intention contexts is a very weak statement in particular only b elief

in the existence of some recip e or intention that one exist is claimed not identication of a

particular recip e This result is exactly what is needed for certain p ortions of partial plans and for

representing what collab orating agents know ab out their collab orators abilities

However the knowledge agents have ab out their own ability to p erform actions in their full

individual plans or full SharedPlans is greater than that represented byCBAandCBAGemb edded

inside b elief contexts but less than that represented by the unemb edded metapredicates The

denitions of FIP and FSP implicitly enco de this level of abilityknowledge In a similar manner

the denitions of PIP and PSP implicitly enco de agen ts knowledge ab out their own abilities to act

when they know only partial recip es for subsidiary actions eg when they know part of the recip e

tree of Figure but not the complete tree

The remainder of this subsection presents CBA CBAG and the metapredicates used to accom

mo date sub contracting within their denitions Sections and discuss additional constraints

on agents knowledge ab out actions they p erform themselves in individual plans and collab orative

plans resp ectivelyTo aid in designing agents we dene subsidiary metapredicates that explicitly

represent this level of abilityknowledge in App endix A

The metapredicate CBA given in Figure represents an agent Gs ability to do the action

using the recip e R at time T and under constraints The agentmay either do all of the



subactions in R itself or maycontract out some of them The constraints argument enco des

various situational constraints on the p erformance of the action these constraints derive from the

particular recip e b eing used and the context in which the action is b eing done In particular

subactions inherit the constraints of the actions of which they are a part Clause b For

example if Dan decides to make homemade tomato sauce for the lasagna in the dinner he and

Kate are preparing then in deciding whether he can bring ab out the action of making the sauce

he must consider the time constraints on the overall action of making dinner eg b eing done by

PM as well as any constraints within the sauce recip e itself eg having the ingredients b eing

able to use the pressure co oker for an hour

In the case of an agent doing the action itself if the action is basic level CBA reduces to Exec

Clause If the action is not basic level then CBA is determined recursively on the basis of

the recip e R Clause F or each subsidiary action in the recip e this recursion provides

i

either for the agent to carry out itself Clause b or to contract it out to another agent

i

Clause b The recursion on acts the agent p erforms itself ends in basiclevel acts from the



Clause b of the CBA denitions includes simple disjunction or rather than exclusive or The use of or

reects the p ossibili ty that an agentmay b e able to bring ab out the subsidiary action in more than one way it may

i

b e able to do the action by itself to contract it out or b oth to p erform it itself and to contract it out Because CBA

represents ability rather than any commitment to act in a particular way or is the appropriate logical connective

CBA G R T

N

basiclevel Exec G T

basiclevel

a R f gR Recipes

i j

b R T

i

i

f g T CBAG R b R

j i

i i i

f g b CCG T

j i

i

CCG T

G T R

c

CBAG R T

GTDG T G T

c

Figure Denition of CBA can bring ab out and CC can contract

complete recip e for for subsidiary actions that the agent contracts out a contracting action and

a recip e for p erforming it enter into the recursion The recursion ends in an extended recip e tree

with basiclevel acts that the agent p erforms itself as leaves Thus CBA requires that the agent

b e able to execute the basiclevel acts entailed in p erformance of the original action with the

exception of those actions contracted out or entailed bycontracted actions according to the

given recip e and under the sp ecied constraints For those subsidiary actions that are contracted

out the agentmust b e able to execute the basiclevel actions in or entailed by the recip e for the

agents contracting action again with the exception of any that are contracted out or entailed by

contracted actions

The metapredicate CC sp ecies the conditions under whichanagent is able to contract out

an action to another agent In particular the original agent Gmust identify a contractor G

c

and some action that it G can p erform Clause such that by doing the action G can get

G to do at the appropriate time and under the appropriate constraints Clause

c

The denition of CBAG a metapredicate for groups and multiagent actions analogous to

CBA is given in Figure The ma jor dierence b etween CBAG and CBA is that some of the

actions in the recip e for the necessarily complex action ie some of the maybemultiagent

i

actions For these actions there must b e a subgroup of the whole group that can bring ab out

the action Clause ie CBAG recurs on a subact with a subgroup For those that are

i

singleagent actions there needs to b e a memb er of the group who has an ability to p erform the

action Clause of CBAG Furthermore CCG generalizes CC to handle situations in whicha

group of agents do es the contracting Clause of CCG The singleagent case of CCG is likeCC



but requires identication of a group membertodothecontracting

The metapredicate GTD Figure treats b oth single and multiagent actions Thus the

arguments G and G may refer either to a single agent or a group of agents and the arguments

c

and may b e either single or multiagent actions GTD holds of two agents or groups G and G

c



Because an action may b e either singleagentormultiagent but not b oth and agents b eliefs are correct with

resp ect to whether actions are single or multiagent exclusive or is used in Clause a of the CBAG denition

However the group GR maybeabletocontract out a particular in several dierentways Some individ ual agent

i

may b e able to use a singleagent action or a subgroup might use a dierent action whichismultiagent or

b oth typ es of contracting actions may b e p ossible This is indicated by the use of or rather than exclusiveorin

Clause c of the CCG denition Figure

CBAGGRR T

R f gR Recipes

i j

a R T

i

i

singleagent

i

GRR a G

i i

f g T a CBAG R

j i

i i

multiagent

i

a GR GRR

i i

W

f g T R a CBAGGR

j i

i i i

f g CCGGR T

j i

i

CCGGRT

G T R

c

singleagent

a G GR

b CBA G R T f g

j

W

c GTDG T G T

c

G T R

c

multiagent

a GR GR

b CBAGGR R T

c GTDGR T G T

c

Figure Denition of CBAG can bring ab out group and CCG can contract group

two actions and the times of those actions T and T and a set of constraintsifasaresult

of Gs doing at T G commits to doing at T The constraints originate as constraints

c

er some of those constraints eg constraints on resources are on the p erformance of Howev

also applicable to the p erformance of hence is a parameter of the Do mo dal op erator in

clauses a and a as well as of the CBA and CBAG metapredicates in clauses c and d

For singleagent actions GTD states that Gs doing of will leave G in the state of intending

c

to do and having a particular recip e by which it is able to do it Clauses b and c The

subscript notation on the context parameter of the IntTo in clause b indicates that G s intention

c

to do results from ie is an eect of Gs doing Incontrast with most situations encountered

in the denitions in this pap er in this case G do es not intend do in order to do The functional

c

notation f makes this clear the reason for doing is some functional relationship b etween

and For instance if Dan pays his son to chop the onions then the context in which his

son intends to chop the onions is that of b eing paid to do so The constraints comp onentofthe

context constrC includes the constraints

f

If is a multiagent action then Gs doing of will result in the group of agents G having

c

a SharedPlan to do theymust also have a particular recip e which they as a group can use to

bring ab out Clauses c and d The subscript notation on the context parameter of the

SharedPlan in clause c indicates analogously to that of the IntTo that the SharedPlan to do

results from Gs doing Again the constraints are part of constrC

f

Both the individual plan underlying the IntTo in the individual case and the SharedPlan in

the multiagent case may b e partial Even so the denition of GTD may seem to o strong as it

GTDG T G T

c

singleagent

aDoG T

b T IntToG T T C

i c i

f

N

c R CBA G R T

c

multiagent

aDoG T

b P T R

i

T T C c SPP G

c i

f

d CBAGG R T

c

Figure Denition of GTD get to do

presumes b oth lack of will on the part of G and a great deal of knowledge ab out recip es for actions

c

However in the plan denitions and other metapredicates GTD is only used within an emb edding

b elief context Hence the claim within any of our plans is only that the agent G b elieves its doing

of will leave G in the state of b eing able to p erform according to a particular recip e and either

c

intending to do or having a SharedPlan to do it

Acontractors plan is not under the control of the contracting agents Thus even when the

contracting is done within a full individual plan or a full shared plan we do not require that the

contractors have a complete plan Furthermore as we describ e in presenting the SharedPlan

denitions Section contracting diers from having a SharedPlan in the IntThs whichmust

hold

Complex Actions for Planning

The terms Select Rec and Select Rec GR refer resp ectively to the acttyp es for the complex

planning actions that agents p erform individual ly or collectively to identify ways to p erform do

main actions The terms Elab orate Individual and Elab orate Group similarly refer resp ec

tively to the acttyp es for individual and group actions for extending partial plans to complete ones

To construct computer agents based on our formalization requires dening pro cesses for selecting

recip es and elab orating plans ie dening sp ecic complex actions of the typ e referred to by

Individual Elab orate Group Select Rec and Select Rec GR In this pap er we use the Elab orate

term Elab orate Individual pro cesses to refer to computational pro cesses eg mechanisms that

implement the complex actions in computer agents that instantiate actions of the typ e referred to

by Elab orate Individual we similarly app end pro cesses to the other acttyp e terms to refer to



pro cedures implementing actions referred to by those terms

Although for eachofthesetyp es of complex activityavariety of pro cesses are p ossible we

restrict these terms to refer to a subset that meet certain constraints In particular we restrict

each to incremental pro cesses that can b e interleaved with p erforming domain actions and we



require that they incorp orate mechanisms for recovering from failures Some general constraints

on the individual pro cesses are given b elow additional constraints are sp ecied in Sections and

using the terminology develop ed in the plan denitions



We recognize in so doing we are somewhat abusing the formal vo cabulary however the alternative is more

complex and less easily understo o d language



In addition to b eing more realistic for planning systems incremental algorithms are crucial for dialogue mo d

els Lo chbaum

p

Select Rec G R T refers to the activity of an individual agent G extending its partial

p p

recip e R for If the agent G has not yet b egun to form a recip e for the action then R

will b e empty in this case Select Rec G T refers to the initial construction of a recip e for

Select Rec is used in the denitions of partial plans to help representanagents commitmentto

nding a way to do the actions it intends and its b eliefs that it can do so Standard AI planning

Rec actions However agents may also select pro cedures can form the core of one class of Select

recip es by retrieving them from memory lo oking them up in manuals or asking others Toavoid

unnecessarily complicating the formalization we include as part of the Select Rec pro cess the task

of adding p otential intentions for subactions in the recip e extension to the agents set of intentions

Elab orate Individual P G T T C refers to the pro cess of extending agent Gs partial

p

plan P at time T to do action at time T The ma jor task for an Elab orate Individual pro cess

p

is ensuring that the agent has a means of carrying out each of the constituent actions in the recip e

for asso ciated with P and is committed to doing so Atanypoint in the planning pro cess for

each in the recip e constructed so far an Elab orate Individual pro cess must initiate pro cedures

i

for reconciling an intention to do with currently adopted intentions To do so the reconciliation

i

pro cess must takeinto account resource constraints and the need to op erate in a dynamic world

Russell and Wefald Bratman Israel and Pollack Shoham inter alia If is a

i

basiclevel action then the elab oration pro cess must also establish a commitmenttodo and the

i

b elief that it can b e p erformed If is a complex action then the Elab orate Individual pro cess

i

must ensure that a full individual plan is constructed for it In doing so it will initiate a Select Rec



and an Elab orate pro cess for a recip e for Individual pro cess for

i i

Thus to design pro cesses for expanding partial individual plans to more complete ones it is

p ossible to draw on existing AI planning mechanisms b oth for recip e construction and intention

reconciliation However signicant additional mechanisms are needed to design pro cesses for the

more complex multiagent actions referred to by Select Rec GR and Elab orate Group These ac

tions incorp orate many of the constituents of Select Rec and Elab orate Individual but each also

includes some group decision making pro cesses including mechanisms for negotiating among com

p eting recip e prop osals handling resource conicts and reaching consensus Furthermore these

multiagent planning pro cesses require that a group have some means of forming mutual b elief and

agreed up on pro cedures for reaching consensus

p

Rec GRGRR T refers to the activity of a group of agents extending their partial Select

p

recip e R for Analogously to the individual case if the group has not yet b egun to form a

p

recip e R will b e empty The realization of this group recip e selection pro cess is more complex

than the one for an individual agent Eachagent in the group must have its own internal pro cess for

Rec but leads to dierent kinds of intentions identifying recip es this pro cess is equivalent to Select

b eing considered as we discuss in Section In addition a group decision making pro cedure

is needed for mediating among dierentagents prop osals The agents may also need metho ds

for constructing a new recip e using information from dierent group memb ers The interaction

between recip e selection and intentionadoption is also more complex esp ecially if no single agent

is in charge For example Kate mayhave a recip e for making dinner that she b elieves will work

only if Dan agrees to p erform certain actions Osawa and Tokoro describ e one p ossible

Select Rec GR based on mechanisms similar to contract nets Davis and Smith However

many collab orative planning situations exhibit less centralized management than these techniques

presume

GroupP GRT T C refers to the group pro cess of extending a collab orating Elab orate

p

groups partial plan P at time T to do the collective action at time T The ma jor comp onents of

p



The rationale for this is given in Section

this pro cess are identifying agents able to do the constituent actions cho osing a particular agentor

subgroup to do them and ensuring that the agents adopt the requisite intentionsto and intentions

that toward these actions In addition to having a means of assessing its own capacity to p erform

actions each participant in a collab orative activitymay need to assess the abilities of others Agents

also need means of communicating ab out their abilities Mechanisms for reaching consensus may

be invoked to decide who will b e the agent of the constituent subactions in the groups recip e for

Group pro cesses deal Dierent groups of computer agents mayvary in the ways their Elab orate

with selection of the agent to do an action just as the b ehavior of groups of p eople varies

The additional tasks to b e done and the particular typ es of intentions to b e adopted dep end on

whether the constituent action from the recip e constructed so far is a singleagent action or a

i

multiagent action If it is a singleagent action then the choice of agentfollows a pro cess analogous

to that for Elab orate Individual and the other group memb ers adopt p otential intentionsthat this

agent will b e able to do the action If it is a multiagent action then the Elab orate Group pro cess

must result in the subgroup that is chosen as agent constructing a full collab orative plan For



this to o ccur the subgroup must initiate a Select Rec GR pro cess for a recip e for and an

i

Elab orate Group pro cess for

i

Group pro cesses constitutes a large area of inquiry in itself Sonen The design of Elab orate

b erg et al describ e one set of mechanisms for group elab oration and role assignment within a

formalization that includes complex actions but do es not allow for partial recip es Jennings

describ es another mechanism one in which a central organizer identies team memb ers deter

mines the recip e and gets agreement This approach allows for the organizer to have partial recip e

knowledge only in that the organizer do es not need to knowhow the individual team memb ers will



carry out their parts Groups comprised solely of human agents often struggle a while to reach

consensus on such matters To construct computer agents within the framework our formalization

requires providing at least some builtin pro cedures of Elab orate Group

Individual Plans

The denitions for individual plans given in this section extend in three principal ways previous

mentalstate denitions within AI of plans of single agents First they accommo date more complex

recip es in particular they accommo date the action relations and constructors dened byBalka

nski Second they intro duce the p ossibilityofcontracting a constituent action to another

agent Third they generalize to complex actions and to contracting the notion of an agents ability

to execute an action The denition of partial individual plan further extends this work to rep

resentanagents mental state when its knowledge of how to do a complex action is partial its

commitment to the basiclevel actions entailed in doing the complex action is partial or it has not

fully reconciled some intentions to do some subsidiary actions

FIP the metapredicate for full individual plans dened in Section represents the mental

state of an agent after it has completely determined a recip e R for action and has fulledged

intentions to do the actions in R Thus FIP is distinguished by the requirement that the agent

know a complete recip e for doing the action that is the ob jective of the plan ie as a result

the recip e that the agent has adopted for doing R is a parameter of the metapredicate Most



The rationale for this is given in Section



Several algorithms have b een prop osed for negotiation and task allo cation in work in Distributed AI Durfee

Decker Durfee and Lesser Ephrati and Rosenschein Kraus Nirkhe and Sycara Kraus and

Wilkenfeld Zlotkin and Rosenschein Shehory and Kraus Sycara inter alia however the

appropriateness of these algorithms for a collab orative situation remains to b e explored

FIPP G T T R C

p

Agent G knows a recip e for doing ie it knows the subactions entailed and the constraints on

them

R f gBel G R RecipesT

i j p

For each either or

i

Core case Agent G intends to do the subact itself

i

Contractingout case G intends to contract out to another agent G the p erformance of subact

c i

Figure English description of the FIP full individual plan denition

typically an agent will not have a full plan until after it has done some of the actions in R

thus most often agents have only partial plans However the FIP denition provides a signicant

constraint on Elab orate Individual pro cesses it sp ecies the conditions under which the pro cess has

completed its task When an agents b eliefs and intentions satisfy FIP then the agents intention

to do the planned action satises Clause a of the denition of IntTo and there is no additional

need for elab oration PIP the metapredicate for partial individual plans is dened in Section

the dierences b etween PIP and FIP sp ecify the information an agent needs to acquire and the

intentions it needs to adopt to have a full plan These dierences provide the main driving force

Individual pro cess for an Elab orate

We will give the plan denitions in several stages In each case the denitions have the following

ma jor comp onents of the plan basic assumptions ab out recip e knowledge the core case covering

actions the agentwilldoitselfthecontracting case covering actions the agent decides to contract

out to others and for partial plans the case dealing with unreconciled intentions The gures

included in this section provide English glosses of the ma jor elements of the plan denitions The

full formal denitions are provided in App endix B

Full Individual Plans

The denition of a full individual plan FIP sp ecies those conditions under which an individual

agent G can b e said to have a plan P at time T todoaction at time T using recip e R in the

p

context C The parameter P is a p ermanent identier for a plan as partial plans are completed

the other parameters maychange Hence P is needed to provide a way to refer to the evolving

plan



The ma jor constituents of FIP are given in Figure As noted previously the recip e R is

an argument of FIP FIP requires that the agenthave a particular recip e for doing Clause

represents the agents b elief that R is indeed a recip e for the metalanguage equality statement

vides notation enabling the subactions and the constraints to b e referred to in the pro

i j

remainder of the denition Each subaction in the recip e R will either b e done by the agent

i

itself the core case or contracted out to another agent the contracting case The core case

of FIP is given in detail in Figure the contracting case is given in detail in Figure The full

formal denition of FIP is given in Figure in App endix B



This plan name is a parameter to Elab orate Individual throughout the plan formation pro cess



In this gure and those that followwe put quotation marks around know to indicate this use is its weak

collo quial sense with no assumption of correctness of b elief the philosophi cal l y more correct b elieve pro duces an

incorrect English statement We do not use scare quotes in the b o dy of text as we presume the collo qui al sense is

apparent there

FIPP G T T R C

p

Core case Agent G intends to do the subact by itself

i

a G intends to do the subact

IntToG T T C

i p

i

i

b If the subact is not a basiclevel action G has a full individual plan for using a recip e R

i

i

P R FIPP G T T R C

i p

i i i i i

i

Figure FIP Core case

An agentmay b elieve it can do a particular action b oth by p erforming the action itself and by

contracting it out However when developing a plan the agentmust commit to one of the options

Thus when an agent has a full individual plan either the core case applies or the contracting case

eorbetween FIP Clauses and applies but not b oth This prop erty is captured by an exclusiv

see Clause b in the complete denition of FIP Figure Because having a full individual

plan for entails intending to do by Theorem T the denition of FIP do es not need to include

the prop osition IntToG T T C within it

p

The core case of a FIP for given in Figure requires that the agentintend to do each of the

subactions in the recip e for Each of the intentionsto do a subaction in the recip e is covered

i

either by Clause if the subaction is basic level or by Clause a if the action is complex

of the denition of IntTo Figure If the action is complex ie not basic level then there

i

must b e some recip e R that G can use to do and G must have a full individual plan to do

i

i

using that recip e The context parameter in Clauses a and b C records the fact

i

i

that is b eing done as part of doing eg it includes the prop osition C ontr ibutes This

i i

Contributes comp onentofC is used in any replanning inv olving The constraints comp onent

i

i

constrC is equal to the union of constrC and f g As discussed in Section Gs b eliefs

j

i

that it will b e able to p erform each of the and hence are established by recursion in FIP in

i

combination with the Exec clause in the denition of IntTo

The p ossibility of an agentcontracting out an action to another agent has not b een discussed

in previous work on multiagent plans but clearly is an option often employed byhuman agents

The example of Kate contracting out the oilchange op eration required for car maintenance is but

one instance of such contracting As shown in Figure to contract out an action an agent G

must b elieve there is some action that it can use to get another agent G todo Clause a

c i

uses the GTD metapredicate to represent this requirement This metapredicate is emb edded in

a b elief context b ecause the ecacy of in getting G to do is a matter of b elief G could b e

c i

wrong

For contracting out the agentmust have the same intentions and abilities with resp ect to

that the core case requires with resp ect to The agentmust intend to do Clause b and if

i

is not basic level have a full individual plan to do it Clause d

Contracting has one additional requirement An agent who employs a contractor must have

some commitment to the contractor b eing able to complete the job for whichitwas hired Thus

G should not adopt anyintentions that would conict with G b eing able to do For example

c i

Kate should not b oth intend to use her car to drive to a meeting on Monday afterno on and exp ect



Previous work that employs the term contracting Davis and Smith Malone Fikes and Howard

interalia has used it to refer either to the kinds of co ordination we accomplish with SharedPlans or to helpful

b ehavior likethatachieved by the intentionthat axioms describ ed later in the pap er Contracting as we use it is

closer to the concept of incentive contracting used in the economics literature Arrow inter alia

FIPP G T T R C

p

Contractingout case G intends to get another agent G to do the subact

c i

a G believes that by doing it can get G to do the subact

c

BelG GTDG T G T constr C f gT

c i j p

i

b G intends to do the contracting act

IntToG T T C

p

i

c G is committed to G s success in doing the subact

c

T constr C f gT T C IntThG R CBA G R

j p c i

cba

i i i i

i

d If the contracting action is not basic level G has a full individual plan for using a recip e R

R P FIPP GT T R C

p

i

Figure FIP Contractingout case

the p erson she hires to change the oil to do that Monday afterno on Clause c represents this

commitment using the IntTh mo dal op erator and the CBA metapredicate Contracting unlike

collab orative plans do es not require recipro city in this commitment contracting is not in and of



itself collab orative Kraus Thus there is no correlate of Clause c for the contractor G

c

A dierent situation holds among the agents of a SharedPlan as will b e discussed in Section

According to the current denition an agent can contract out part of its individual plan only

to another single agent However there are situations in which an agent might include multiagent

subacts in its individual plans with a presumption that it could contract out such actions to some

group For example Dans individual plan to sell his car might include con tracting out to a group

of mechanics a complete checkup of the car The denition of FIP do es not include this case

b ecause it would complicate all parts of the denition However the only signicantchange would

b e to Clause c this clause would need to b e replaced by the following

c singleagent

i

N

c IntThG R CBAG R T constrC f gT T C

c i j p

i i i i

i

c multiagent

i

constrC f gT T C c IntThG R CBAGG R T

j p c i

i i i i

i

We will illustrate the FIP byshowing its use in describing Dans individual plan for making the

lasagna in the meals example According to Clause Dan b elieves that a particular recip e say

his mothers recip e for lasagna is a go o d recip e to use This recip e provides a sp ecication of a set of

actions the doing of which under certain constraints constitute the p erformance of making lasagna

For each action in the recip e eg making no o dles preparing sauce he must either intend to do

i

the action Clause or b elieve that he can get someone else to do the action Clause Supp ose

Dan decides that the most ecientwaytomake the lasagna is to get Tony to make the no o dles

and sell them to him but to do the other actions himself Then the make no o dles subaction of

the recip e will b e contracted out while all of the other actions will fall under the core case

Dans individual plan will include an action say making a barter agreementtoexchange the

no o dles for an evenings child care that results in Tonys providing the no o dles For Dans plan

to b e complete Dan must b elieve that this action is either a basiclevel action that he is able to



Some mechanism typically involving communication is needed for G to b elievethatG will actually p erform

c

the contracted action Legal contracts serve this purp ose Kraus

do or is an action for whichheknows a recip e and for which he has a full individual plan As a

consequence of Clause c Dan must not knowingly do anything that would preventTonyfrom

making the no o dles from the axioms of helpful b ehavior describ ed in Section and given in

Figure Dan must also b e willing to assist in Tonys success eg helping him nd a place to

hang the no o dles to dry if necessary

When Dan has a full individual plan he will also have recip es for all of the actions in his

mothers lasagna recip e other than make no o dles as well as for making the barter agreement

and he will have a full individual plan for using each of these recip es to do the action for whichit

is a recip e

Thus the FIP denition for full individual plans extends previous work by treating more com

plex recip es the formalization of recip es is more general than that in the original formulation Grosz

and Sidner a providing an expanded notion of what it means to b e able to carry out a com

plex action and allowing for contracting to another agent When an agents mental state satises

the FIP denition the agentknows a complete recip e tree and is fully committed to all of the

basiclevel actions in it Thus it satises the most stringent correlate of the conditions for intend

ing to do a basiclevel action However as discussed in Section this constraint is to o strong

in general partial individual plans whichwe describ e next are essential to providing the weaker

constraint in the denition of IntTo

Partial Individual Plans

When an agent adopts an intention to do a complex action its knowledge of how to do that action

may b e partial Furthermore its commitment to the basiclevel actions entailed may b e partial it

may not have fully reconciled some of these subactions and it cannot intend any basiclevel actions

it do es not yet know ab out The denition in this section treats b oth partialit y of knowledge and

partialityofintention Although we are considering partial individual plans in the context of an

agentintending to do an action it is p ossible for an agenttohave a partial plan to do some action

without having yet formed an intention to do that action For example Dan may know a recip e

for making lasagna and havepotential intentions to do the actions in this recip e but may not yet

have committed himself to fully elab orating a partial plan using this recip e The PIP denition

thus accommo dates a lower level of commitment than intending to do an action By using PIP

the formalization is able to representmental state at an imp ortant stage in the planning pro cess

without having to overly weaken the notion of intending to do an action

The PIP denition provides for individual plans to b e partial in four ways First the agent

mayhave only a partial recip e for the plans action this partiality is represented by the dierence

between Clause in the denition of PIP in Figure and Clause in the FIP denition

Figure Second the agentmayhave only partial plans for some of the in the recip e for

i

this partiality is represented by the dierence b etween Clause in the PIP denition and the

corresp onding clause in the FIP denition Third there may b e some subactions in the recip e for

which the agent has only p otential intentions In particular when an agent selects a recip e for

it directly adopts PotIntTo do the actions in that recip e these p otential in tentions must b e

i

reconciled with other intentions and partial plans constructed for them This typ e of partiality

underlies the additional clause Clause in the PIP denition Finally there may b e partiality

in the contracting out case Clause the agentmayhave only a partial plan for its contracting

action

The bicycle kit example may b e used to illustrate all four typ es of partiality Kates initial

partial plan to assemble her bicycle from a kit might include the b elief that the accompanying

PIPP G T T C

p

Agent G b elieves that there is a way to p erform its recip e for doing may b e partial ie it may

know only some of the subactions that need to b e p erformed it intends to complete its partial

recip e

For each subaction in the partial recip e one of through holds

Core case Agent G intends to do the subaction by itself but mayhave only a partial plan for doing it

Contractingout case G intendstocontract out to another agent G the p erformance of the subaction

c

but may not have a full plan for doing the contracting action

Unreconciled case G has not yet reconciled the intention to do the subaction ie it has only a

p otential intention to do it

Figure English description of the PIP partial individual plan denition

instructions are complete that she can read the instructions and that she b elieves she can p erform

or contract out each of subactions describ ed in the instructions at the requisite time While reading

the instructions Kate will adopt p otential intentions to do the subactions As she reconciles these

p otential intentions with other commitments she has she will determine ways of doing each subaction

or of contracting it out For example she might decide to attach the front fork and the wheels to

the frame herself but to pay Dan to attach and lubricate the chain If so her partial plan will

expand to include her having an intention to pay Dan and intentions that he will b e able to do

the attachment and lubrication actions as well as a set of potential intentions to do the subactions

involved in assembling the frame and attaching the wheels

We will examine each of these sources of partiality in turn and discuss the requirements they

imp ose on an Elab orate Individual pro cess Figure contains the p ortion of the denition of PIP

that deals with the case of the recip e b eing partial In this case the minimal requirements for the

agenthaving a partial individual plan are that the agentbelieve there is a recip e for and that

it have a complete individual plan for determining that recip e The PIP unlike the FIP do es not

have the recip e R as a parameter instead the existence of the recip e is asserted within a b elief

context in Clause The set of constituent acts and constraints that the agent knows f g

i j

may b e only a subset of those in the full recip e Clause a the set mayeven b e empty

In this case the PIP denition requires that three conditions hold First the agentmust intend

to identify a recip e for Clause b As we discussed in Section the action Select Rec that

app ears in this denition takes a partial recip e f g for the action and extends this partial

i j

recip e to a complete one f g It also adds p otential intentions for all the new subactions to the

v e

agents set of intentions The Select Rec pro cess may b e general It mayinvoke a planformation

pro cess to construct a new recip e or select among existing recip es in the agents recip e libraryor

it may giveaway of nding a recip e eg lo oking up how to do the action in a manual knowing

someone to ask pro cesses that combine several of these options with a decision among the results

of each are also instances of Select Rec

Second the agents intention to determine the recip e must have more than a partial plan

asso ciated with it the agentmust have a full plan FIP for determining the recip e Clause b

Rec itself can b e general This requirement is less strong than it may rst app ear b ecause Select

This clause emb o dies a claim that an agentdoesnothave a partial plan to do an action unless

it knows some way of nding out how to do the action and is committed to nding out This

constraintderives from the role PIP plays in the denition of IntTo it represents a commitmentto

meansend reasoning ab out the intended act Requiring an agenttohave this minimal commitment

PIPP G T T C

p

Agent G b elieves that there is a recip e for p erforming

Bel G R R Recipes f gR T

i j p

a If G has only a partial recip e

Bel G R R Recipes f g R T

i j p

b there is a recip e R for determining an appropriate complete recip e for such

selectr ec

that

b G intends to determine ie select or nd an appropriate recip e for

IntToG Select Rec G f gT T T C

i j selectr ec p selectr ec

selectr ec

b G has a full plan using R to nd an appropriate recip e for

selectr ec

FIPP GSelect RecG f gT T

selectr ec i j selectr ec p

T R C

selectr ec selectr ec

selectr ec

where every subaction in the recip e R G selects for is one that G b elieves it can

either p erform or contract

constrC

selectr ec

R f gBel G R Recipes f gR T

v e i j selectr ec

R Bel G T

v

v

R CBA G T R constrC f g

v e

v v v

CCG T constrC f gT

v e selectr ec

v

Figure PIP Finding a recip e

to meansends reasoning also constitutes a reasonable constraint on what it means to have a plan

to do an act

In addition the agentmust b elieve that the recip e or recip e extension it nds or selects is an

appropriate one namely a recip e or extension comprising constituent subactions that the agent

b elieves it either will b e able to p erform under the constraints in the recip e or will b e able to contract

p

is b eing extended then the actions and constraints in the out successfully If a partial recip e R

p

new recip e must b e a sup erset of those in R ie this must b e an extension of the original partial

recip e These additional constraints are enco ded in the constraints comp onentofC a

selectr ec

formal sp ecication of this constituent of constrC is noted at the end of the gure and

selectr ec

in the complete formal PIP denition in App endix B

Rec action the agent G will haveat As was discussed in Section as a result of the Select



least a PotIntTodoeach constituent subaction in the recip e that it has for The plan denition

distinguishes those subactions for which the agent has adopted fulledged intentions from those

that still need to b e reconciled The former subactions fall into the core case Figure or

the contracting out case Figure and are denoted as The subactions corresp onding to

r

unreconciled intentions Figure are denoted as

k

For eachaction in the PIP core case Figure the agent G has an intention to do

r r

Clause This requirement of the partial individual plan denition resembles the one for the

full individual plan However in the PIP the plan asso ciated with this IntTomay b e only partial

Hence there is no correlate in the PIP denition of the FIP in Clause b in Figure In addition



Rec pro cess might op erate incrementally If it do es then PotIntTos will b e formed only for a subset A Select

of the subactions at any one time

PIPP G T T C

p

Core case Agent G intends to do the subaction by itself but may not have a full plan for doing

r r

IntToG T T C

r p

r

r

Figure PIP Core case

PIPP G T T C

p

Contractingout case G intends to contract out to another agent G the p erformance of the subact

c

but G may not have full plan for the contracting action

r

a G believes that by doing it can get G to do the subact

c

gT constr C f BelG GTDG T G T

j p c r

r

b G intends to do the contracting act but maynothave a full plan for doing

IntToG T T C

p

r

c G is committed to G s success in doing the subact

c

IntThG R CBAG R T constr C f gT T C

c r j p

cba

r r r r

r

Figure PIP Contractingout case

the recursion of partial plans in this case imp oses a muchweaker requirement on the agents b eliefs

ab out its abilities to do actions in a recip e for than that imp osed in the FIP this dierence is

r

discussed in Section

To remove the partiality of the core case requires that the agent identify recip es for each non

basiclevel and form full plans for doing the actions they require The formation of the full plan

r

will entail determining that the agent is able to p erform the constituent subactions in the recip e or

contract them out in particular that it can execute all the basiclevel actions Clause b of the

denition of IntTo Figure and in particular the agents p erformance of the Elab orate Individual

action is the lo cus of the actions an agentmust taketoachieve these completions

The dierence b etween the contractingout cases of the partial and full individual plans is similar

to that of the core cases The p ortion of PIP detailed in Figure diers from the FIP version in

Figure only in the lack of a correlate to Clause d In the PIP case the agentmayhave only a

partial plan to do the contracting action This typ e of partiality is resolved analogously to that

for the core case the only dierence is that the agent is dealing with the contracting action rather

than a subaction of the recip e for

The nal way in which a plan may b e partial is for the agenttohave unreconciled p otential

intentions ab out some of the subactions As detailed in the comp onent of the PIP denition

k

given in Figure the agentmay consider b oth doing the action itself and contracting it out

The agents consideration of doing itself has two comp onents the agentmust haveapotential

k

intention to do the subaction Clause a and b elieve that some recip e exists bywhich it will

k

b e able to p erform Clause a Clause a makes only the weakest form of claim on the

k

agents ability to act the agent G must b elieve there is some recip e R for but G may not

k

k

et have gured out how to determine that recip e Furthermore Gs b elief ab out its abilityto y

carry out the subactions of the recip e are necessarily weak b ecause G do es not yet know what the

actions are The emb edding of CBA in a b elief context represents this weak b elief

The agents consideration of contracting out has two similar comp onents the agentmust

k

have a p otential intentionto p erform a contracting action Clause b and a b elief that it can

p erform Clause b In addition the agentmust b elievethatby p erforming it will get some

PIPP G T T C

p

Unreconciled caseAgent G has not reconciled the intention to do the subaction

k

a Core case G considers doing the subact by itself

k

a G has a p otential intention to do the subact

PotIntToG T T C

k p

k

k

a G b elieves that there is a recip e which it can use to p erform the subact

BelG R CBA G R T constr C f gT

k j p

k k k

b Contracting Case G considers getting another agent G to do the subact

c k

b G has a p otential intention to do a contracting action

PotIntToG T T C

p

f

k k

b G b elieves that there is a recip e which it can use to p erform the contracting action and

bydoing it can get G to do the subact

c

BelG R CBAG R T constr C f g

j

GT D G T G T constr C f gT

c k j p

k

Figure PIP Unreconciled case

other agenttodo Clause ba

k

To remove this last kind of partiality for each action in Clause the agentmust mov e

k

the either to the core case or to the contractingout case Tomovethe to the core case

k k

the agentmust turn its p otential intention to do Clause a into a fulledged intention to

k

do this action that has an asso ciated partial individual plan and a FIP to p erform the action of

Individual on this PIP Tomovethe to the contractingout case the agentmust turn Elab orate

k

its p otential intentionto do a contracting action Clause b into a fulledged intention to do

the contracting action that has an asso ciated partial individual plan its b eliefs ab out its ability

to do the action and thereby get another agenttodo Clause b play a role in this transition

k

In addition the agentmust adopt an intentionthat a particular contractor b e able to do

k

The pro cess of transforming the p otential intentionsto into fulledged intentionsto for the

core and contracting cases is similar only the target action diers itself or we will describ e

k

only the transformation to the core case First the agentmust reconcile the PotIntTodo with

k

all other intentions b oth IntTos and IntThs it currently has If is a basiclevel action then

k

G also needs to establish that it can execute and adopt a commitmenttodosoIf is not

k k

basic level then G must select a recip e R for determining a recip e for and develop a

selectr ec k

k

full individual plan for determining a recip e for using R The agents having a full plan

k selectr ec

k

for selecting a recip e will satisfy the minimal constraints for the agenttohave a partial individual

plan P to do In addition to satisfy the minimal conditions for having an intention to do

k k

k

the agentmust form a full individual plan to elab orate using its Elab orate Individual pro cess the

partial plan P The contracting case requires additional delib eration to transform the p otential

k

intentionthat the contractor b e able to p erform into a fulledged intention this intention must

k

also b e reconciled with all other intentions the agent has

If the Elab orate Individual pro cess succeeds in these transformations it removes the PotIntTo

for from its set of p otential intentions However it may fail in several ways For example it may

k

not b e able to gure out a way to obtain a recip e for doing Alternatively the reconciliation

k

pro cess may result in the agent deciding it cannot now adopt an intention to do In either case

k

the partial individual plan might regress and b ecome more partial while the agentsearches for a

recip e for that do es not require

k

The partial individual plan might also regress if in the pro cess of reconciling intentions the

agent decides to drop an intentionto for one of the core case subactions or a contracting action In

these cases the agent will once again have a p otential intention to do the relevant subaction ie

what was a might again b ecome a

r k

The PIP denition extends previous work by treating situations in whichagents have incomplete

knowledge ab out how to do a complex action The minimal constraints on having a partial plan

to do action are such that the agent do es not initially need even a partial recip e for it just

needs some idea of howtogetarecipe By accommo dating this lower level of knowledge the

formalization is able to cover an imp ortant class of planning situations eg the one that arises

in the construction kit example that have not b een handled by previous formalizations The

denition also treats partialityinintention adoption including the state in whichanagent has not

yet decided whether to do an action or to contract it And partiality is allowed recursively in the

plans for constituent actions The analysis and formalization of what it means for agents to have

partial plans revealed several interesting new issues including determining a minimal level of

knowledge required ab out how to do an action to rule out cases of agents planning to do actions

for whichtheyhave no p ossibilityofovercoming insucientknowledge sp ecifying a minimal

wledge and commitment for an agenttointend to do an action b efore it has complete level of kno

information ab out how to p erform the action ie dening IntTo for partial plans identifying

core recip e determination and intention reconciliation pro cesses for extending a partial plan to a

more complete one ie sp ecifying Elab orate Individual and sp ecifying conditions under which

they have completed their tasks when FIP clauses hold and sp ecifying what agents need to

ascertain ab out their ability to p erform a complex action given incomplete information ab out how

to do the action to allowagents to have a plan b efore they can completely establish capabilities

The PIP denition has clauses that directly refer to the rst three issues We address the ways in

which the fourth issue is handled in the next subsection

Capabilities to Perform Actions in Individual Plans

For an agenttointend to do some action it must b elieve that it is capable of doing the action

see caveat in Section If the action is basic level the denition of IntTo requires explicitly

that the agent b elieve it can execute the intended action If the intended action is complex the

requirements on an agents b eliefs ab out its capabilities to p erform the action dep ends on whether

the agents plan is complete or partial The denitions of FIP and PIP implicitly enco de the

requisite b eliefs ab out capabilityHowever b oth to understand the kinds of agentbehavior these

plan denitions engender and to guide agent design it is useful to sp ecify this ability knowledge

separately In this section we briey describ e the constraints the plan denitions place on ability

knowledge formal denitions and theorems establishing these constraints are given in App endix A

For an agenttohave a complete individual plan satisfying FIP it must know a complete recip e

for the action to b e p erformed that is it must have determined recip es for the complete extended

recip e tree to all levels of detail for doing the action eg the full tree for the example in Figure

From the FIP denition by recursion it must intend to do all the subsidiary actions except those

covered bycontracting and for contracting it must intend to do the contracting action As a result

from the IntTo denition the agentmust b elieve that it can execute all of the basiclev el actions

in the extended recip e tree for

This level of capabilityknowledge is less strong than that CBA represents b ecause the agents

b eliefs ab out the recip es may b e in error the agentmay b elieve R is a recip e for when it is not

However the requirement is stronger than b elief in CBA ie than Bel G R CBAG

A mental state intermediate b etween CBA emb edded in Bel and CBA unemb edded is needed

Because recip es may include complex subactions to arbitrary levels it will not suce simply to

pull the quantier outside the emb edding b elief context at a single level of description

The metapredicate BCBA b elieve can bring ab out dened in App endix A Figure rep

resents the level of b elief in ability to p erform an action required for an agenttohave a complete

individual plan As is the case for FIP the recip e for R isanargument of BCBA reecting the

fact that a particular set of constituent subactions and constraints is known to the agent and not

just the existence of some recip e Only the b elief that R is a recip e for is part of the denition

of the BCBA the existential binding for R is outside the scop e of the denition BCBA app ears

recursively within its denition with the constituentacts of as arguments and the recip e R

i

i

stipulated outside any b elief context

This same level of recip e knowledge is represented implicitly in the denition of FIP through

interaction with the denition of IntToFor basiclevel actions IntTo yields BCBA Clause For

complex subactions Clause a in BCBA is just Clause of FIP if G plans to p erform the action

itself FIP Clauses a and b combine recursively with IntTo to yield BCBA Clause b for

subactions G contracts out FIP Clauses b and d similarly yield BCBA Clause b and FIP

Clause a gives BCBA Clause bb Thus as stated in Figure this level of recip e knowledge

is entailed by the FIP denition A formal pro of is given in App endix A

In contrast when an agent has a partial plan for its b eliefs ab out its capabilities may b e quite

limited b ecause its knowledge of the recip e it will use is incomplete The agentmay only b elieve

that there is some way to nd a recip e that it can use to p erform Until it knows the constituent

actions in the recip e for the agent cannot makeany determination ab out its abilities to p erform

these subactions While the lackofarecipemakes the agents knowledge in this situation weaker

than in the FIP the agents b eliefs ab out its abilitymust b e stronger than the CBA emb edded

in Bel yields In particular the agentmust b elieve that it can determine a complete recip e and

will b e able to p erform or to contract out each of the actions in the complete recip e once it is

v

determined As the agent identies pieces of the recip e it must also establish its ability to p erform

the actions in that piece or to contract them

The metapredicate WBCBA weakly b elieve can bring ab out dened in App endix A Fig

ure represents the level of b elief an agent G must have ab out its abilities to select an appropriate

recip e and p erform or contract out each of the constituent subactions in this recip e This same level

of b elief is represented implicitly in the denition of PIP as stated in Theorem T Clause of

WBCBA is established by PIP Clause the condition in Clause a of WBCBA is similar to that

of Clause a of PIP Clause b of WBCBA follows from the FIP in PIP Clause b and Theo

rem T as shown in Figure the constraints comp onent of the FIP context constrC

selectr ec

contains the constraints in Clausesbabe of WBCBA If G intends to do the subaction

i

by itself and is basic level action then Clause of IntTo Figure and Clause of WBCBA

i

tends to do a complex subaction by itself used recursively yields Clause of WBCBA If G in

i

then Theorem T applied recursively to Clause b of IntTo yields Clause of WBCBA For

subactions G contracts out Clauses a and b of PIP similarly yield WBCBA Clause a and

Clause b For the unreconciled subactions Clause a of WBCBA is established by Clause a

of PIP and Clause b is established by Clause b of PIP

SharedPlans and Intendingthat

The denitions in this section utilizing those given in the preceding sections provide a mo del of

collab orative b ehavior that has several distinguishing prop erties all of which are maintained under

conditions of partial knowledge The key prop erties of the mo del are as follows

it uses individual intentions to establish commitment of collab orators to their joint activity

it establishes an agents commitments to its collab orating partners abilities to carry out their

individual actions that contribute to the joint activity

it accounts for helpful b ehavior in the context of collab orative activity

it covers contracting actions and distinguishes contracting from collab oration

the need for agents to communicate is derivative not stipulated and follows from the general

commitment to the group activity

the meshing of subplans is ensured it is also derivative from more general constraints

The attitude of intendingthat plays a signicant role in establishing several of these prop erties

It is the basis for agents to avoid adopting intentions that conict with those that arise from the

groups plan needed for prop erties and and it engenders helpful b ehavior prop erty The

way in whichIntTh is used in SharedPlans captures the dierence b etween agents having a Shared

Plan and one agent contracting to another agent prop erty When agents haveintentionsthat

they are required to provide information ab out their progress to each other in certain circumstances

leading to communication prop erty Together with mutual b elief intentionsthat contribute to

meshing subplans prop ertyWe discuss each of these roles in Section

The b elief and intention op erators are used in dierentways in the SharedPlan denitions

Mutual b elief requires innite nestings of individual b eliefs but utilizes only a single b elief op erator

Bel In contrast to handle the intentions that arise in SharedPlans weneedtwo op erators In tTo

and IntTh but there is no need for innite em b eddings of these op erators either in themselves or

within one another However b oth op erators maybeemb edded within the mutual b elief op erator

MB

Two imp ortant prop erties of collab orating agents b eliefs and intentions are captured in the

denitions that follow First an agentonlyhasintentionsto toward acts for which itisthe

agent intentionsthat represent its resp onsibilitie s with resp ect to the actions of other agents

Second agents do not need to know complete recip es for those actions that they are not p ersonally

committed to doing Werner In the meals example Kate and Dan need to establish mutual

b elief of a recip e for making dinner namely that it will comprise Kates making the app etizer Dan

the main course and the two of them together making the dessert Only Kate needs to know the

recip e for the app etizer but Dan and Kate must havemutual b elief that Kate has such a recip e and

can carry it out The analogous case holds for Dan and a recip e for the main course In contrast

Dan and Kate need mutual b elief of the recip e to b e used for making dessert

The SharedPlan denitions stipulate only minimal constraints on what agents need to know

ab out the recip es for actions to b e done by other agents As a result it is p ossible that an agent

constructed according to the SharedPlan sp ecications will not recognize some conicts b etween its

intentionsthat its collab orators succeed and its other intentions In particular if an agent do es not

know particulars of a recip e it maynotknow ab out a conict and thus Axiom A Figure

do es not apply Resource conicts presentanobvious case of this problem If Kate do es not know

that Dans lasagna recip e calls for using mushro oms she will not detect the conict b etween an

intention to makemushro om pus using all the mushro oms currently on hand and an intention

that Dan b e able to make the lasagna

Collab orativeagents could only b e sure they could detect all conicts if either a they could

compute all the p ossible ways that other agents might do their actions and all the resources they

would use and thus all the conicts that might arise or b they continuously communicated full

information ab out their plans Possibility a not only has computational problems but would lead

to so many alternatives that avoiding conict with all of them would signicantly limit options For

every group memb er to b e told ab out the full details of the recip es b eing used by other agents and

subgroups as suggested by approach b would require an enormous amountofcommunication

Thus neither of these alternatives seems practical

Several mechanisms havebeendevelop ed for conict detection and resolution in the context of

co op eration of autonomous agents Klein Polat Shekhar and Guvenir Lesser

inter alia and for global information management using lo cal autonomous agents Huhns et al

inter alia Other research has addressed this problem in the context of task allo cation among

autonomous agents under incomplete information Mo ehlman Lesser and Buteau Each

of these approaches requires that dierent sp ecic information b e communicated when less than

the full information can b e Thus a range of options are p ossible all of which provide reasonable

though dierent supp ort for collab orative activity The SharedPlan denitions stipulate only

minimal constraints on shared knowledge of recip es they provide a framework in which designers

may implement dierent strategies dep ending on the sp ecics of the collab orative activity and the

environment We conjecture that the determination of an appropriate strategy is in part domain

dep endent for example the recip es for a domain might need to sp ecify the resources that could

b e in contention Furthermore agent design will v ary dep ending on the level of risk of failure from

unforeseen conicts that designers are willing to incur the more costly such failures are the more

designers will err on the side of enco ding additional constraints on recip es and on the elab oration

pro cesses so that agents have sucient knowledge to avoid intention conict

Denition of SharedPlan

The SharedPlan metapredicate SP representing that a group of agents GR has a collab orative plan

to p erform together some action is dened recursively in terms of full and partial SharedPlans

A ful l SharedPlan FSP is the collab orative correlate of a full individual plan and includes full

individual plans among its constituents A partial SharedPlan PSP is the collab orative correlate

of a partial individual plan A principal way in which SharedPlans and individual plans dier is that

knowledge ab out how to act ability to act and commitment to act are distributed in SharedPlans

Even when a groups plan is complete there may b e no one individual who knows the complete

recip e tree no single agent needs to b e able to p erform all the basic level actions the collab orative

action comprises and the requisite intentions to act are distributed among group memb ers The

group has a SharedPlan but no individual memb er alone has the SharedPlan

The challenge in dening SharedPlans is to provide for this distributed knowledge and commit

ment to act while ensuring that the group members have adequate knowledge ab out each others

capabilities and sucient commitment to their joint activity In particular the group analogue of

the Exec and Commit constraints in the basiclevel action comp onent of the denition of IntTo

must not only treat complex actions and partial knowledge but also accommo date the distributed

character of group activity In addition the establishment of certain mutual b eliefs plays a cen

tral co ordinating role in the SharedPlan denitions Communication among agents is essential to

establishing the requisite m utual b eliefs

As shown in Figure a group of agents GR has a SharedPlan P at time T to do at

p

time T in the context C just in case either they have a full SharedPlan for doing or

SPP GRT T C

p

The group has a full shared plan

N

R FSPP GRT T R C

p

The group has a partial shared plan and a full shared plan to complete it

P P T R

elab elab elab

a PSP P GRT T C

p

GroupP GRT T C T T R C b FSPP GR Elab orate

p p elab elab elab

elab

Figure Denition of SP SharedPlan

they have a partial SharedPlan to do and a full SharedPlan to complete that partial plan

The metapredicates SP PSP and FSP enable representation of the mental states of agents in

a collab orating group throughout the planning pro cess from inception of a partial SharedPlan

through to completion and execution of the full SharedPlan

SP plays a role for plans of groups of agents analogous to the one played byIntTo for individual

plans but there are several imp ortant dierences Group memb ers mayhave dierent reasons

for engaging in the collab orative activity of doing soC mayvary across group members

For example hunger might underlie Kates making dinner with Dan whereas a desire for so cial

interaction underlies Dans making dinner with Kate cf Bratman In addition b ecause

the b eliefs and intentions ab out the plan are distributed each of the agents in GR will haveits

own internal name for the plan P referstoanagentinternal name Thus the distributed prop erty

Group of SharedPlans yields an additional constraintonagent design To engage in an Elab orate

pro cess agents must have a means of referring to their collab orativeplanintheircommunication

ie they must b e able to form an externally useful reference to P

The most signicant dierence b etween SP and IntTohowever is that SP is a metapredicate

not a mo dal op erator There is no attitude of weintending Searle or jointintention

Levesque Cohen and Nunes As a consequence the denition of SP has one less clause

than that for IntTo Whereas the denition of IntTo separately asserts that the agentintends

to do the elab oration Clause b in Figure there is no separate clause in the SP denition

asserting SP of the Elab orate Group Although the IntToisentailed by the denition of FIP

including this clause in the denition of IntTomakes explicit the assertion of an additional agent

attitude and thus may b e useful for agentdesignTheSPislikewise entailed by the denition of

FSP In this case however there is no additional agent attitude to assert separately b ecause SP

is a metapredicate not a mo dal op erator Furthermore there are no axioms constraining the SP

metapredicate that are analogous to those for the mo dal op erators IntToandIntTh

The intentionbased constraints on agent design that are imp osed byhaving SharedPlans are

derived from those entailed by the individual intentions that are part of the agents SharedPlans

including any subsidiary individual plans Both FSP and PSP entail individual intentions to do

actions including actions of elab orating or extending partial plans As others have argued Searle

Bratman Cohen and Levesque individual intentions to act and mutual b elief of

suchintentions are not sucient for representing the mental state of the participants in collab ora

tive activities To satisfy the additional requirements of collab oration the SharedPlan denitions

include various IntTh clauses

The denitions of FSP and PSP like those for individual plan have four comp onentsbasic

assumptions ab out recip e knowledge the core case the contracting case and for partial plans the

unreconciled intentions case However for SharedPlans the core contracting and unreconciled cases



sub divide dep ending on whether the subaction to b e done is singleagentormultiagent Our

discussion of the plan denitions will fo cus on dierences b etween SharedPlans and their individual

counterparts Again gures in this section provide English glosses of the ma jor elements of the

plan denitions while the full formal denitions are provided in App endix B

Full SharedPlans

The metapredicate FSP is used to represent the situation in which a group of agents has completely

determined the recip e by which they are going to do some group activity and memb ers of the group

have adopted intentionsto toward all of the basiclevel actions in the recip e as well as intentions

that toward the actions of the group and its other members Most typically a group of agents will

not havesuch a complete plan until after they have done some of the actions in the recip e Groups

like the individual agents they comprise typically have only partial plans Analogously to FIP the

Group pro cess has completed its FSP denition sp ecies the conditions under which the Elab orate

task Dierences b etween FSP and PSP sp ecify the information agents need to acquire individuall y

and mutually and the intentions they need to adopt to have a complete collab orative plan

The denition of the metapredicate FSP sp ecies when the group GR has a complete plan

P at time T to do action at time T using recip e R in context C Figure gives the

p

ma jor constituents of the denition of the metapredicate FSP the full formal denition app ears

in App endix B The plan denition uses P to identify the plan

Twokey characteristics of collab oration derive from the IntTh in Clause agents avoiding

the adoption of intentions that conict with the joint activity and agents adopting intentions to

communicate ab out the plan and its execution The intentionthat in Clause explicitly represents



each group memb ers commitment to the groups p erformance of Through Axiom A this

IntTh directly contributes to Some of the ways in which it leads to communication actions

are describ ed in Section

When agents have a complete collab orative plan to do an action they must have a complete

recip e for that action However the recip e knowledge is typically distributed Clause ensures

that the agents agree on the recip e they will use to p erform The distributed knowledge ab out

how to p erform the constituent actions is handled in the core and contracting cases

i

For each constituent action in the core case the FSP denition requires that some agentor

i

subgroup is committed to doing and is able to carry it out and that the full group has knowledge

i

of the agents or subgroups commitment and capability In addition to ensure that subplans are

compatible or mesh in Bratmans terminology Bratman and provide suciently for helpful

b ehavior the denition requires that the full group form a commitment to the ability of the agent

or subgroup to carry out

i

The singleagent p ortion of the core case of FSP shown in Figure and the multiagent p or

tion given in Figure address these constraints in analogous ways The two principal distinctions

between these p ortions of FSP and the core case of FIP are the representation of the commit

mentofevery memb er of the group to the ability ofanagent or subgroup to carry out a constituent

action Clauses a and b and the distinction b etween what the agents who are do

ing an action must know ab out the recip e and their ability to act Clauses aa and b and



The recip e case applies to the action which is the ob jective of a SharedPlan and hence is necessarily multiagent



Because agents are assumed actually to hold anyintentionsthat that they b elieve they hold Axiom A in

Figure this clause establishes not only mutual b elief in the intention but also that the agents hold the intention

FSPP GRT T R C

p

The group GR has mutual b elief that all memb ers of the group are committed to the success of the

groups doing

MBGR G GRIntThG DoGRT constrC T T C T

j j p p

The group GR has mutual b elief of the acts that they need to p erform to accomplish and the

i

constraints on them

j

R f gMB GRR RecipesT

i j p

For each either or

i

Core case

a Subaction is a singleagent action Some memb er of the group will do the subaction

i

is a multiagent action Some subgroup will do the subaction b Subaction

i

Contracting case

a Subaction is a singleagent action The group will get another agent G to do the act

i c

b Subaction is a multiagent action The group will get another group of agents to do the

i

subaction

Figure English description of the FSP full SharedPlan denition

the information that other group memb ers require Clauses ab and b represented by the

dierence in quantier scoping b etween the relevant clause pairs Wepresent the singleagentcase

rst contrasting it where relevant with individual plans and giving rationale for these distinctions

We then discuss the additional issues raised by the multiagent case

Clauses a and a sp ecify the commitments group members must havetoward the p erfor

mance of and the mutual b eliefs they must have of these commitments Clause aa establishes

i

G s intention to do and Clause ab requires group mutual b elief that G has this intention

k i k

Clause a represents commitment on the part of all other agents in the group to ensuring that

G is able to p erform That each G actually has the appropriate intentionthat can b e inferred

k i j

from Axiom A in Figure Because G has an inten tionto toward there is no need for

k i

G to haveanintentionthat to provide for avoiding conicting intentions other entailments of

k

intendingthat eg helpful b ehavior that are not also entailments of intendingto do not apply

for G

k

Although the preceding clauses have some analogue in the denition of FIP Clause a do es

not This clause establishes the intentions IntThs needed to mesh G s individual plan for

k

doing with the plans for other subsidiary actions Together with the axioms to avoid conicting

i

intentions Figure it ensures that agents will not knowingly adopt subplans that conict In

addition as discussed in the next subsection the IntTh in Clause a is the source of other group

memb ers helping G to do which again would b e much more dicult to achieve with Clause

k i

and b eliefs alone

For example Clause a ensures that Kate will not adopt an intention to use the only

lasagna pan for making her app etizer b ecause that would conict with her intention that Dan b e

able to make a lasagna main course The IntTh of Clause is not sucient in itself to ensure

meshing subplans Kates intention that she and Dan make dinner will not by itself prevent her

from using the lasagna pan she mightbelieve there is an alternative recip e for making dinner eg

FSPP GRT T R C

p

Core case

a Subaction is a singleagent action Amemb er of the group G will do the subaction

i k

a G s intentions and the groups related b eliefs

k

aa G intends to do

k i

IntToG T T C

k i p

i

i

ab GR mutually b elieve that the agent G intends to do the act

k

MBGR IntToG T T C T

k i p p

i

i

a The subaction is a basiclevel action

i

aa The group mutually b elievethatG is able to p erform the subaction

k

MBGR CBAG R T constr C f gT

k i Empty b j p

i

a The subaction is not a basic level action

i

aa There is a recip e R for subaction such that G has a full individual plan for the

i k

i

subact that uses the recip e R

i

R P FIPP G T T R C

k i p

i i i i i

i

ab The group mutually b elieve that there is a recip e R such that

i

MBGR R P

beta

i i

ab G is able to p erform the subaction using the recip e R

k

i

CBA G R T constrC f g

k i j

i i

ab G has a full individual plan to do the subaction that uses the recip e R

k

i

FIP P G T T R C T

k i p p

i i i

i

a GR mutually b elievethatallmemb ers of the group are committed to agent G s b eing

k

able to do subaction

i

CBAG R T MBGR G GRG G IntThG R

k i j j k j

i i i

constr C f gT T C T

j p p

cba

i

i

Figure FSP Core case singleagentaction

Dan could make spaghetti instead that would not conict with her intention to use the lasagna

pan Although Kates b elief that Dan intends to make lasagna as part of their plan to make dinner

together with Clause could b e used to achieve the same constraint as Clause a suchan

approachwould necessitate more complex mechanisms for reconciling intentions

Clause a sp ecies the b eliefs and intentions that G and the other group memb ers must

k

haveif is a complex action Clause aa sp ecies that G have a complete individual plan

i k

to do Clause ab states that the other group memb ers must mutually b elieve that there

i

is some recip e which G can use to p erform and that G has a complete plan to do The

k i k i

tial quantier in Clauses aa and ab accurately capture an dierent scopings of the existen

imp ortant distinction Whereas G must know the recip e it will use in its FIP to p erform the

k i

other memb ers of the group do not need to know this recip e Rather the other memb ers of the

group need only to mutually b elieve that there is some recip e that G can use

k

In addition to having shared knowledge ab out G s intentions to p erform the group must also

k i

have shared knowledge ab out G s ability That agent G itself b elieves it will b e able to p erform

k k

is established directly bytheIntTo in Clause aa if is basic level and as describ ed in

i i

Section from the FIP in Clause aa and Theorem T if it is a complex action Other

memb ers of the group must hold twomutual b eliefs rst they must mutually b elieve that G is

k

able to p erform second they must mutually b elieve that G has a complete recip e for and

i k i

b elieves it is able to p erform according to that recip e Neither of these b eliefs entails the other

i

so they must b e indep endently established

The meals example may b e used to illustrate these twotyp es of b elief and their dierence

First Dan must b elieve that there is some recip e Kate can use to make the app etizer ie he must

b elieve that Kate will b e able to make the app etizer Second he must b elieve thatKateknows a

particular recip e and b elieves she can make the app etizer using that recip e ie he must b elieve

that Kate b elieves she can make the app etizer Dan might hold the rst b elief and not the second

he might think Kate can make the app etizer but also that she do es not herself b elieve she can

Alternatively he mightbelieve she thinks herself capable and yet himself not b elieve she has a

recip e that will work For Kate and Dan to have a complete plan Dan must hold b oth b eliefs

For basiclevel Clause a establishes the groups b eliefs in G s ability Their mutual b elief

i k

that G b elieves it is capable is entailed by their mutual b elief in its intentionto Clause ab

k

and the denition of IntToFor complex Clause ab establishes that the group b elieves G

i k

is able to do Their mutual b elief that G has a complete recip e for and b elieves it is capable

i k i

of doing the actions in the recip e ie that BCBA holds follows from their mutual b elief that G

k

has a complete plan Clause ab and Theorem T

The dierence in scoping b etween Clauses aa and ab is imp ortant here as well G

k

must know the recip e and b elieve it is able to p erform or contract out all the subactions entailed in

doing In contrast the other memb ers of the group can only haveaweak form of b elief in G s

i k

ability to p erform Theemb edding of the CBA in Clause ab in MB accurately represents

i

this weaker b elief it reects the fact that other memb ers of the group may not know the recip e

G is using To establish even this weak form of b elief however agents must communicate enough

k

ab out their individual or subgroup plans to convince other agents of their abilities to carry out

constituent actions

As discussed in the intro duction to this section this denition provides only minimal constraints

on shared knowledge of the recip es for constituent acts Agents can only avoid conicting intentions

form subplans that mesh and assist their collab orators to the extent they have knowledge ab out

recip es and the resources they require By stipulating minimal constraints the denitions provide a

framework in which designers can examine tradeos stronger constraints b oth on recip e knowledge

and on communication demands can b e added where warranted

The multiagent comp onent of the core case Figure is signicantly missing two elements

of the singleagent comp onent First there are no clauses representing an intention to do the

subaction corresp onding to Clause a Inten tions are individual attitudes is a multiagent

i i

action to b e done by a group The need for the memb ers of the group to haveintentions to do

the singleagent subactions entailed in the recip e selected for or its children subactions will

i

b e established in the recursively emb edded individual plans for these subactions Second b ecause

is a multiagent action it is necessarily a complex action thus there is no clause for basiclevel

i

actions corresp onding to Clause a

Clauses b and b have the same dierence in quantier scoping as Clauses aa

and ab Again the full group needs to havemutual b elief that there is some recip e that

the subgroup GR plans to use for doing whereas the memb ers of the subgroup must know the

k i

recip e This dierence in recip e knowledge is also reected in dierent ability constraints on the

p erforming subgroup and the rest of the group As in the singleagent case b ecause the members

of the group who are not in the subgroup GR may not know the recip e the subgroup is using

k

they can only haveaweak form of b elief in the abilities of the subgroup to p erform the action

Clause ba emb eds CBAG in MB to represent this level of b elief in ability The constraints

on memb ers of the subgroup GR are stronger they must know the recip e for and b elieve that

k i

together they will b e able to p erform or contract out each of the actions in the recip e Just as in the

FSPP GRT T R C

p

Core case

b Multiagent action A subgroup GR will p erform the subaction

k i

b There is a recip e R such that the subgroup has a full SharedPlan to do the subaction

i

using this recip e

R P FSPP GR T T R C

k i p

i i i i i

i

b The group GR mutually b elieve that there is a recip e R suchthat

i

MBGR R

i

ba the subgroup is able to p erform the subaction using the recip e R

i

CBAGGR R T constr C f g

k i j

i i

bb the subgroup has a full SharedPlan to do the subaction using this recip e

FSPP GR T T R C T

k i p p

i i i

i

b The full group GR mutually b elieve that all memb ers in the group are committed to the

subgroup GR b eing able to do the subaction

k

MBGR G GR n GR IntThG R CBAGGR R T

j k j k i

i i i

constr C f gT T C T

j p p

cbag

i

i

Figure FSP Core case multiagent action

singleagent case the full group must also b elieve that the subgroup GR knows a complete recip e

k

for and b elieves it is capable of doing the actions in the recip e As describ ed in Section all

i

of the requisite ability b eliefs are entailed by the FSP denition

As with singleagent actions the full group must b e committed to the subgroups abilityto

p erform Clause b in Figure is identical to Clause a in Figure for singleagent

i

actions with the exception of not including the subgroup GR rather than just the individual

k

agent G in the memb ers who hold the IntTh The subgroup is excluded from this IntTh to avoid

k

unnecessary redundancy the commitments and intentions related to of memb ers of the subgroup

i

are established through the FSP in clause b Meshing subplans and helpful b ehavior derive

from this intentionthat

Clauses a and b establish a signicant distinction b etween the full SharedPlans of

two agents and the situation in which one of these agents contracts to another In a full SharedPlan

the group GR comprises agents all of whom are committed to the p erformance by the group of

through IntTos and IntThs to the subactions in the recip e they use for doing and

i

through the context parameter to s b eing done as part of doing Incontrast when in

i

doing an action one agent Gcontracts to another G the doing of some subsidiary action

c

i

but G do es not necessarily have G has an intentionthat toward G s successful p erformance of

c c

i

anyintentionsthat toward Gs success in doing

The contracting case for SharedPlans divides into four sub cases These vary along two dimen

sions the subaction may b e either singleagentormultiagent and the contracting action

i

may b e either singleagentormultiagent requiring resp ectively that an individual or a subgroup

do the contracting As a result the full denition of this case is quite long and Figures and

contain only the highlevel detail However this case can b e formalized simply bycombining ele

ments of contracting from the FIP with elements from the core case of FSP The only additional

Group pro cess The machinery needed to handle contracting comes in extending the Elab orate

group needs mechanisms for deciding on a contractor We note though that the determination of

group memb ers who will p erform the contracting action follows the same pro cess as identication

FSPP GRT T R C

p

Contracting Case FSPCGR T T C f g

i p j

i

a singleagent subaction By doing the group GR will get another agent G to do the subaction

c

i

a The group GR mutually b elieve that all memb ers of the group are committed to G s

c

ability to p erform

i

MBGR G GRIntThG R

j j

i

T CBAG R T constr C f gT T C

p c i j p

cba

i i i

i

aa The contracting act is singleagent there is a memb er of the group G such that

k

aa The group mutually b elieve that bydoingG can get G to do

k c i

MB GR GTDG T G T constrc f gT

k c i j p

i

aa G intends to do the contracting action

k

IntToG T T C

k p

i

aa The group mutually b elieve that G intends to do the contracting action

k

MB GR IntToG T T C T

k p p

i

aa The group has the requisite mutual b eliefs ab out G s abilities and plans to do

k

and IntThs G succeed G has the requisite b eliefs abilities and plans

k k

MP GRG T T C

k p

i

ab The contracting act is a multiagent action there is a subgroup GR of the group

k

suchthat

ab The group mutually b elievethatbydoing subgroup GR can get G to do

k c

i

MB GR GTDGR T G T constr C f gT

k c i j p

i

ab The group has the requisite mutual b eliefs ab out GR s abilities and plans to

k

do and IntThs GR succeed GR has the requisite abilities and plans

k k

SGPGR GR T T C

k p

i

Figure Contracting in a FSP singleagent subactions

of agents for subactions in the core case

To simplify the presentation of the contracting case we identify two subsidiary metapredicates

MP MemberPerform and SGP SubgroupPerform MP is directly analogous to the singleagent

p ortion of the FSP ie to Clausesa through a in Figure with the contracting action

replacing the subaction and other parameters of the op erators adjusted accordingly Similarly

i

SGP is directly analogous to the multiagent p ortion of the FSP ie to Clausesb through b

in Figure with the contracting action replacing the subaction and other parameters of the

i



op erators adjusted accordingly These metapredicates are expanded in Figure in App endix B

Intentionsthat in SharedPlans

It is quite apparent from the FSP denition that IntTh plays a central co ordinating role in the

formalization of collab orative plans Agents intentionsthat toward the capabilities of other agents

and toward the successful p erformance of the actions of groups of which they are a part are key to

achieving the collab oration needed for their joint actions to succeed The IntTh of Clause of

the FSP denition is the source b oth of avoiding the adoption of intentions that conict with the



To simplify the full denitions given in Figure in the App endix the MP and SGP metapredicates are used

there as well

FSPP GRT T R C

p

Contracting Case FSPCGR T T C f g

i p j

i

b Multiagent subaction By doing the group GR will get another group of agents GR to do

c

the subaction

i

b The group GR mutually b elieve that all memb ers of the group are committed to GR s

c

ability to p erform

i

MBGR G GRIntThG R

j j

i

T CBAGGR R T constr C f gT T C

p c i j p

cbag

i i

i

ba The contracting act is singleagent there is a memb er of the group G such that

k

ba The group mutually b elievethatby doing G can get GR to do

k c i

MBGR GTDG T GR T constrC f gT

k c i j p

i

ba G intends to do the contracting action

k

IntToG T T C T

k p p

i

ba The group mutually b elievethatG intends to do the the contracting action

k

MBGR IntToG T T C T

k p p

i

ba The group has the requisite mutual b eliefs ab out G s abilities and plans to do

k

and IntThs G succeed G has the requisite b eliefs abilities and plans

k k

MPGRG T T C

k p

i

bb The contracting act is a multiagent action there is a subgroup GR of the group such

k

that

bb The group mutually b elieve that bydoing subgroup GR can get G to do

k c i

MBGR GTDGR T GR T constr C f gT

k c i j p

i

bb The group has the requisite mutual b eliefs ab out GR s abilities and plans to do

k

and IntThs GR succeed GR has the requisite b eliefs abilities and plans

k k

SGPG GR T T C

k p

i

Figure Contracting in a FSP multiagent subactions

joint activity and of communication actions Intentionsthat required in the core and contracting

cases ensure that the subsidiary plans individual and group for doing the subsidiary actions

i

in R mesh and lead agents to form intentions to help each other in the p erformance of the group

action

Alternative approaches to mo deling collab oration Levesque Cohen and Nunes Jennings

Jennings Sonenb erg et al represent the Clause asp ect of commitmentto

the joint activity using some kind of jointintention op erator These jointintention op erators do



not treat meshing subplans the approaches neither provide in general for this constraint nor

accommo date helpful b ehavior In contrast we are able to use a single mo dal op erator IntTh to

provide all three prop erties of collab orative activity

Several axioms are needed to supp ort the roles of IntTh in ensuring that agents avoid conict

assist each other and provide status information when necessary The axioms to avoid conicting

intentions in Figure constrain an agents adoption of intentions b oth intentionsto and intentions

that so that it do es not simultaneously hold conicting intentions Figures and provide

vior We describ e them briey here but a full axioms that represent the adoption of helpful b eha

formalization of IntTh must b e the sub ject of another pap er



Sonenb erg et al op cit achieve meshing subplans but only do so when agents have complete plans The

meshing is assured by using preestablished recip es As will b ecome apparent in the next section wecover partial

plans and partial recip e knowledge

A Axiom

G IntTh some prop which G does not believe is true

T

IntThG pr op T T C Bel G pr op T

i pr op pr op i

G believes it can do something to help

Bel G R DoG T constr C pr op

pr op

CBAG T R constr C T

pr op i

G wil l consider doing

PotIntToG T T C

i

pr op

A Axiom

G IntTh some prop which G does not believe is true

T

V V

IntThG pr op T T C Bel G pr op T

i p pr op i

G believes it can do something that wil l help indirectly by al lowing another agent to help directly

BelG DoG T constrC

pr op

G R T singleagent

CBAG R T constr C

pr op

DoG T constr C pr op

pr op

multiagent T GR R

constr C T CBAGGR R

pr op

V

constrC pr opT DoGR T

pr op i

BelG R CBA G T R constrC T

pr op i

G wil l consider doing

PotIntToG T T C

i

pr op

Figure Axioms for intendingthat

tionthat toward some prop osition currently Axiom A applies when an agent has an inten

do es not b elieve this prop osition holds and furthermore b elieves it is able to do some act that

will bring ab out the prop ositions holding Thus the axiom will only apply if the time of the

prop osition T is in the future The axiom states that under these conditions the agent will

pr op

consider doing The agent adopts a p otential intention to do that will cause delib eration ab out

adopting an intention to do it and barring conicts lead to this b ecoming a fulledged intention

For example if Kate b elieves Dan may not be able to make the main course and furthermore

b elieves that she can take some action to remove a p ossible roadblo ck to his b eing able to do so

eg pickuphischild at child care then Kate will adopt a p otential intention to do that action

However if Kate b elieves that Dan is capable of making the main course in the current situation

then Axiom A would not apply

Axiom A provides for more indirect helpful b ehavior It states that if an agent has an

intentionthat toward some prop osition that it currently do es not b elieve holds and the agent

b elieves it is able to do some act that will bring ab out a condition enabling another agent or

group of agentstodoanaction that will bring ab out the prop ositions holding then the agent

will consider doing For instance if Kate b elieves if she calls Jon he will pick up Dans child

and thus enable Dan to make the main course then she will adopt a p otential intention to do so

The p otential intention to do will cause delib eration ab out adopting an intention to do it and



barring conicts lead to this b ecoming a fulledged intention



The conjunct and assuming sucient resources b elongs in this phrase however as mentioned in Section

A Axiom

G T T

i

G is committedtoG s success in doing as part of G s participation in a SharedPlan for

singleagent

T R G

multiagent

GR

G GR SP GRT T C

i

singleagent G GR IntThG R CBAG R T constr C T T C

i

cba

multiagent G GR IntThG R CBAGG R T constrC T T C

i

cba

It is cheaper to G to help G in doing by doing

costG DoGRT constr C T C R

DoG T constr C DoG T constr C

cba

cost G DoGRT constrC T C R

DoG T constr C DoG T constrC

cba

econ costG DoG T constrC T C R

cba cba

G believes it can perform

Bel G R CBAG T constr C T

i

cba

G wil l consider doing

PotIntToG T T C

i

cba cba

Figure Helpfulb ehavior axiom for intendingthat

Axiom A provides a basis for helpful b ehavior in the SharedPlan context ie for helping a

collab orative partner It uses two auxiliary functions cost and econ The

function cost computes the costs to an agent of the p erformance of an action

costG DoG T constrC T C R refers to G s cost given the constraints of

e p e

G doing at time T in the context C using recip e R G may b e either an individual or a

p p

group if an individual it maybe G or some other agent The function econ provides a means

e

of relativizing cost tradeos it sp ecies the prop ortionate amountofsavings required for helpful

b ehavior to b e worth the eort required

The initial clauses in Axiom A establish a collab orativecontext agent G is a member of



a group GR that has a SharedPlan to p erform the action G is either a memberofGRora

subgroup of the group GR G has an intentionthat G will b e able to p erform CBA or CBAG



dep ending on whether G is a single agent or a subgroup the action where is b eing done

as part of GRs plan to do In this context the axiom asserts that G will adopt a p otential





intention to do an action if G believes that its own overall cost of the group GRs doing is



do es not help less when it do es to assist G s p erformance of than it is when G do es and G



by doing In the meals example Axiom A would account for whyDanwould oer to pickup

the ingredients Kate needs for the mushro om pus It also would accountforwhy while chopping

onions for the sauce for the lasagna Dan would chop an extra one for Kate to use in making the

mushro om pus

The consequent in Axiom A is a p otential intention rather than a fulledged intention

b ecause the cost computation is lo cal it do es not involve consideration of comp eting intentions

The axiom reects an intuition that it is useful to delay the pro cesses involved in forming a full

the sp ecication of the pro cesses for reasoning ab out costs and resource b ounds is b eyond the scop e of this pap er



This axiom is more straightforward than though it presumes a less charitable G than an alternative axiom in

which the cost to other agents and not just to G would b e lower

PSP P GRT T C

p

The group GR has mutual b elief that all memb ers of the group are committed to the success of the group

doing

MBGR G GRIntThG DoGRT constrC T T C T

j j p p

The group GR mutually b elieve that there is a recip e for but their recip e for doing may b e partial

ie they may only haveidentied some of the subactions that need to b e p erformed They havea

FSP to complete their partial recip e

For each subaction in the partial recip e one of through holds

i

Core case

a Singleagent subaction A memb er of the group G intends to do the subaction but mayhave

k

only a partial plan for doing it

b Multiagent subaction A subgroup GR has a shared plan SP to do the subaction but this

k

plan may b e only partial

Contracting case

a Singleagent subaction The group has decided to sub contract an outside agent G to do the

c

subaction but mayhave only a partial plan PIP or PSP for doing the contracting action

b Multiagent subaction The group has decided to sub contract an outside group GR to do the

c

subaction but mayhave only a partial plan PIP or PSP for doing the contracting action

Unreconciled case GR has not delib erated ab out the subaction no decision has b een made ab out

which agents will do it

Figure English description of the PSP partial SharedPlan denition

edged intention for a helpful action until after an agent has determined that the p erformance of

the action would b e b enecial

Subgroups can also provide helpful b ehavior ie the helping action mightbeamultiagent

action for which a subgroup of GR forms a SharedPlan In this case the cost evaluation is dierent

Furthermore the formation of the helping subgroup and its adoption of a subsidiary SharedPlan

to do are more complicated

Helpful b ehavior is also appropriate in contracting situations For instance in the meals exam

ple Dan might oer to pick up the no o dle ingredients for Tony if hes contracted to Tony to make

the no o dles for the lasagna A straightforward analogue of Axiom A that captures this case is

given in App endix B A separate axiom is needed b ecause the cost evaluation diers this dierence

arises b ecause in contracting the agentevaluating the cost of p ossible helpful b ehavior is by itself

the agent doing Although the underlying intentional motivations also dier an IntTo rather

than a SP this dierence alone could b e captured with a simple disjunction in Axiom A

Partial SharedPlans

Partial SharedPlans like their counterpart partial individual plans dier from full ones in four

ways as identied in Clauses through of the outline of PSP in Figure In particular the

agents mayhav e only a partial recip e for doing the action they mayhave only partial individual

plans or partial SharedPlans for doing some of the subsidiary actions in the recip e they may

have only partial individual plans or partial SharedPlans for doing some of the contracting actions

and there may b e some subactions ab out which the group has not delib erated and for which

there is as yet no agent individual or subgroup selected to p erform the subaction Thus as in

the case of PIP the formalization of PSP distinguishes those actions ab out which the group has

r

delib erated and for which it has chosen an agent Clause the core case from those actions

for whichithasnotyet decided on an agent Clause the unreconciled case Because

k

the contracting case Clause for PSP diers from that for FSP in the same ways that the core

cases do we do not discuss it further and in App endix B we include only the abridged version

with English glosses of the contracting case

By handling b oth complex typ es of actions and partiality the formalization of partial Shared

Plans constitutes an advance over previous approaches The complexities intro duced by doing so

are most evidentintwo places the treatment of partialityofknowledge ab out the recip e to

b e used Clause and the corresp onding Select Rec GR pro cess the handling of unrecon

Group pro cess Partiality in the core case can b e ciled actions and the corresp onding Elab orate

treated by recursion on either individual plans singleagent actions or SharedPlans multiagent

actions We treat this case briey rst and then discuss the recip e and unreconciled cases In

each instance we lo ok rst at the constraints on mental state imp osed by the denition and then

at the constraints on the various pro cesses involved in completing the partial plans

Figures and give the ma jor constituents of the core case of the PSP for singleagentand

multiagent subactions Two constraints are placed on the design of collab orating agents First in

elab orating their individual and group plans for subactions they must develop plans that mesh so

that the intentionsthat in Clauses a and b hold Thus agents elab oration pro cesses must

takeinto account the constraints imp osed by the agents intentionsthat other agents are able to

do their parts The constraints that are imp osed are contained in the constraints parameters of

the IntTo IntTh and SP clauses in the PSP denition Second collab orators must communicate

sucient information for the mutual b eliefs of intentions Clause ab plans Clause b and

ability Clauses a and b to b e established As in the case of individual plans PSP imp oses

weaker constraints on agents b eliefs in their own capabilities to p erform the constituent actions

either individuall y or in subgroups than do es FSP Section describ es how these constraints

r

are met by PSP

Partiality in the recip e as sp ecied in Figure leads to the need for the group to agree on

away to nd construct or complete a recip e for the action As we discussed in Section the

group action Select Rec GR like the individual action Select Rec takes a partial recip e f g

i j

for the action and extends this partial recip e to a complete one f g Although this pro cess

v e

is analogous to Select Rec it leads to dierent kinds of intentions b eing considered by the agents

Rec generates Select Rec GR in the group In particular in place of the PotIntTos that Select

generates the PotIntThs in Clause of PSP for all the group memb ers Select Rec GR is more

complex than Select Rec for several reasons First any Select Rec GR pro cess must include a way

for the group to reach agreement on the recip e Because we allowvery general Select Rec GR

actions some may include ways for the group to reach consensus on the recip e for getting a recip e

as well as on the recip e itself Second Select Rec GR pro cesses will often entail individual agents

Rec pro cesses b ecause partial recip es of dierent group memb ers may invoking their own Select

be combined for a complete recip e agents need ways to determine when to stop with a partial



solution

The unreconciled case of the PSP is given in Figure The denition allows for either to

k



We note that there is no clause in this part of the PSP denition corresp onding to the IntTo in Clause b of

the PIP denition The formalization do es not require any group intention that the group has a FSP for selecting

an appropriate recip e suces to represent the necessary mentalstate conditions The commitment represented by

the IntTo of the individ ual case is satised by the intendingthat in Clause of the FSP

PSP P GRT T C

p

The group GR mutually b elieve that there is a recip e for

MBGR R f gR R RecipesT

i j p

a GR has only a partial recip e

MB GR R f g R R Recipes T

i j p

b There is a recip e R for nding the full appropriate recip e for such that the group GR has a

selectr ecg

Full SharedPlan for nding the recip e for using the recip e R

selectr ecg

Rec GRGRf gT T T FSPP GR Select

i j selectr ecg p selectr ecg selectr ecg

R C

selectr ecg

selectr ecg

where every subaction in the selected recip e R is one that GR mutually b elieves it can either p erform or

contract

constr C

selectr ec

R f g

v e

GR mutually b elievethatR is an extension of f g

i j

MBGRR Recipes f gR T

i j selectr ecg

GR mutually b elieve that for all the subactions in the recip e for it nds the following holds

R MB GR

v

Singleagent subaction there is an agent G in the group that can bring ab out the act

v

G GRR CBA G T R constrC f g

v e

v v v v v

Multiagent subaction there is a subgroup that can bring ab out the subaction

GR GRR CBAGGR T R constrC f g

v e

v v v v v

Contracting case the group can contract the subaction to another agent or a group of agents

CCGGR T constrC f g

v e

v

Figure PSP Finding a recip e

PSP P GRT T C

p

Core case

a Singleagent subaction A memb er of the group G will do the subaction but may not have

k

a full plan for it

a G s intention and related b eliefs

k

aa G intends to do

k r

IntToG T T C

k r p

r

r

ab GR mutually b elieve that the agent G intends to do the act

k

MBGR IntToG T T C T

k r p p

r

r

a GR mutually b elieve that G can bring ab out the action

k

MBGR R CBA G R T constr C f gT

k r j p

r r r

a The group mutually b elieve that all of its memb ers are committed to G s success

k

MBGR G GRG G IntThG R

j j k j

r

CBA G R T constrC f gT T C T

k r j p p

cba

r r r

r

Figure PSP Core Case singleagentact

b e done directly by group memb ers or to b e contracted out For each unreconciled action to b e

k

done by a group memb er the PSP denition requires that the memb ers of the group GR mutually

PSP P GRT T C

p

Core case

b Multiagent action Subgroup GR will do the subaction but they maynothave a FSP for

k

it

b The subgroup has SharedPlan for the subaction

SPP GR T T C

k r p

r r

r

b GR mutually b elieve that the subgroup has a SharedPlan to do the subaction

MBGR SPP GR T T C T

k r p p

r r

r

b The group GR mutually b elieve that the subgroup can bring ab out the subaction

T MBGR R CBAGGR R T constr C f g

p k r j

r r r

b The group mutually b elieve that all of its memb ers are committed to GR s success

k

MBGR G fGR n GR gIntThG R

j k j

r

CBAGGR R T constrC f gT T C T

k r j p p

cbag

r r r

r

Figure PSP Core Case multiagentact

b elieve some agent singleagent actions or subgroup multiagent actions is capable of doing the

action In addition all memb ers of GR must p otentially intendthat there b e an individual or

subgroup to p erform the action Clauses ab and ab engender this second constraint from

Axiom A and the denition of MB each agentmust actually have the p otential intentionsthat

emb edded in these clauses

The notable feature of the treatment of unreconciled actions that are con tracted out is that

k

the denitions allow for participants to consider b oth individual and subgroup contracting That is

regardless of whether is singleagentormultiagent b oth singleagent and multiagent contract

k

ing actions are p ossible In addition to stipulating mutual b elief that the group can contract out

k

Clause b the denition requires that all memb ers of the group adopt p otential intentionsthat

there b e a contracting action and a contractor G individual or group such that some member or

c

subgroup p erforms and this p erformance of will suce to get G to p erform Clause bb

c k

The dierences b etween the intentions and b eliefs ab out capability required in the unreconciled

case Clause and those in the core Clause and contracting Clause cases yield additional

requirements on the Elab orate Group pro cess Tomove constituent actions from this case to the

core case the Elab orate Group pro cess must provide for the agents to reach agreement on which

agents will p erform the action to adopt appropriate intentions to communicate sucient

information that the requisite mutual b eliefs ab out agents abilities and intentions to do actions

are established

The unreconciled case of the PSP is thus more complex than that of the PIP for several reasons

First group decision making pro cesses are required to determine which individuals or subgroups

will do each Second if the action is multiagent after the subgroup has b een identied its

k

memb ers must form a partial plan to do Third agents must communicate sucient information

k

to the group to establish the mutual b eliefs required in the core case Finallyagents reconciliation

pro cesses must b e able to handle a greater varietyofintentions and to weigh tradeos among

intentions that derive from group activities and intentions that stem solely from individual plans

The selection of an agent or subgroup is driven by the p otential intentionthat there exist some

agent or subgroup who do es the action This p otential intention in Clauses ab and ab re

sp ectively must rst b e reconciled and turned into a fulledged intentionthat The intentionthat

will then lead to some agent adopting an intentionto do or some subgroup forming a SharedPlan

PSP P GRT T C

p

Unreconciled case GR hasnt delib erated on the subaction

a GR considers that one of its memb ers or a subgroup will do the subaction

a singleagent subaction

aa The group GR mutually b elieve that there is a memb er of the group G that can

k

p erform the action

MBGR G GRR CBA G R T constr C f gT

k k k j p

k k k

ab The group GR mutually b elieve that all its memb ers are considering b eing committed

to the p erformance of the subaction bythatagent

MBGR G GRPotIntThG G GRT

j j k

k

constrC f gT T C T DoG T

j p p k k

do

k k

k

a Multiagent subaction

aa The group GR mutually b elieve that there is a subgroup GR that can p erform the

k

action

MBGR GR GRR CBAGGR R T constrC f gT

k k k j p

k k k

ab The group GR mutually b elieve that all of its memb ers are considering b eing com

mitted to the p erformance of the subaction by a subgroup

MBGR G GRPotIntThG GR GRT

j j k

k

DoGR T constr C f gT T C T

k k j p p

do

k k

k

b Contracting Case GR considers getting another agent or a subgroup G to do the subact

c k

b The group GR mutually b elieve that they can contract the subaction

k

MBGR T CCGGR T constr C f gT

k j p

k k

b The group GR mutually b elieve that all its memb ers are considering b eing committed to

the p erformance of a contracting action byamemb er or a subgroup G and that bydoing

k

G can get a contractor or a group of contractors to do the subact

k k

G GRPotIntThG T G G MBGR

j j c k

singleagent G GR multiagent G GR

k k

DoG T constrC f g

k j

GTDG T G T constrC f gT T C T

k c k j p p

cont

k k

k

Figure PSP Unreconciled case

for and the remainder of the full group forming an intentionthat they will b e able to do the

k

action So long as a group memb er can take some action that will lead to some agent or subgroup

forming an intentionto do or SharedPlan for doing Axioms A and A ensure that this

k

action will b e considered That is once an agent forms the intentionthat someone do itmust

k

consider doing actions that will help contribute to this intentionthat b eing satised For instance

it will consider doing itself or trying to convince someone else to do Thus the selection

k k

pro cess requires several steps not evident from the PSP denition

If is a singleagent action then some agent G must rst adopt a p otential intentionto

k k

do then reconcile this intention with others and form b oth a partial individual plan to do this

k

action and a full plan to elab orate the partial plan In some circumstances several group members

may consider doing ie they may go through the cycle of forming a p otential intention and

k

reconciling it This intentionadoption pro cess is similar to the one an agent uses when forming an

Individual pro cess for an individual plan However intention to do a subaction within its Elab orate

the alternatives to b e weighed by the reconciliation pro cess in the context of a SharedPlan dier

from those available in the context of an individual plan For instance G maytakeinto account the

k

p ossibility and costs of having another agent in the group do G may also consult the members

k k

of the group for assistance in forming the partial individual plan required by the denition of IntTo

including asking for advice ab out the recip e to use

If is a multiagent action then some subgroup GR must construct a partial shared plan to

k k

do to satisfy Clause b of the core case for multiagent actions Figure Todosoits

k

memb ers need a to agree to act jointly to do this is required to satisfy Clause of the PSP

k

for doing b to agree on the pro cedure R they will use to determine a recip e for

k selectr ecg

k

doing Clause b and form a full shared plan for using R and c to agree on the

k selectr ecg

k

Group pro cess to b e used as required by Clause b of the SP denition Figure Elab orate

Again the subgroup may consult other group memb ers for advice on recip es

In forming the full shared plan to use recip e R to determine a recip e for the

selectr ecg k

k

group will transform the weak b elief represented in Clause aa that some subgroup could do

k

into the stronger b elief ab out ability required for them to have a partial shared plan In particular

they will establish the mutual b elief that the recip e they select comprises constituent subactions

that the memb ers of GR mutually b elieve they either will b e able to p erform or will b e able to

k

contract out successfully These mutual b eliefs are required to satisfy the constraints comp onentof

C of the FSP in Clause b In the next section we describ e how the PSP represents

selectr ecg

the ability knowledge agents must have for subactions in the core case

For b oth single and multiagent other group members must transform their p otential

k

intentionsthat some individual or subgroup do in Clauses ab and ab into a fulledged

k

intention that the chosen agents b e able to p erform the action required by Clauses a and b

of PSPs denition Tomake this transition the agents must individuall y accept and together agree

on the choice of agents and reconcile p otential intentionsthat the agents b e able to do Thus

k

these other group members must go through an intention reconciliation pro cess similar to G s or

k

but they reconcile an intentionthat not an intentionto the memb ers of GR

k

Furthermore in b oth cases the agents committed to p erforming must communicate su

k

cient information for other group memb ers to b e able to form the mutual b eliefs ab out the abilities

and intentions or SharedPlans of the individual or subgroup to do required by Clauses ab

k

and a or Clause b and b of PSPs denition In addition the other group agents must

communicate the information required to establish mutual b elief of their commitment to the indi

vidual or subgroup p erformance of Clauses a and b resp ectively

k

Rec GR and Elab orate Group are more complex than their Thus the multiagent actions Select

singleagent counterparts Each of these multiagent actions must include participation in some

group decision making pro cess as well as incorp orating many of the actions in Select Rec and

Elab orate Individual Furthermore the group needs to agree on pro cedures for reaching consensus

Sonenb erg et al describ e one set of mechanisms for group elab oration and role assignment

within a formalization that includes complex actions but do es not allow for partial recip es As

describ ed previously Jennings utilizes a central organizer to make these decisions his system

handles partiality only in letting the time and agent of an individualagent action b e unsp ecied

initially The problems of formalizing and designing such pro cesses remain signicant areas of

inquiry Designers of computer agents need to weigh the tradeos b etween the time required to

identify an appropriate agent and the work entailed bymultiple agents considering doing the same

Group pro cesses to use dep ending on action They may decide dierently ab out the Elab orate

tradeos in areas such as communication demands negotiating time and centralityofcontrol The

SharedPlan denition serves to constrain the range of p ossibilities

Capabilities to Perform Actions in SharedPlans

Just as individual agents must b elieve they are capable of p erforming an action in order to have

an intention to do that action groups of agents must have a certain level of b elief in their ability

to p erform actions for which they form SharedPlans As in the case of individual plans the

requirements on agents b eliefs ab out their capabilities vary dep ending on whether their plan is

complete or partial The denitions of FSP and PSP only explicitly state some of the requisite

b eliefs others are implicit in the denitions of these metapredicates and their interactions with

the denitions of IntTo FIP and PIP To understand the kinds of collab orativebehavior FSP

and PSP yield and to guide agent design it is useful to extract this information and sp ecify it

separatelyFormal denitions and theorems establishing the requisite ability constraints are given

in App endix A In this section we briey describ e the constraints the plan denitions place on

ability knowledge

For a group to have a complete SharedPlan to do the complex multiagent action ie for

FSP to hold the members must have determined a recip e for must b elieve that group members

or contractors can p erform all of the basiclevel actions entailed by that recip e and that group

memb ers can p erform all of the basiclevel actions required for anycontracting Because knowledge

of how to p erform is distributed in SharedPlans no single agentmay know the complete extended

recip e tree for The nature of the particular b eliefs agents must have ab out subactions in the

recip e for dep ends on whether the subaction is single or multiagent and on whether it is to b e

ever the individual agents p erforming done by a group memb er or contracted out In all cases how

an action must have strong b eliefs that they can p erform the action other group memb ers must

have b oth the weaker b eliefs that the p erforming agents can bring ab out the action representable

by CBA or CBAGemb edded in one of the b elief op erators and a b elief that the p erforming agents

themselves have the requisite stronger b eliefs in their own abilities

A constituent singleagent subaction p erformed by a group member G engenders the same

i k

b elief constraints on G as FIP would in particular BCBA G must hold A constituent

k i

multiagent subaction p erformed by subgroup GR requires that GR have ability b eliefs for

i k k i

analogous to those the original SharedPlan for requires the full group to haveforthus the

requisite ability b eliefs for this case can b e obtained by recursion In addition the full group must

mutually b elieve b oth that G or GR will b e able to do ie that CBA or CBAG resp ectively

k k i

hold and that the G or GR has a recip e it b elieves it will b e able to carry out For actions

k k

contracted out analogous b eliefs must hold ab out the con tracting action in addition the group

must mutually b elieve that the contracting action will have its intended eect

CBAGemb edded in MB is to o weak a constraint on the p erforming agents b eliefs it lacks a

requirement that they know the relevant recip es Unemb edded CBAG is to o strong it presumes cor

rect b eliefs The subsidiary metapredicate MBCBAGmutually b elieve can bring ab out group

dened in App endix A Figure represents the appropriate intermediate level of b elief As was the

case for BCBA the recip e for R is an argument of the MBCBAG metapredicate reecting the

fact that a particular recip e is known to the subgroup memb ers and not just the existence of some

recip e Only the mutual b elief that R is a recip e for is part of the denition Within its deni

tion MBCBAG app ears recursively for that are multiagent actions and BCBA is stipulated for

i

is that are singleagent actions For each of these recursive uses the existence of the recip e R

i

i

stipulated outside any b elief context reecting the agentss having identied a particular recip e

Thus MBCBAG is stronger than CBAGemb edded in MB however MBCBAGisweaker than

unemb edded CBAG b ecause it do es not presume the agents b eliefs ab out the recip es are correct

As Theorem T states FSP entails MBCBAG The b elief requirements for singleagent

i

w from the FIP in FSP Clause aa and done by a group memb er MBCBAG Clause follo

Theorem T or are in FSP Clauses aa and ab The b elief requirements for multiagent

done by a subgroup Clause are entailed by FSP Clause b and recursion The full

i

groups b elief that the subgroup GR has a complete recip e for and b elieves it is capable of

k i

doing the actions in the recip e followsfromGRsmutual b elief that GR has a complete plan

k

Clause bb The b elief requirements for actions that are contracted out are entailed byFSP

Clause and either FIP Clauses aa and ba or FSP Clauses ab and bb applied

recursively to the contracting action The pro of of Theorem T is similar to that of Theorem

T

When a group has only a partial SharedPlan for its b eliefs ab out capabilities of agents to

carry out the necessary subactions may b e quite limited b ecause its knowledge of the recip e it will

use is incomplete The group may only b elieve that there is some way to nd a recip e that it can

use to p erform Until it knows the constituent actions in the recip e for the group cannot make

any determination ab out which individual or subgroup will p erform the subactions or ab out their

abilities to p erform these subactions While the lack of a recip e makes the agents knowledge in

this situation weaker than in the FSP the groups b eliefs are still stronger than CBAGemb edded

in MB yields In particular the agents must b elieve that they can determine a complete recip e

and will b e able to nd memb ers able to p erform or to contract out each of the actions in the

v

complete recip e once it is determined As the agents identify p ortions of the recip e they must also

establish that they will b e able to p erform the actions in that p ortion or contract them out

The subsidiary metapredicate WMBCBAGweakly mutually b elieve can bring ab out group

dened in App endix A Figure represents the b eliefs the group GR must have ab out its abilities

to select an appropriate recip e and p erform or contract out each of the constituent subactions

in this recip e This set of b eliefs follows from the PSP denition as stated in Theorem T

Clause of WMBCBAG is established by PSP Clause Clause b follows from the FSP in

PSP Clause b and Theorem T as shown in Figure the constraints comp onent of the FSP

context constrC contains the constraints in Clausesbabh of WMBCBAG

selectr ec

Clauses sp ecify the b eliefs in capabilities required for the subactions of the p ortion of

i

the recip e that has b een identied The mutual b eliefs of Clauses a and b are established

resp ectively by Clauses a and b of PSP If a group memb er is going to p erform itself the

i

Clause aa of PSP holds If is basic level action then Clause a is established by Clause

i

of IntToIf is a complex action then the application of Theorem T to Clause b of IntTo

i

yields Clause a of WMBCBAG

If a subgroup is going to p erform then Clause b of PSP holds and Theorem T

i

applied recursively to Clause a of SP yields Clause b of WMBCBAG Clauses and

of WMBCBAG are established similarly by Clauses and of PSP

An Example SharedPlan for Dinner

In this section we illustrate the SharedPlan formalization of collab orative activityby presenting the

full shared plan for the example of Kate and Dan making dinner together As presented in Section

in forming their collab orative plan Kate and Dan decide that Kate will make the app etizer Dan

will make lasagna for the main course and the two of them together will make the dessert To

esh out the example we add some additional details Kate and Dan will co ok at Dans house

There is one constraint from the context in which they decide to form their joint plan that the

dinnermaking b e done indo ors There is also one constraint in the recip e they cho ose for making

dinner that the kitchen of Dans house b e clean

To simplify the example we presume that the intentional context is the same for Kate and

Dan They b oth wanttoentertain their b est friends Joan and Max However more realistically

the motivations that lead Kate and Dan to decide to make dinner together might b e dierent eg

Kate may decide to make dinner with Dan b ecause she intends that she will not b e hungry or tired

whereas Dans motivation is his intention that they have fun together

We use the following representation in the formalization

md represents the group action of Kate and Dan making dinner together on Maybetween

and at Dans house md is the toplevel action ie the binding of in the SP

denition

T denotes the time of md T May

md md

makedinner denotes the action typ e of md

D house denotes Dans house the lo cation of md

T the time of their collab orative plan is May

p

enter tainfK Dg fJMgT denotes the prop osition that Kate and Dan entertain

enter tain

Joan and Max T is the time over which this prop osition holds

enter tain

C denotes the context of md

md

the intentional comp onentofC contains Kates and Dans individual intentionsthat they

md

entertain friends ie the intentional context sp ecies that the following hold a for Kate

IntThK enter tainfK Dg fJMgT T T C and b for Dan

enter tain i enter tain enter tainK

IntThD enter tainfK Dg fJMgT T T C

enter tain i enter tain enter tainD

constrC indoor smd ie this is the constraint from the planning context namely

md

that md b e done indo ors

ma denotes Kates making the app etizer the action typ e of ma is makingapp etizer

mmc denotes Dans making the main course the action typ e of mmc is makingmaincourse

gmd denotes the group action of Kate and Dan making the dessert the action typ e of gmd

is gmakingdessert

R denotes a particular recip e for md this recip e has constituent actions ma mmcand

md

gmd and the constraint on Dans kitchen In particular

R ffmakingapp etizer May D house

md

makingmaincourse May D house

gmakingdessertMay Dhouse g

fcleankitchen D housegg

C C and C denote the contexts for the three constituent subactions ma mmc and

ma mmc gmd

gmd resp ectively These contexts are all similar in each case the intentional context for

action is the individual intention that they make dinner together and the constraints are

constrC fcleankitchen D houseg

md

Using this notation the full shared plan denition sp ecies that Kate and Dans complete plan

FSPP fK DgmdMayMay R C expands to the following conjunction of

md md

clauses

MBfK Dg IntThK DofK DgmdMay constrC

md

MayMay C May

md

MBfK Dg IntThD DofK DgmdMay constrC

md

May C May May

md

MBfK DgR RecipesmdMay

md

a Because ma is a singleagent action

aa IntToK ma M ay May C

ma

ab MBfK Dg IntToK ma M ay May C May

ma

a Because ma is not basiclevel

aa P R FIPP KmaMayMay R C

ma ma ma ma ma

ab MBfK Dg P R

ma ma

ab CBAK ma R May constrC

ma ma

ab FIPP KmaMayMay R C May

ma ma ma

a MBfK Dg IntThD R CBAK ma R May constr C

ma ma ma

aa MayMay C May

cbama

a Because mmc is singleagent

aa IntToD mmc M ay May C

mmc

ab MBfK Dg IntToD mmc M ay May C May

mmc

a Because mmc is not basiclevel

R C aa P R FIPP DmmcMayMay

mmc mmc mmc mmc mmc

ab MBfK Dg P R

mmc mmc

ab CBAD mmc R May constrC

mmc ma

ab FIPP DmmcMayMay R constrC May

mmc mmc mmc

a MBfK Dg IntThK R CBAD mmc R May constrC

mmc mmc mmc

MayMay C May

cbammc

b Because gmd is multiagent and therefore complex

b P R FSPP fK DggmdMayTgmdaR C

gmd gmd gmd gmd gmd

b MBfK Dg P R

gmd gmd

ba CBAGfK Dggmd R May constrC

gmd gmd

bb FSPP fK DggmdMayMay R C May

gmd gmd gmd

Implications of the Formalization

The ma jor goal of the formalization presented in this pap er is to provide a sp ecication of the

mental state of the participants in a collab orative activity that handles complex actions and is

comprehensive in its treatment of partiality of b elief and intention The denitions of partial

plans provide constraints on agents b eliefs and intentions as they initiate and expand partial

plans they suggest what snapshots of the agents mental state should show during this pro cess

The denitions of complete plans provide the stopping conditions for planning pro cesses The

formalization includes a sp ecication of the minimal mental state requirements needed for the

ue to have a plan for collab orative activity It also ties plans closely to intentions agents to contin

in particular requiring that an agenthave a partial plan to do an action when the agent adopts

an intention to act

As promised in the Intro duction the formalization presented in this pap er handles more com

plex relations b etween actions for b oth individual and group plans than the original formulation of

SharedPlans provides a means of representing the commitments of agents in collab orations to their

group activities and treats the partiality that naturally arises in most planning situations Its treat

ment of individual and collab orative plans is integrated Lo chbaum shows the imp ortance

of this integration for mo deling collab oration in dialogues The mo del also handles contracting out

actions The formalization is more general than alternative approaches in its combined treatmentof

partiality of recip e and ability knowledge complex actions with recip es that decomp ose recursively

and contracting

The complexities that arose in developing a formalization that handles b oth complex actions

and incremental development of partial plans stem from one of three dimensions along whichgroup

activities dier from an individual agentintending to do a basic level action commitmentto

actions knowledge ab out how to p erform actions and capabilities to p erform actions

The treatment of commitment b ecomes more complex b oth b ecause of partial knowledge and

b ecause agents need to form commitments toward others activities As a result we needed to

intro duce a new typ e of intention intendingthat a prop osition hold and to dene its interactions

with intendingto do an action Finallytohave a reasonable accountofintendingto do a complex

act in the state of partial recip e knowledge the formalization provides a treatment of commitment

to meansends reasoning

Agen ts knowledge of how to p erform the group activitymay b e partial and distributed No

single agentmayhave the complete recip e to all levels of detail for the group activity As a result

the pro cesses for establishing partial plans and for elab orating them to form complete plans are more

complex they must incorp orate capabilities for group decisionmaking and reaching consensus In

addition agents assessments of their own and other agents capabilities to p erform actions is more

complex

The representation of agents states of knowledge ab out abilities to act is thus also more complex

Were it not for complex actions and partial knowledge the formalization would require only a single

ability predicate The predicates we dene allow us to distinguish among dierent degrees of recip e

knowledge and the corresp onding assessment of abilities to act In particular they distinguish

an agents assessment when it knows the full recip e BCBA from when it knows only a partial

recip e WBCBA and likewise for groups of agents MBCBAG and WMBCBAGrespectively

The formalization also enables distinguishing what an agent can reasonably know ab out another

agents abilities from what it knows ab out its own Although only one pair of metapredicates CBA

and CBAG are needed for the plan denitions themselves the auxiliary predicates provided in

App endix A provide explicit descriptions of the b elief and knowledge that is required when agents

p erform complex actions and mayhave partial plans and are thus useful for agent design

Searle and Grosz and Sidner a argued that the prop ositional attitudes of b elief

mutual b elief and individual intention to act were insucient for representing the mental state of

participants in collab orative activity Collab orative plans were more than a simple combination of

individual plans Some means of representing that the actions within a collab orative plan to act

were b eing done in the context of collab oration was needed Cohen Levesque and Nunes

subsequently argued that collab orative activitygaverisetocommunication demands to deal with

execution problems and termination of collab oration Bratman established three criteria that

amultiagent activitymust meet to b e a shared co op erative activity a mutual resp onsiveness

b commitmenttothejoint activity c commitmenttomutual supp ort Furthermore he argued

that as a result of a and b the agents must form meshing subplans In the remainder of this

section we discusses the way in which our formalization addresses these claims ab out prop erties of

collab orativeorcooperative activity In the next section we compare our approach with alternative

accounts

To address the concerns raised by Searle and Grosz and Sidner the formalization intro duces

tentions the denitions require the attitude of intendingthat and a context parameter for all in

intentionsthat toward the overall group action and the actions of others The formalization do es



not require a separate attitude of jointintention Although the SharedPlan metapredicates

can b e viewed as representing a kind of jointintention they are not new mo dal op erators Each

reduces to individual intentions plus b eliefs and mutual b eliefs The SharedPlan denitions entail

that individual s in a collab orating group have certain mental prop erties mutual b elief ensures that

group memb ers all know when they have these attitudes

To provide other prop erties the formalization imp oses several constraints on agent design Some

of these are on the agents mental states and consistency of its b eliefs and intentions others are

requirements on agents planning and communication pro cesses In particular

As a minimal constraintonintending to do an action the formalization requires that the

agent will do meansends reasoning The denition of IntTo requires that agents not only

reconcile intentions but also have some knowledge ab out how to do or to nd out howtodo

the action This constraint is essential if agents are to b e able to rely on others to do their

part in the group activity

As a minimal constraint on a group having a plan the formalization requires that they have

agreed ab out certain decision pro cedures In particular they need pro cedures for selecting

recip es and for identifying agents to p erform subactions

The formalization requires that groups have pro cedures for establishing mutual b elief and

reaching consensus these form essential comp onents of the plan elab oration pro cesses Agents

must communicate sucient information for other agents to know what they are able to do

and to ascertain what they intend to do Comm unication actions result from this constraint



Searle argued that the requisite prop erties of collab orative activity could not b e achieved without such an attitude

Our formalization meets all the criteria he sets

The denitions of the ability predicates require that agents compute the context in which

they are planning actions

The formalization sp ecies that agents cannot hold intentionsto and intentionsthat that

they b elieve conict with each other or one another

Bratmans meshing subplans criteria is accomplished in the SharedPlans formalization by the

intentionsthat each agent forms toward the other group memb ers b eing able to p erform their

subactions Clauses a and b of the FSP denition and Clauses a and b in the

PSP denition these intentionsthat together with the axioms to avoid conicting intentions

Figure ensure meshing subplans Our formalization treats the case of subplans for multiagent

actions as well as those for individual actions which Bratman discusses

In discussing mutual resp onsiveness Bratman distinguishes b etween mutual resp onsiveness of

intentions and mutual resp onsiveness in action The SharedPlans formalization treats mutual

resp onsiveness of intentions similarly to meshing subplans through intentionsthat It also handles

one asp ect of mutual resp onsiveness in action namely the resp onsiveness required when plans

must b e mo died to cop e with problems in execution Its treatment of partial plans provides a

basis for interleaving of planning and action Plans may b ecome more partial as well as more

complete failures lead to increased partiality Thus this asp ect of resp onsiveness in action is

accommo dated by the constraints on pro cesses for elab orating partial plans cf discussion b elow

of communication obligations That asp ect of mutual resp onsiveness in action which has to do

with continual monitoring of another agents actions is b eyond the scop e of this pap er However

y we b elieve it should b e treated as part of the interleaving of planning and acting rather than b

making a sharp distinction b etween planning and execution

Commitment to the joint activity Bratmans second criterion is directly represented by the

IntTh in Clause of the FSPs denition Commitmenttomutual supp ort Bratmans third

criterion is realized in a more complex way It requires a combination of the intentionsthat the

agents form and the axioms for helpful b ehavior that originate from intentionsthat

Each of the three basic roles of intention that Bratman describ es in earlier work Bratman

also play a signicant role in the formalization That an intentionto engenders meansends

reasoning is built into the denition of IntTo the FIP to Elab orate Individual represents this

commitment Conictavoidance is also explicitly represented in Axiom A of Figure The use

of intentions in replanning is only implicit the context parameter that is asso ciated with each plan

enco des the reason for doing the plans action and thus is available for use in replanning

Other researchers Levesque Cohen and Nunes Cohen and Levesque Jennings

Werner have discussed the communication obligations that arise from failure or suc

cess in p erforming the actions a co op erative or collab orative activity comprises As describ ed

ab ove the plan elab oration pro cesses required by SharedPlans entail additional communication

requirements Intentionsthat playacentral role in the way our formalization addresses these com

munication obligations We examine briey their use in dealing with communication requirements

stemming from action failures intention reconciliation decisions and resource conicts

First we consider the situation in whichamember G of a collab orating group nds itself

k

unable to successfully complete an action that it initially agreed to do This might o ccur for

k

several reasons For example G mighthave failed to successfully carry out some of the subactions

k

in its recip e for Alternatively in the pro cess of reconciling some other intention it mighthave

k

decided to drop its IntTodo Once this o ccurs G no longer has an intention or a full individual

k k

knows that the groups shared plan is now less complete Indeed if the group plan to do G

k k

had a FSP it no longer do es But until G communicates with the other group memb ers they will

k

not know

Intentionsthat in the SharedPlan will lead G to communicate this changed status as follows

k

G still has an intentionthat of the form in Clause of PSP or FSP Because G has dropp ed

k k

an intentionto do a subaction there is now a prop osition emb edded in this intentionthat that is

false ie the Doprop osition As a result of this false prop osition and the Clause intention

that Axiom A for intendingthat Figure will yield G s having a p otential intention to

k

do any actions it b elieves will contribute toward making the prop osition true If G b elieves that

k

communicating its failure to the group will help reestablish the future p erformance of the action

and hence make the Doprop osition true it will attempt to communicate Hence so long as G

k

maintains its intentionthat the group do the activity of which is a constituent all is well

k

A dierent situation arises if G has reason to drop the Clause intentionthat and opt out

k

of the collab orative plan If G has some other intentionthat one which obligates it to some or

k

all memb ers of the group then that intentionthat will in a manner similar to that just describ ed

has an intentionthat the lead G to communicate this fact to the memb ers For instance if G

k k

other agents will want to agree to collab orate with it at some later time and a b elief that opting

out without explanation will cause this not to b e the case then G will adopt a p otential intention

k

to explain its opting out of this collab oration Thus whether or not an agent communicates when

it opts out dep ends on its other intentions IntThs and its b eliefs Some p eople communicate in

such situations others do not We can design computer agents to exhibit either b ehavior

Finally our plan denitions and axioms also entail that an agentcommunicate when it recognizes

a resource conict If one agent G intendsthat another agent G b e able to p erform an action



and G detects a resource conict aecting G s abilitytodo then the intentionsthat axioms will



lead G to consider doing all of the actions it can to prevent this resource conict Typically the act



of informing G and discussing the problem will help resolve the problem Again one implication

of deciding not to take action is that there is no longer a SharedPlan And again this constraint

provides for a range of agent designs dep ending on the tradeos b etween extra communication

costs and the costs of error recovery

Comparison with Alternative Approaches

In this section we compare our formalization to three alternative approaches to sp ecifying co op

erative activity those of Cohen Levesque and Nunes Sonenb erg et al

and Jennings

Cohen Levesque and Nunes henceforth CLN study notions of join t commitment represented

by a mo dal op erator for joint p ersistent goal JPG and jointintentions JI and the ways in which

they relate to individual commitments of group memb ers they address in particular the need for

agents to inform one another whenever they drop a joint commitment

Although not dened in terms of individual intentions jointintentions entail individual inten

tions and commitments For b oth individual and jointintentions CLN employ a strong notion of

commitment JPG stipulates that agents are committed to their joint goal until they b elieve the

goal is satised or come to the conclusion that it is imp ossible to reach the goal The individual

p ersistent goal PGOAL has a similar constraint In b oth cases CLN also allow for a commitment

to b e relativetoaformula q that can serve as an escap e clause agents may drop their commit

ments if they b elieve q is false The denitions of joint and individual intentions utilize JPG and

PGOAL and thus intentions entail commitment in this strong sense

CLNs mo del also emb o dies a strong and rigid communication requirement According to the

denition of JPG if a participant in a collab oration comes to b elieveprivately that the joint

goal is satised or is imp ossible to achieve it incurs a commitment to makethismutually known

ie to inform the other agents That is an agentmay not abandon a joint commitment without

communicating with its partners

Our formalization allows for more exible b ehavior Agents reconcile their intentions when

considering adopting new intentions They may decide to drop intentions for a variety or reasons

eg resource limitations Although communicating with partners in a collab oration plays an

Group pro cess agents are not required to communicate when they imp ortant role in the Elab orate

drop intentions Instead communication is only one option in such situations As was explained in

the previous section the intentionsthat and mutual b elief comp onents of the SharedPlan denitions

yield the commitment prop erties CLN argue for in the case that the SharedPlan is maintained

however we also allow the p ossibilityofagents opting out of collab orations

CLN consider actions and plans only at a highlevel of abstraction and do not address partiality

in a signicantway They do not discuss or represent in detail partial plans for individual or joint

action In two pap ers Levesque Cohen and Nunes Cohen and Leveque only actions

with all constituent subactions sp ecied are considered A subsequent pap er Cohen and Levesque

allows some partiality in the denition of individual and jointintention by allowing the

op erators INTEND and IJ to take op en action expressions as arguments

In contrast we examine in detail various typ es of partiality As describ ed in Section doing

so complicates our denitions However it also yields detailed sp ecication of the p ossible mental

states of agents that have partial individual plans or SharedPlans As a result our denitions

provide more precise constraints on the design of elab oration pro cesses Our formalization also

includes more detailed sp ecication of recip es for actions the context of planning and acting and

the information that collab orating agents must have ab out their joint activity Because CLN do

not provide detailed sp ecication of subactions of complex actions they also do not consider issues

related to the pro cesses of recip e selection and subaction allo cation for participants and subgroups

In addition they do not discuss in detail the ways in which helpful b ehavior is generated

Sonen b erg et al henceforth STWKLR do provide detailed sp ecications of the various

planconstructs that arise in mo deling collab orative activity Their work diers from ours most in

that they do not handle partial plans In addition they typically provide a single mechanism in

cases in whichwegive general restrictions on agents mental states and their elab oration pro cesses

Although Sonenb erg et al have more detailed semantics than we do they also do not address

issues of soundness and completeness

As in our framework STWKLR assume that each individual agent is supplied with a set of

plan structures similar to our recip es known as its plan library The plan library of a group of

agents is the intersection of the plan libraries of its participants However they do not consider

situations in which agents have partial plans Their formalization do es not allow for a group to

construct a new plan structure using elements from individual memb ers libraries as wedowith

recip es It also do es not allow for sub contracting of actions to agents outside the group

In place of our ability metapredicates Section and App endix A STWKLR dene the



notion of skil ls of teams The skills of a team are the set of primitive actions that can b e

p erformed by that team team skills include skills of the individual s the team comprises and skills

of the comp osite These skills are statically determined the formalization do es not allow for them

to vary with time nor to dep end on the situation of use Thus their agents can reason in what



In their formalization an individu al agent is also a team

 

STWKLR call compiletime ab out the p otential of a given team to successfully execute a plan

ie p erform a complex action and compute the groups that might succeed in achieving a goal

This information can b e used to guide the pro cess of team formation at runtime STWKLR

provide a detailed algorithm for team formation that dep ends on centralized control They also

provide a general mechanism for agents to synchronize their group activity an issue we do not

address

The ability metapredicates we dene takeinto account the context in whichanagent is p er

forming an action They representanagents ability to p erform an action using a particular recip e

at a given time and under constraints The formalization considers constraints from the context in

which the action is b eing p erformed eg the complex action of which this action is a constituent

as well as the recip e In the group ability predicates eg CBAG agents b eliefs ab out the ca



pabilities of other agents also playarole Thus our denitions provide more exibili ty in plan

formation

STWKLR like CLN build into their denition of jointintention a requirement that agents

communicate In particular the metho d they use for transforming a general plan structure to a

plan in which teams are assigned to sp ecic actions ie a role plan in their terminology adds

communication actions so that a message rep orting the failure or success of a subaction is broadcast

to the memb ers of the group after the subaction is executed or attempted in the case of failure

STWKLR argue that their formalization meets Bratmans conditions for shared co op erative

activity They treat mutual resp onsiveness by providing for a team to backtrack and cho ose a

dierent subaction or a dierent role assignment if either is available How ever it app ears they can

ensure meshing subplans only insofar as the meshing is enco ded into plan structures in the agents

libraries They do not discuss either mutual supp ort or helpful b ehavior

Jennings used a formal mo del for jointintention in the design of a testb ed environment

for constructing co op erativemultiagent systems He tested this design and the role of explicit

mo dels of intention by implementing a system for electricity transp ortation management The

formal sp ecication in mo dal logic was used to develop a system of pro ductionrules that yielded

agents b ehaving according to the formalization The transformation from formal mo del to agent

design is thus a ma jor contribution of this work

Jennings formal Resp onsibili ty Mo del is a renement of the Cohen Levesque and Nunes

formalization of jointintentions It adds two elements to this formalization recip e selection and

a notion of joint recip e commitment including a sp ecication of the conditions under which joint

recip e commitment can b e dropp ed Although the Resp onsibili ty Mo del treats recip es for complex

group actions these decomp ose immediately into singleagent actions It app ears that the con

stituent singleagent actions may b e complex and that the agentmay form a team for a joint plan

to assist in p erforming the action but there is no connection in the formalization b etween the team

and plan for this subsidiary action and the original one

Jenningss system handles task allo cation byhaving a central organizer that uses information

it has ab out the abilities of all other agents to assign tasks Recip e selection for the complex group

action is also managed by this central organizer The team memb ers select their own recip es for the

singleagent constituent actions there is no description of which information ab out an individual



They call the time prior to engaging in timeb ounded activity compiletime and the time of collab orative realtime

activity runtimeWe do not distinguish b etween these time p erio ds



STWKLRs terminology diers from ours In particular their plan corresp onds approximately to our recip e

executing a plan is executing a particular instantiation of a recip e



Although STWKLR briey mention a notion of capabiliti es that takes into account not only skills but also

compatibili ty with other goals and intentions and constraints on recip es their detailed discussion and algorithm refer

only to skills

recip e needs to b e communicated to others Recip es are partial only in allowing delayed sp ecication

of the agent and time of action there is no partiality of the decomp osition into constituent actions

A ma jor emphasis of this work is an examination of the role of communication in assisting

collab oration In particular Jennings ran several exp eriments comparing the p erformance of a

system based on the Resp onsibili ty Mo del with alternatives that did not utilize an explicit mo del

of jointintention These exp eriments fo cused on the execution phase of collab orative activityand

the b enets of communicating to the group when an agent cannot carry out actions it committed

to doing as part of the group activity The results suggest that communication lessens wasted

work Jennings argues further that the explicit mo del of collab oration enables this savings without

a system designer needing to determine in advance all of the problems that might arise during

execution and the information that needs to b e communicated once one of them do es

Conclusions and Future Work

To provide an account of collab orative activity Searle intro duced the notion of weintention

Grosz and Sidner Grosz and Sidner a argued that such a notion should not b e necessary

and their initial formulation of SharedPlans avoids use of one However the denitions provided

in that formulation could only accommo date group activity that directly decomp osed into actions

of individual agents In this pap er wehaveprovided a formalization that handles complex actions

and that allows for plans to b e partial In this work SharedPlans servetwo ma jor roles They

summarize the set of b eliefs and intentions needed for collab orativeactivity and they provide

the rationale for the pro cess of revising b eliefs and intentions Consequently they motivate the

collab orative correlate of meansends reasoning in the plans of an individual agent SharedPlans

ground out in the individual intentions of individual agents and the individual plans that they

engender Our formalization accommo dates the prop erties of shared co op erative activity prop osed

by Bratman Intentions to do constituent actions form the basis of each individuals actions

Intentionsthat directed toward other agents abilities to act and success in acting as well as toward

the success of the joint activity ensure meshing subplans and helpful b ehavior

The development of this formalization uncovered several interesting new problems in designing

agents for collab orativework These include

The need to develop more exible metho ds for reasoning ab out resources and resource conicts

in the context of collab orative activity and to examine the tradeos among them

The need to develop more complex metho ds for groups to construct and agree on recip es

The need to understand more fully the ways in whichcommunication supp orts collab oration

and to develop a more complete set of communication axioms Agents need to communicate

ab out more than the completion of subtasks or errors the two situations for which alternative

approaches cf Section have built in the need to communicate For instance communi

cation actions playacentral role in establishing requisite mutual b eliefs and ensuring the

satisfaction of intentionsthat

The formalization undersp ecies several asp ects of collab orative planning First the plan de

nitions entail that the reasoning mechanisms individual agents utilize for elab orating partial plans

have certain prop erties but a complete sp ecication of these elab oration pro cesses has not yet

b een provided Second the formalization includes only the most basic axioms for the attitude of

intendingthat ie the IntTh mo dal op erator Third wedonotprovide sp ecic mechanisms for

reconciling intentions In addition we do not formalize commitment in this pap er This issue is

enormous in its own right it is most relevant to SharedPlans in the way it aects the development

of pro cedures for reconciling intentions

Each of these p oses a signicant research problem whichwehave left to future research The

ma jor next steps weenvision are to develop strategies and proto cols for elab orating partial plans

including mechanisms for combining information p ossessed by dierentagents ab out how to p erform

a complex action and strategies for negotiating among comp eting approaches handling resource

conicts and reaching consensus on how to allo cate p ortions of the activity among dierent par

ticipants

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Mo ehlman T V Lesser and B Buteau Decentralized negotiation An approach to the

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Morgenstern L Foundations of a Logic of Know ledge Action and Communication PhD

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Osawa E and M Tokoro Collab orative plan construction for multiagentmutual planning

In DecentralizedArticial Intel ligence Volume Elsevier Science Publishers pp

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A Abilities and Beliefs

This section contains the formal denitions of the metapredicates BCBA WBCBA MBCBAG

and WMBCBAG representing dierent kinds of b elief in an agents ability to carry out actions and

related theorems

T Theorem

T T GR P

p

FIPP G T T R C

p

BCBAG R T T constrC

p

BCBAG R T T

bel

N

basiclevel Bel G ExecG T T

bel

basiclevel

a R f gBel G R RecipesT

i j bel

b R T

i

i

b R BCBAG R T T f g

i bel j

i i i

b G T R

c

ba BCBAG R T T f g

bel j

bb Bel G GTDG T G T f gT

c i j bel

i

Figure Beliefs and capabilities to p erform actions in FIP and the denition of BCBA b elieve

can bring ab out and related theorem

A Pro of of Theorem T

To prove Theorem T we formally dene the concept of an extendedrecipetree As describ ed in

Section this concept is an extension of a recip e tree that takes into accountcontracting actions

Without loss of generalitywe assume that a recip e consists of at least two actions

Denition Extended Recip e Tree

If is a basiclevel action and IntToG T T C holds then s extendedrecipetree with

i

respect to that intention is a tree with one node labeledby

Suppose is a complex action such that

R PFIPP G T T R C holds where R f g

p i j



An extendedrecipetree for TR with respect to the ful l individual plan FIPP G T T R C

p

isatree that satises the fol lowing conditions

the root TR is labeledby

If according to P G intends to do by itself then

i

if is a basiclevel action the ith child of the root of TR is the extendedrecipetree for

i

with respect to IntToG T T C

i i p

i

i



We will drop the FIP when it is clear from the context

otherwise the ith child of the root of TR is the extendedrecipetreefor with respect

i

to FIPP G T T R C

i p

i i i

i

If G subcontracts according to P then the ith child of the root of TR is the root of a sub

i

tree that has its root labeledby and the child of this node is the root of the extendedtree

i i

if is basic level action and with respect to for with respect to IntToG T T C

p

i

FIPP GT T R C otherwise

p

i

Pro of of Theorem T

Supp ose FIPP G T T R C holds for some R PGT T and C IfG has a FIP for

p p

then is a complex action However it is imp ortanttoobserve that from the Denition of IntTo

Figure and the denition of BCBA if an agentintends to do a basic level action BCBA

holds for ie

basiclevel IntToG T T C BCBAG R T T constrC

i Empty i

e T by induction on the height of the extended recip e tree of with resp ect to Wenowprov

FIPP G T T R C Since is a complex action the height of the extended recip e tree for

p

is at least

Base Case

If the height of the extended recip e tree for with resp ect to FIPP G T T R C is and

p

R f g then all are basic level actions and G intends to do each of the by itself

i j i i

from Clause of the FIP denition Bel G R RecipesT and therefore Clause a

p

of the BCBA denition holds Since all the subactions in R are basiclevel actions and G intends

to do each subaction by itself Clause b of BCBA follows from Clause a of the FIP denition

and ab ove Thus we can conclude that

BCBAG R T T constrC

p

Induction case Supp ose T holds when the heigh t of the extended recip e tree is less than

k We consider the case in which the height of the extended recip e tree with resp ect to the full

individual plan is k

As in the base case Clause a of the BCBA is established from Clause of the FIP denition

For any R we need to show that Clause holds

i

If according to plan P G intends to do by itself then

i

if is a basic level action then the pro of that Clause b of BCBA hold pro ceeds as

i

in the base case

if is complex action then Clause b of FIP sp ecies that

i

P R FIPP G T T R C where constrC constrC f g

i p j

i i i i i

i i

R C is the height of extended recip e of with resp ect to FIPP G T T

i i p

i i i

i

less than k since this extended tree is a subtree of the extended tree for By the

induction hyp othesis we can conclude that

R BCBAG R T T constrC f g

i i j

i i i

If G contracts out then Clause bb of BCBA follows from Clause a of the FIP

i

denition Since the height of extended recip e tree for is less than k it is a subtree of the

extended recip e tree for the pro of that Clause ba of BCBA holds is similar to the

pro of that Clause b holds when G intends to do by itself

i

Thus we can conclude that BCBAG R T T constrC

p

T Theorem

T T GP

p

PIPP G T T C

p

p p

R WBCBAG T R T constrC

bel

p

WBCBAG T R T

bel

basiclevel Bel G ExecG T T

bel

p

abasiclevel R f g

i j

R T Bel G R Recipesf g

bel i j

a Bel G R R Recipes f g R T

i j p

b T R

selectr ec selectr ec

b BCBA G Select Rec G f gT R T T

i j selectr ec selectr ec selectr ec bel

ba R f g

v e

bb Bel G R Recipes f gR T

i j selectr ec

bc R

v

bd Bel G T R CBAG R T f g

v e

v v v v

be T CCG T T

v selectr ec

v v

p

T R

i

i

p p

T f g WBCBAG T R R

bel j i

i

i i

p

G T R

c

a Bel G GTDG T G T f gT

c i j bel

i

p

b WBCBAG T R T f g

g bel j

a Bel G R CBAG R T f gT

i j bel

i i i

b T T G

c

i

b Bel G R CBAG R T f g

j

G T f gT ba GT D G T

c i j bel

i

Figure Beliefs and capabilities to p erform actions in PIP and the denition of WBCBA weakly

b elieve can bring ab out

B Formal Plan Denitions and Additional Intentionthat Axiom

This app endix contains the full formal denitions for the individual plan metapredicates FIP and

PIP and the group plan metapredicates FSP and PSP

T Theorem

T T GR

p

R PFSPP GRT T R C

p

R MBCBAG GRR T T constrC

p

MBCBAGGRR T T

bel

R f gMB GRR RecipesT

i j bel

b R T

i

i

singleagent

i

a G GR

i

a R BCBAG R T T f g

i bel j

i i i i

a MBGR R CBAG R T f gT

i b j bel

i i i i

multiagent

i

a GR GR

i

R MBCBAGGR R T T f g a

i bel j

i i i i

W

a MBGR R CBAGGR R T f gT

i j bel

i i i i

aG singleagent

c

a G GRT

G R T T f gT a MB GR R CBA

bel j bel

a MB GR GTDG T G T f gTbel

c i j

i

a R BCBA G R T T f g

bel j

bG multiagent

c

b GR GRT

b MBGR R CBAGGR R T T f gT

bel j bel

b MB GR GTDG T G T f gT

c i j bel

i

b R MBCBAGGR R T T f g

bel j

Figure Beliefs and capabilities to p erform actions in FSP and the denition of MBCBAG

mutuallyb elievedcanb ringab outgroup

T Theorem

T T GR

p

P PSPP GRT T C

p

p p

R WMBCBAGGRT R T

p

p

WMBCBAGGRT R T

bel

p

R f g MBGR R Recipesf g R T

i j i j bel

g R R RecipesT a MBGR R f

bel i j

bT P R

selectr ecg selectr ecg selectr ecg

b MBCBAGGR Select Rec GRGRf gT R T T

i j selectr ecg selectr ecg selectr ecg bel

ba R f g

v e

bb MBGRR Recipes f g R T

i j selectr ecg

bc R MBGR T

v

v

bd singleagent

v

be G GR R CBAG R T f g

v e

v v v v v

bf multiagent

v

W

bg GR GRR CBAGGR R T f g

v e

v v v v v

bh CCGGR T f gT

v l selectr ecg

v

p

T R

i

i

a singleagent G GR

i k

p p

a R WBCBAG T R T f g

i bel j

i

i i

a MBGR R CBAG R T f gT

k i j bel

r r

i

GR GR b multiagent

k i

p p

b R WMBCBAGGR T R T f g

k i bel j

i

i i

b MBGR R CBAGGR R T f gT

k i j bel

r

i i

WMBCCGR T T f g

i j

i i

a singleagent

i

aa f gT T CBAG R T MBGR G GRR

j bel k i k

i i i i

a multiagent

i

f gT T CBAGGR R T aa MBGR GR GRR

j bel k i k

i i i i

CCGGR T f gT b MBGR T

i j bel

i i

fCOMMENT WMBCC includes all the b elief and mutual b elief required

for contracting out when the group has PSPg

i

Figure Beliefs and capabilities to p erform actions in PSP and the denition of WMBCBAG

weakly mutually b elieve can bring ab out group

FIPP G T T R C

p

R f gBel G R RecipesT

i j p

T

i

i

a IntToG T T C

i p

i

i

b basicl ev el

i

N

b P R FIP P G T T R C

i p

i i i i i

i

G T

c

a BelG GTDG T G T constr C f gT

c i j p

i

b IntToG T T C

p

i

c IntThG R CBAG R T constrC f gT T C

c i j p

cba

i i i i

i

d basicl ev el

d R P FIPP GT T R C g

p

i

fCOMM EN T constr C constr C f g

j

i

constr C constr C f gg

j

i

Figure Denition of Full Individual Plan

PIPP G T T C

p

f g

i j

Bel G R R Recipes f gR T

i j p

a BelG R R Recipes f g R T

i j p

bT P R

selectr ec selectr ec selectr ec

b IntToG Select Rec G f gT T T C

i j selectr ec p selectr ec

selectr ec

V

b FIP P GSelect Rec G f gT T T R C

selectr ec i j selectr ec p selectr ec selectr ec

selectr ec

set set set

i k r

set T

r r

r

N

IntToG T T C

r p

r

r

G T

c

a Bel G GTDG T G T constrC f gT

c r j p

r

b IntToG T T C

p

r

V

c IntThG R CBAG R T constr C f gT T C

c r j p

cba

r r r r

r

set

k k

a T PotIntToG T T C

k p

k k

k

a Bel G R CBAG R T constr C f gT

k j p

k k k

b T T PotIntToG T T C

p

f

k

k k

b BelG G R CBA G R T constr C f g

c j

ba GT D G T G T constr C f gT

c k j p

k

fCOMMENT

constr C

selectr ec

R f gBelG R Recipes f g R T

v e i j selectr ec

R Bel G T

v

v

f g R CBA G T R constrC

e v

v v v

CCG T constrC f gT

v e selectr ec

v

constr C constr C constr C f g g

j

r r

Figure Denition of Partial Individual Plan

FSPP GRT T R C

p

MBGR G GRIntThG DoGRT constrC T T C T

j j p p

R f gMB GRR RecipesT

i j p

R T

i

i

a singleagent G GR

i k

aa IntToG T T C

k i p

i

i

ab MBGR IntToG T T C T

k i p p

i

i

a basiclevel

i

aa MBGR CBAG R T constrC f gT

k i E mpty b j p

i

a basiclevel

i

aa P R FIPP G T T R C

k i p

i i i i i

i

ab MB GR P R

i i

ab CBA G R T constrC f g

k i j

i i

ab FIPP G T T R C T

k i p p

i i i

i

a MBGR G GRG G

j j k

N

aa IntThG R CBA G R T constrC f gT T C T

j k i j p p

cba

i i i i

i

bmultiagent GR GR

i k

b P R FSPP GR T T R C

k i p

i i i i i

i

b MBGR P R

i i

ba CBAGGR R T constrC f g

k i j

i i

bb FSPP GR T T R C T

k i p p

i i i

i

G GR n GR b MBGR

j k

N

ba IntThG R CBAGGR R T constr C f gT T C T

j k i j p p

cbag

i i i i

i

FSPCGR T T C f g

i p j

i

fCOMMENT constr C constr C f g g

j

i

Figure Denition of Full SharedPlan

FSPCGR T T C f g

i p j

i

T

a singleagent G

i c

a MBGR G GRIntThG R

j j

i

aa CBAG R T constr C T T C T

c i p p

cba

i i

i

singleagent G GR aa

k

aa MB GR GTDG T G T constrc T

k c i p

i

aa IntToG T T C

k p

i

aa MB GR IntToG T T C T

k p p

i

C aa MP GRG T T

p k

i

ab multiagent GR GR

k

ab MB GR GTDGR T G T constr C T

k c i p

i

N

ab SGPGR GR T T C

k p

i

bmultiagent GR

i c

b MBGR G GRIntThG R

j j

i

constr C T T C T T ba CBAGGR R

p p c i

cbag

i i

i

ba singleagent G GR

k

ba MB GR GTDG T GR T constr C T

k c i p

i

ba IntToG T T C

k p

i

ba MB GR IntToG T T C T

k p p

i

ba MPGRG T T C

k p

i

bb multiagent GR GR

k

bb MBGR GTDGR T GR T constr C T

k c i p

i

bb SGPGR GR T T C

k p

i

Figure FSPCContracting in FSP

MP GRG T T C

k p

basicl ev el

a P R FIP P G T T R C

k p

b MB GR P R

constrC b CBAG R T

k

V

b FIPP G T T R C T

k p p

MB GR G GRG G IntThG R

j j k j

a CBAG R T constr C T T C T

k p p

cba

SGPGR GR T T C

k p

P R FSPP GR T T R C

k p

i

MB GR P R

a CBAGGR R T constr C

k

b FSP P GR T T R C T

k p p

MB GR G GR n GR IntThG R

j k j

a CBAGGR R T constrC T T C T

k p p

cbag

i

Figure The p erformance of the contracting action in the contracting cases of FSP MP

Memb er of the group p erforms the contracting action SGPsubgroup p erforms the contracting

action

PSPP GRT T C

p

f g

i j

MB GR G GR IntThG DoGRT constr C T T C T

j j p p

MB GR R f g R R Recipes T

i j p

RecipesT a MBGR R f gR R

p i j

bT P R

selectr ecg selectr ecg selectr ecg

b FSP P GR Select Rec GRGRf gT T T

selectr ecg i j selectr ecg p selectr ecg

V

R C

selectr ecg

selectr ecg

set set set set T

i k r r r

r

a singleagent G GR

r k

aaIntToG T T C

k r p

r

r

IntToG T T ab MB GR C T

k r p p

r

r

a MB GR R CBA G R T constr C f gT

k r j p

r r r

a MB GR G GRG G IntThG R

j j k j

r

N

constr C f gT T C T aa CBA G R T

j p p k r

cba

r r r

r

b multiagent GR GR

r k

b P SPP GR T T C

k r p

r r r

r

b MB GR P SPP GR T T C T

k r p p

r r r

r

b MB GR R CBAGGR R T constrC f gT

k r j p

r r r

b MB GR G fGR n GR gIntThG R

j k j

r

N

ba CBAGGR R T constr C f gT T C T

k r j p p

cbag

r r r

r

V

PSPCGR T C f g

r j

r

set

k k

a singleagent

k

aa MBGR G GRR T CBAG R T constrC f gT

k k k j p

k k k k

ab MB GR G GRPotIntThG G GRT

j j k

k

ab DoG T constrC f gT T C T

k k j p p

do

k k

k

a multiagent

k

aa MBGR GR GRR T CBAGGR R T constrC f gT

k k k j p

k k k k

ab MB GR G GRPotIntThG GR GRT

j j k

k

W

ab DoGR T constr C f gT T C T

k k j p p

do

k k

k

b MB GR T CCGGR T constrC f gT

k j p

k k

b MB GR G GRPotIntThG T G G T

j j c k

k

ba singleagent G GR multiagent G GR

k k

f g bb DoG T constrC f g GTDG T G T constrC

j k j k c k

k

T T C T

p p

cont

k

k

fCOMMENT

constr C

selectr ecg

R f g

v e

MBGRR Recipes f gR T

i j selectr ecg

R MB GR

v

T singleagent

v

v

G GRR CBA G T R constr C f g

v e

v v v v v

multiagent

v

GR GRR CBAGGR T R constrC f g

v e

v v v v v

constrC f gT CCGGR T

e selectr ecg v

v

constr C constr C f g g

j

r

Figure Denition of Partial SharedPlan

PSP P GRT T C

p

Contracting case PSPCGR T C f g

r j

r

a singleagent subaction The group will get another agent G to do the subaction

c r

a The group GR mutually b elieve that all memb ers of the group are committed to G s

c

success

MBGR G GR

j

IntThG R CBA G R T constrC f gT T C T

j c r j p p

cba

r r r r

r

tracting act is singleagent there is a memb er of the group G such that aa The con

k

aa The group mutually b elievethatG can get G to do the subact by doing

k c

constr C f gT MBGR GTDG T G T

j p k c r

r

aa G intends to do the contracting action

k

IntToG T T C

k p

r

aa The group mutually b elievethatG intends to do the contracting action

k

MBGR IntToG T T C T

k p p

r

aa The group mutually b elievethatG is able to do the contracting action

k

MBGR R CBA G T T constr C f gT

k p j p

aa The group mutually b elievethatallitsmemb ers are committed to G s success

k

MBGR G GRG G

j j k

IntThG R CBA G R T constrC T T C T

j k p p

cba

r r

ab The contracting act is multiagent action there is subgroup GR of the group such

k

that

ab The group mutually b elieve that the subgroup GR can get G to do the subaction

k c

bydoing

r

MBGR GTDGR T G T constrC f gT

k c r j p

r

ab The subgroup has SharedPlan for doing

P SP P GR T T C

k p

r

ab The group mutually b elieve that the subgroup has SharedPlan for doing

MBGR P SP P GR T T C

k p

r

tracting action ab The group mutually b elievethatGR can bring ab out the con

k

MBGR R CBAGGR T T constr C f gT

k p j p

bb GR mutually b elieve that all its memb ers are committed to GR s success

k

MBGR G fGR n GR g

j k

IntThG R CBAGGR R T constrC T T C T

j k p p

cba

r r

Figure PSP Contractingout case singleagent

PSP P GRT T C

p

Contracting case PSPCGR T C f g

r j

r

b Multiagent action The group will get another group of agents GR to do do the subaction

c

r

b The group GR mutually b elieve that all memb ers of the group are committed to GR s

c

success

MBGR G GRIntThG R

j j

r

CBAGGR R T constrC f gT T C T

c r j p p

cbag

r r r

r

ba The contracting act is singleagent there is a mem b er of the group G such that

k

ba The group mutually b elievethatG can get GR to do the subact by doing

k c r

MBGR GTDG T GR T constrC f gT

k c r j p

r

ba G intends to do the contracting action

k

IntToG T T C T

k p p

r

ba The group mutually b elievethatG intends to do the contracting action

k

MBGR IntToG T T C T

k p p

r

ba The group mutually b elievethatG can bring ab out the contracting action

k

MBGR R CBA G T T constr C f gT

k p j p

ba The group mutually b elieve that all its memb ers are committed to G s success

k

MBGR G GRG G

j j k

IntThG R CBA G R T constrC T T C T

j k p p

cba

r r

bb The contracting act is multiagent action there is subgroup GR of the group such

k

that

bb The group mutually b elieve that the subgroup GR can get G to do the subact

k c

bydoing

MBGR GTDGR T G T constrC f gT

k c r j p

r

bb The subgroup has SharedPlan for doing

P SP P GR T T C

k p

r

bb The group mutually b elieve that the subgroup has SharedPlan for doing

MBGR P SP P GR T T C

k p

r

bb The group mutually b elieve that GR can bring ab out the con tracting action

k

MBGR R CBAGGR T T constr C f gT

k p j p

bb GR mutually b elieve that all its memb ers are committed to GR s success

k

MBGR G fGR n GR g

j k

IntThG R CBAGGR R T constrC T T C T

j k p p

cba

r r

Figure PSP Contractingout case multiagent

A Axiom

G T T

i

G is committedto G s success in doing as part of G s intention to

T R G

IntToG T T C

i

IntThG R CBA G R T constrC T T C

i

cba

It is cheaper to G to help G in doing by doing

cost G DoG T constrC T C R

DoG T constrC DoG T constr C

cba

costG DoG T constrC T C R

DoG T constr C DoG T constr C

cba

econ cost G DoG T constr C T C R

cba cba

G believes it can perform

BelG R CBA G T constrC T

i

cba

G wil l consider doing

PotIntToG T T C

i

cba

Figure Another helpfulb ehavi or axiom for intendingthat