Levels of help, levels Cristiano of delegation Castelfranchi, and agent modeling Rind Falcone From: AAAI Technical Report WS-96-02. Compilation copyright © 1996, AAAI (www.aaai.org). All rights reserved. IP-CNR, Group of "Artificial Intelligence, CognitiveModeling andInteraction" Viale Marx,15 - 00137ROMA - Italy E-mail:{cris, falcone}@pscs2.irmkant.rm.cnr.it Introduction The huge majority of DAIand MA,CSCW and negotiation systems, communication protocols, cooperative software agents, etc. are based on the idea that cooperation works through the allocation of sometask (or sub-task) of a given agent (individual or complex) to another agent, via some "request" (offer, proposal, announcement,etc.) meeting some"commitment"(bid, contract, adoption, etc.). This core constituent of any interactive, negotial, cooperative system is not so clear, well founded and systematically studied as it could seem. Our claim is that any support system for cooperation and any theory of cooperation require an analytic theoly of delegation and adoption. We will contribute to an important aspect of this theoo, with a plan-basedanalysis of delegation. In this paper we try to propose a foundation of the various levels of delegation and adoption(help), characterizing their basic principles and representations. Wetry also to identify different agent modelingrequirements in relation to the different levels of delegation and/or adoption. Wecharacterize the various levels of the delegationadoption relation (executive or open; implicit or explicit; on the domainor on the planning; etc.) on the basis of theory of plans, actions and agents. Our claim is that each level of task delegation requires specific beliefs (modeling) about both the delegate and the delegee. Delegation, adoption and their meeting In this section we supply a general definition of delegation, adoption, and contract, before entering into a more formal and detailed ,analysis of these concepts. Let A and B be two agents. There are two main forms of delegation: - A delegates to B a result ? (goal state): i.e. A delegates B to "bring it about that g", where"to bring it about that g" means to find and execute an action that has g mnongits relevant results/effects. Sub-delegation is not excluded. Delegation from A does not require that A knowswhich is the action that B has to c,’uxy out: A has only to guess that there is such an action. -A delegates to B an action a, i.e. A delegates B to perform(or sub-delegate) Weassumethat, to delegate an action necessarily implies to delegate some result of that action [postulate I]. Conversely, to delegate a result alwa~,s implies the delegation of at least one action that producessuch a result [postulate II]. Thus, in the following we will consider as the object of the delegation the couple action/goMx=(a,g) that we call task. Withx, we will refer to the action, to its resulting world state, or to both: this is because a or g might be implicit or non specified in the request. By definition, a task is a piece/part of a plan (possibly the entire plan); therefore the task has the s,’une hierarchical structure of compositionand of abstraction of plans. WeakDelegation ("to rely on", "to exploit") Given two agents A and B, and a task x, to assert that A weakly-d~legatesx to B meansthat: la) (A believes that) is a goal or subgoal of A; that implies [1] that: - A believes that (to perform)x is possible; - A believes that (to perform)x is preferable; - A believes that Not (performed) lb) A believes that B is able to perform/bringit about that x; lc) (A believes that) A has the goal that B performs/brings it aboutthat x; ld) A believes that B will performz in time (or A believes that B is internally committedto performx in time). le) A has the goal (’relativized’ to ld) of not performingz by itself. In WeakDelegation A exploits B’s activities while B might be unawareof this. WeakAdoption ("to take care of") Given two agents A and B, and a task x, to assert that B weakly-adopts’r for A meanstlmt: 2a) B believes that z is a goal or subgoal of A; 2b) B believes that B is able to perform/bringit about that 2c) (B believes that) B has the goal to performzfor A; that hnplies that: - B believes that (to perform)’r is possible; - B believes that (to perform)x is preferable for - B believes that Not(performed)x 2d) B believes that B will performT in time (or B believes that B is internally committedto performx in time). 2e) B believes that A will not performz by itself. Notice that this help can be completely unilateral and spontaneousfrom B (without any request of A), and/or even ignored by A. Delegation.Adoption (Contract) In Strict Delegation, the delegate knowsthat the delegee is relying on him and accepts the task; in Strict Adoption, the helped agent knowsabout the adoption and accepts it. In other words, Suict Delegation requires Strict Adoption, and vice versa: they are two facets of a unitary social relation that we will call "delegation-adoption" or "contract". Given two agents A (the client) and B (the contractor), a task x, to assert that there is a delegation-adoption relationship betweenA and B for x, means that: (la) (2a) (lb) (2b) (lc) (2c) (ld) (2d) (le) (2e). 3a) A and B believe that the other agent believe that x is goal or subgo,’dof A; 3b) A and B believe that the other agent believes that B is able to perform/bringit about that x ; 3f) A and B believe that A’s goal is that B performs x for A; 3g) A and B believe that B is socially committedwith A to performx for A [2]; 3h) A is socially co~mnitted with B to not perfonning x by hhnself; 3i) A and B mutually believe about their reciprocal commitments. Levels of delegation and adoption In the following we will consider only Strict Delegation and Adoptionbased on implicit or explicit request~offer. Levels of delegation Corollary_ of cognitive asynun~lry: - in asking for an action, tile client has in mindat least one of its results (postulate II), while, - in asking for a result, the client might be unawareof any specific action needed to achieve it even being aware that his request is an implicit request of action¯ Whenx is an action a, it can be: an elementary action or a complexaction (plan). The object of delegation/adoption process can be a practical or domainaction as well as a meta-action, that is an action about plans, such as searching, choosing, problem solving and so on. For example, if x-ot and t~ is a complex action, also the meta-actions of searching in some plan library and selecting a specific decompositionfor ct, are delegated. If tile delegation is about a result x--g, also tile meta-action of choosing among possible plans for g is delegated. Both cases belong to open delegation: from the client’s point of view, file contractor h~s to decideabout file specific actions to carry out. Onthe contrary an executive delegation does not foresee any decision about the delegation object. Again, another possible delegation regards the control on the actions themselves. In short, one can distinguish mnongat least the following types of delegation: -pure executive delegation Vs open delegation; - delegation Vs non delegation of the control over the action; - domain task delegation Vs planning task delegation ( meta-actions ) - delegation to petfolvn Vs delegationto delegate. Otherlevels of delegation will be analyzedlater in relation with tile levels of help, entitlement, and the formalization of actions and plans. Levels of adoption 1) simple help: tile contractor adopts exactly what has been delegated by the client (simple or complexaction, etc.); 2) overhelp: the contractor goes beyond what has been delegatedby tile client withoutch,’mgingtile client’s plan. 3) critical h~lp: the contractor fulfils tile results of tile requested plan/action, but modifiesthat plan. 4) hyper-critical help: the contractor adopts goals or interests of tile client that the client himself did not take into account: by doing so, the contractor does not realize the action/plan nor the results that weredelegated. The contractor can modify the delegated task for several reasons: - Impossibility: x cannot be done or its preconditions do not hold; . Inability: tile contractor is not able to do x; -Inappropriateness: unlike the client, the contractor believes that x is not useful for tile goal; tile contractor thinks that tile intended task cannot produce the expected results (somethnes,the client’s plan is evenself-defeating); - Optimization:according to the contractor there is a better wayto achieve tile client’s goals and/or interests; - Conflict: tile contractor thinks that x could dmnageother goals or interests of the client: those that the client did not take into accountin his planning; -Personal Preference: the contractor subordinates his adoption to his own preferences or interests which mc in conflict with tile tasks. In this work we will not consider this case: we just consider fully cooperative cases; if the contractor changesor refuses the task, this is just for the wellbeingof the client. Contractor’s critiques of the delegation (request) can aimedto safeguardvarious goodsof the client: a) the expectedresult of the requestedaction; b) somehigher goal of that action in that plan; c) someother active goal of the client; d) someclient’s goal, the client itself did not consider; e) a client’s interest; 39 a goal of the role the client is holding; g) a goal~interestof a third agent the client is representing; h) sonuegoal of the organizationthe client is acting in~for. Although(f), (g), (h) are very important points for CSCW and organizations, we will not analyze them here. Let’s just put this question: whena software agent B helps another software agent A whichacts on the behalf of a user, shouldit care onlyof A’s request or also of user’s interests? Plan Ontology In tiffs section we will introduce a formal representation of agents and actions, and in particular a theory of the relationships betweenactions and results, whichwill be the basis for a moreprecise analysis of delegation and adoption levels¯ As in [3,4] we consider the mappingfrom Kautz’ plan hierarchies [5] to context-free grammars. Basic Notions Let Act={ 0q ..... ~} be a finite set of actions, let Agt={ A~, .., A~,B, C.... } a finite set of agents. Each agent has an action repertoire, a plan library, resources, goals, beliefs, lnotivations, interests. The general plan library is FI = FP U FId, where U~ is the rule set con’espondingwith tile abstraction hierarchy (is-a relation) and FId is the rule set corresponding with the decompositionhierarchy (part-qfrelation). As usual for each action there are: body, preconditions, constraints, results¯ Wewill call a a composedaction (plan) in YI if there is in YId a rule: a --> a~ ..... t~,. Tile actions ot~ ..... ~n are called comlxmentactions of ct. Wewill call a au abstract action (plan) in rI if there is YPa rule: ~ --> {tj. a~ is called a specialized action of a. Anaction ct’ is called elementaryaction in FI if: 1) there are no rules in a l ike: ~’ - -> aj . .... oq and 2) there are no rules in I’P like: a’ --> Wewill call BAct (Basic Actions), the finite set elementary actions in FI; BActCAct. Wewill call CAct(ComplexActions) the set of actions Act which do not belong to BAct: CAct = Act - BAct; Given~l, a2 mid I-I, we will say that £t~, dominatesa, (or ct, is dominated bYa,) if there is a set ot rules (r~ .... r~) in such that: (oq = Lr~)A(Ot2~ Rrm)^(Lrl~ Rri.l) where" the left part and the " Lr. j and Rr, are, respectively, ~ , ¯ right part of tile rule r~ and 2<~<m. Wewill say that ct~ dominatesat level k a, if the set (r~, .., rm) includesk rules. We will call Act^, the set of actions known by A. ActAC_..Act.The set of tile not reducible actions (through decomposition or specification) included in a (the A’s plan library) is composed of two subsets: tile set of actions that A conceives as elementary actions (BAct^) and the set of actions that A conceives as plans but for which he has not reduction rules (NRActA:Non Reducedactions). Then BAct^CActbut it is possible that BActACBAct. In fact, given an elementary action, an agent knows(or not) the body of that action. Wewill call skill set of an agentA, SA, the actions in BActA whose body is known by A (action repertoire of A). SA.~CBACtA. USAi(on all AiE C BAct, then it is possible that for someaction o~e BAct, there is no agent, AjEAgt such that ae SA,. Act=UACtAi (on all ~e AgO:for each actibn a in Act, there is at least one agent ~e Agt such that: Ai knowsabout a. To execute an action ot means: - to execute the bodyof or, if tz is an elementaryaction; - to execute the body of each elementary action to which a can be reduced (through the rules in FI), if a is not elementary action; If an agent A does not know how to execute an elementary action t~ then it does not knowhowto execute any plan a’ in HA with: i) (dominate a’ a) ii) all reductionrules of ct’ ill A containing ait self. A simplification factor is: given any two agents A and B and any elementary action a, with aeSAand a~Ss: the body of ot is the same for A and B: an elementary action cannot be performedin different ways. Fromthe previous assertions follows that an action tx can be an elementary action for a given agent A and a plan for another agent B. This is true when: ((~E BActg)^(aE CActa))v ((ae BACtA)^(txeNRActB))v ((a~ SA)^(C~ NRActQ) Again, the same plan a could have, for different agents, different reductionrules. Agents execute actions to achieve goals: they look up in their memorythe actions fitting the goals, select and execute them. Wewill say that an agent A has complete executable knowhowof an action ~ if either o~ S~ or in rI A there are a set of rules (r~ .... r m) able to transform tx in t~ .... otk with oq~ SAfor each l<i_<k. The operator CEK(A,a)returns (r~, .., r~), then CEK(A,a)~0(0 is the empty set) when complete executable know-howof a. It is possible that CEK(A,a)returns several sets of rules, one for each different wayto reduce c~ in elementmyactions of A(all included in SA). Fixed someworld states c, we will call R(tx,c) the operator that, whenapplied to an action a and to c, returns the set of the .r¢svlls produced by a (when executed alone). will assume that changing the world states in which an action is applied, its results will change and changes the nameof the action itself. ThenR(cz,c) maybe denoted with R(a) because c are defined in a univcxlue way. Wewill call c the conditions of an action and they represent the preconditionsplus the consu’aints of the action itself. An action ~ can be executed if preconditions and constraintsof o~ are satisfied. Wecan distinguish two kinds of conditions: Execution conditions Ec(a) and Success conditions Sc(ct). If formerare satisfied then o~ can be executed; if the latter are satisfied then a, whenexecuted will succeed. Wewill call Pc the operator that when applied to any action a returns the set of the preconditions of o~ (either ce Ep(a)=the set of precondition included in Ec(a) c~ Sp(a)=the set of preconditions included in Sc(o0): Pc(t~)=Ep(ct)USp(c0. Given a multi-agent world, we will call constraint a condition c of ot (either ce Ec(o0or ce Sc(cL)) such that agent has in its action repertory an a’ with cCR(a’). Cn(tx) is the set of constraints of or. If 3cl ce Cn(ct)A(c=false) then o~ is not executable with success. Wewill call P(ct) the conditions of c~.P(a)=Pc(a)UCn(c~). Anaction a realizes g whenthe world states characterizing g are a subset of the a results: g..~R(a). Theory of action results Wewill call R^(a), the results that A believes a will produce when executed. In our model RA(a) might (or correspond with R(~). Whenan action has been executed each agent in Agt has the same perception of its results: exactly R(t~). This semplification produces a transparent world- a unique point of view - regard to the action results fromall the agents. Wewill assume that for each action a (with (ae Act^) (t~e ActQ)it is true this default belief: (Bel A (RA(a)=RB(a)=R(a)))^(BelB (RB(tx)=R^(a)=R(a))) Wewill call relevant resul|,s of an action for a goal (set of world states), the subpart of the results of that action which correspond with the goal; more formally, given a and g, we define the operator Rr such that: Rr(a,g)={giI gie g} if g..~.R(o0, =0 otherwise. Then, the sameaction used for different goals has different relevantresults. The agents "memorize" one (or more) goal for whichthey makeuse of the actions. It is possible that different agents associate different customarygoals to the same actions. Weintroduce the operator Ga (Goal association), such that Ga(A,tx) returns the customarygoal g associated by A to a: Ga(A,a)=g; Whenan agent (A) uses an action (o0 to achieve a subpart of the results (g’) of that action whichare not included the action customary goal (g), then the agent make imorooeruse of the action. g CR(a), g CGa(A,a)=g Wewill assume that to each plan it is associated a goal (plan goal). This goal is the goal that the plan constructor has frozen in the plan structure itself. In a plan, then, the goal associated to the plan corresponds with the relevant results of that plan towards that goal: Ga(A,tx)=Rr(a,g) for each Ae Let us suppose that a is a component (or specialized) action of or’ for g (Rr(t~’,g)~0); wedefine pertinent results of t~ in a’ for g, Pr(a,a’,g), the results of a useful for that ph’mo~’ towards the goal g; they correspond with a subset of R(t~) such that: 1) if a is a component action of o~’: Pr(a,a’,g) = {ril(rie R(a)) ^ ((rte Rr(a’,g)) v ((ri=P(a~)) (dominate-level-1 o~’ a~))) 2) if tx is a specializedaction of a’: Pr(u,a’,g) = {ril(r~e R(a)) ^ (3r~l (qe Rr(ct’,g)) specializationof rj)}; Let us define temporaryresults of an action a in a plan 0t’, the results of a that are not results of et’: Tr(a,a’) = {r~ I(r~e R(o0)^ (ri~ R(a’)))}. Wedefine transitory results (or pertinent temporaryresults) of an action t~ in a plan a’ towardsthe goal g: TRr(a,a’,g) = Tr(t~,0t’) ^ Pr(a,o~’,g) they correspondwith those results of tx that enable another action a~ in ct’ but that are not results of ~’ towards the goal g: TRr(ct,a’,g) = i I (l ie R(t~)) ^ (r i~ R(a’)) ^ (r i=P(a,)) ^ (dominate-level-1 a’ t~)}; Let us define relevant results of a in ct’ towardsg: lh’(c~,tx’,g)= { r~l(r~ R(o0)^(ri~Rr(a’,g)) We,also can write: Rr(a,oC,g)=Pr(o~,a’,g)-TRr(a,a’,g). whereTRr(o~,a’,g)C.~Tr(ot,a’). The pertinent results of an action o: in t~’ representthe real reasonfor whichot is in or’. Wewill call two plans: - synonymousa¢lion~: when they have the same reduction rules and the same conditions (then they necessary have the sameresults); - equifinal actions: whenthey havedifferent reduction rules but they have the sameresults. If a plan a’ is used in an improper wayby the aggnt A, for exampleto achieve the goal gl instead g, where: g~={~l(gieR(0t’))A(g~~ Rr(ot’,g)) then the pertinent results of the component(or specialized) actions in or’ are not relevant results towardsgl. It follows that, if an agent uses a plan in an improper way, some actions included in the plan (in the case of composition rule) are superfluous actions: i.e. their results are all and only pertinent results. Another point is that the results associated by an agent A to an "isolated" elementary action oq, Ga(A,a~), could not correspondwith the pertinent results of a~ in or’ towards g, that is to say: Ga(A,oq)~Pr(a~,a’,g); in some cases could be that Ga(A,~)~Pr(oq,a’,g). Wewill say that there is a goal/subgoal (structuraD relationship betweentwo goals gi ,’rod gj if there are two actions oq %, such that: gi C.Rp(a~,%,gj). The goal/subgoal (deep) relationship between goals expresses the deep reasons because it is possible to reduce an action in a particular way. Anagent able to individuate these reasons is an agent that has a causal view of the actions [6]. There are four kinds of relationships; given twogoals gk gj, we have: - g~ implies gj; - gkcausesgj; 3gI I (gi and gk) causegJ;o 3ore Act I gk Enable ~,j that is to say (gk = P(ot)) (gj~ R((x))); Control Action For each action a, it is possible to plan another action - a meta-action that we will call Control - such that its result is to verify: a) that cx has beenexecuted;b) that the results of a correspond with the expected results; c) howct has beenexecuted (this applies only if a is a complexaction). Givenan action cx, the conu’ol action over ~ is an action of an agent A aimed to match the expected results of ot with its actual results: (Control A ot)=(Verification by A that (RA(a)= R(ct))). In fact, to verify (RA(ct) = R(ot)) permits to satisfy: point (a) becausea necessaryresult of ot is that its bodyhas been executed; obviously the point (b); and the point (c) because controlling how an action has been executed correspondsto controlling points (a) and (b) relative to componentactions. Motivations and Interests of the Agents Each agent A has a set of not instrumental goals: we will call ~ these goals and GA the set containing them. Each time an agent is pursuing a plan through the rules in its plan library (see [6] to distinguish betweento pursue and to knowa plan), the root of the tree in the plan is in GA,i.e. the plan is motivated. It is possible that a motivation g (g~ GA)is not a root any tree producibletltrough the rules in YIA (in other words, not always for a motivation the agent knows a plan to achieve that motivation). Viceversa, it is possible that someof the root of the tree producible through the rules in HAare not included in G^(in other words, the plans known by an agent not necessarily are motivatedfor that agent). Wewill call active plans of an agent, the plans in its workingmemory:those plans that the agent is considering to execute or to decide if they should be executed. WhenA uses an action ot towards a goal g, it wants the relevant results of that action for that goal: Rr(ogg). Wewill call interests of an agent A [7], I^, the set of world states that, if true, allow the achievementeither of some motivation or of the results of someaction A is using. We can say that if A believes iela, then A wants i. The interests of A are in part motivations of A (the interests whose A is aware) and in part potential motivations of (the interests whoseA is unaware). Delegation Delegationis a "social action" [7], and also a meta-action, since its object is an action. We define the Delegation action with 4 parameters: (Delegates A B x d), whereA,B~Agt, %=(a,g), d=deadline; This means that A delegates to B the task % with the deadline d. In the following we will put aside both the deadline of x, and the fact that in delegating x A (very often) implicitly delegates also the realization of ct preconditions (that normally implies someproblem-solving and/or planning). Kinds of delegation in relation to the task Dependingfrom the representation of x in A’s knowledge, we can characterize various types of delegation: - pure executive delegation: when either ct~ S^. or ota BActA,or g is the relevant result of a (and ore S^ or ore BActA). - open delegation: either ot~ CAct^, or a~NRAct^;and also when g is the relevant result of ot (and ore CActAor me NRActA). WhenA delegates not only x but also the rules that decomposeot in actions, we have delegation-with-rules: (Delegates A B (x; r, ..... rm)) where r~ ..... rm are the reduction rules of ot in otj ..... Otn, and r~e FI^ for each l<i<m. There are two subcases: one executive when for each %with l___j___n, (aje SA)v(oqeBAct~);the other or)en where B tx, with l<j<n, such that (otje CAct^)v -" (%e NRActa). Notice that x can belong both to the domainor to the metadomainof planningt,’tsks. hnplicit aspects of delegation produce various possible misunderstandings amongthe agents. Whenan agent leaves hnplicit parts of its request (delegation), in fact she is also delegating the task qf reconstructingthat implicit parts. To delegate an action ot the client have to knowat least some results of ct, since the request/expectation of an action necessarily implies the expectation of at least one of its results (see PostulateII). Levels of adoption w!thin and beyond delegation Since Adoption can be unilateral and spontaneous, or can be "critical", it can go beyondthe request and the delegation of the client. In other words, B can adopt some of A’s goals independently of A’s delegation or request. This create an interesting problem: what kind (or level) of goals can adopt beyondthe possible request-delegationof A ? This problem is well knownin conversation theory [8]. For exmnple what in question-answering domain people call ’,gver-answering"is exactly a sub-case of this problem. By definition an "over-answering"is an answer to a certain request (of information) that goes beyond the required information (ex. "What time will the train from Roma arrive?" "It will arrive at 4 p.m. on rail 4"). Moreover,the additional information is supposed to be useful for the client, i.e. it is supposed to satisfy someother of her current goals: the "over-answer"should be "cooperative" (in Gricean sense) not irrelevant. Thus, the over-answering contractor should have a modelof the plan and goals of the other agent. Exactly the same problem can be found in any kind of "cooperation" or help (goal adoption): also when A ask B for a practical action, B can "ovcr-an,~ver" . Going beyond the request opens different possibilities (dependingon what kind of goal B is adopting): a theory needed about these levels of adoption that characterize different kinds of "over-answering"[9] and different helping relations and roles amongagents [7]. In our view, nugdeling and reasoning about the other agent are not necessary only in case of belief or goal conflicts (like in our "critical" and "hyper-critical help"), but also when there is full agreement and cooperation that goes beyondthe delegation (we call this case "overhelp"). Levels of adoption/help Weidentify several levels of help of B, starting from the general condition: (Delegates A B "t=(c~,g))with dominating ~, where A delegates x within x’=(cx’,g’). i) conservative help: ia) simple help: (AdoptsB x); ib) subhelp: (Adopts B Xl) ^ (dominates a al); in other words, B does not satisfy the delegated task. Ex,’unple in conversation: A: "Whattime is it?", B: "I don’t know".A’s subgoal that B answers, is satisfied, but the goal (to know the time) is not; ic) overhelp: (Adopts B -c~) ^ (dominates o~ co) (dominates-or-equal a’ at). Ex~unplein conversation: "Whattime is it?", B: "Be cahn, is 5pro and our meetingis at 6pro, we are in time". Both, the delegated action (to inform about time) and the higher, non-delegated results (plan) (to knowwhether we are late or not; to not anxious) are adopted and satisfied by the contractor. Practical example: A asks B to prepare the sauce for the ravioli she will prepare for dinner, madB prepares both the sauce and the ravioli. ii) critical help: (Adopts B g); since (Adopts B g) it sufficient for B to find in Act~an action oq whatever, such that gC_R~(o~). Critical help holds in the followingcases: a) (CEK(B,a)--0)v(g~:R~(a))v(P(a)=false); that B either is not able to execute a or, on the basis of his knowledgeon action results, guesses that g is not mnong the results of or, or the conditionsof o~ ,’ue not true (and he is unable to realize them). Con’espondinglyhe must guess that there is an aclion o~ , sucl~ as: (CEK(B,a,)~0)^(g.~R~(a,))^(P(tx,)=true); in other finds another wayto realize g, using another action ~x, such that: B is able to realize it, the new action contains g amongits results and its conditions,are satisfied. b) B thinks that the other results of a (beyond g) are conflict with other goals - in plan or off plan - or interests of the client. Onthe other side, he thinks that there is an action a, with: (CEK(B,ct,)~0)^ (gC_R~(c~,))^ (P(a,)=true) and the results of oq are not in conflict with olher goals or interests of the client. c) There is again the case of optimization, where the conditions in (a) are all false but there is an action ~, such that g is reached in a more profitable way(relative to any criterion). iii) critical overhelp: it is a mixed case in which there are overhelp and critical help at the same time. Given (AdoptsB g’): a) Pr(a,a’,g’)---0 and at the sametime (3a,e Act, I Pr(a,,cx’,g’)~0 ^ CEK(B,cx,)~0 ^ P(oq)=true). other words,there are not pertinent results of o~ in or’; but it exists at least an action ¢x, whichis pertinent in or’ towards g’. This meansthat o~ is unuseful for x’. It is even possible that it is noxious: i.e. that R(cx) produces results that contradict those intended with x’. Ais delegating to B a plan that in B’s view is wrongor self-defeating. b) Pr(a,cx’,g’)~0 ^ CEK(B,o0~0 ^ P(o0=true and in addition (3 ¢x,e Act. I CEK(B,a)~0 ^ P(oq)=true ^ Pr(Qt,,cx’,g’)~’0), moreover bl) R(cx~)achievesthe go,’ds internal to the plan (i.e. g’) in a better way(maximization). Example:A asks B "to buy second class train tickets for Naples"(action a) for her plan "to go to Naplescheaply’,’ (action o~’). B adopts A’s goal "to go to Naples cheaply (goal g’) replacing the wholeplan (o~’) with another plan: "go with Paul by car!". b2) R(oq)achieves not only the goals of the plan (i.e. but also other goals of A external to that plan (ex. g"), other motivationsof A: (g’ C R(a,))^(g" C: R(oq)). Example:A asks B "to buy second class train tickets for Naples"(action a) for her plan "to go to Naplescheaply" (action ~x’). B adopts A’s goal "to go to Naples cheaply" (goal g’) replacing the whole plan (a’) with another (o0 "to go with Paul by car" that satisfies also another motivation of A - that she did not consider or satisfy in her plan - but B knows:"to travel with friends". b3) R(oq) achieves not only the goals of the plan but also someinterests (i) of A: (g’CR(~,)) ^ (iCR(a,)). Example:A asks B "to buy second class train tickets for Naples" (action ~) for her plan "to go to Naples cheaply" (action ¢x’). B adopts A’s goal "to go to Naples cheaply" (goal g’) replacing the wholeplan (¢x’) with another (~,) "to go to Naplesby bus" that satisfies an interest A of "not risking to meet Paul that she ignores to be on the s,’une train". iv) hypercritical help: (Adopts B g,) where g, is interest (or an off-plan goal) of A moreimportantthan g’ (we leave here this notion just intuitive). Since there is a conflict betweenthe result R(~) (and/or the result R(a’)) and some of A, to adopt g, wouldimplyto not obtain R(ot) (or R(ot’)). Thereare subcases: a) (B knowsthat there is a conflict betweeng, and g’) and believes that g, is better than g’ for A) and (A does not know that there is a conflict betweeng, g’), g, is an A’s off-plan goal; b) (B knowsthat there is a conflict betweeng, and g’) and believes that g, is better than g’ for A) and (A knowsthat there is a conflict betweeng, and g’) and (A believes that is better than g,); A and B have different evaluations about the hnportanceof g’ and g,; c) (B knowsthat there is a conflict betweeng, and g’) (B believes that g, is better than g’ for A); g, is an A’s ignored interest, then Aignores the conflict with g’. Agent modeling In this section we will analyse the main aspects of agent modeling on the basis of the delegation-adoption relationship. In particular we examinewhichmodelwill the client have of file conlractor since (DelegatesA B x), and, viceversa, which model will the contractor have of the client since (Adopts B A x). In both cases, depending the believes about x, specific goals or competencies are attributed to the other agent. Such a modeling of the other agent is constructed on different bases: a) previous experience of the other’s behaviour (if B once was able to do x, A assumes that B is able now; if i once was an interest of A by default it will be again so); b) an explicit declaration of the agent 03 declared to A to be able to do x; A explicimtedto B the goals that motivate x); c) an implicit communicationof the agent (B declared to that he intends to do x, that implies that he is able to do x; A asks B to do x, that implicitly informs B that A is not able to do x); d) attributions to the category or role the agent belongs to [10] (if B belongsto a class of agents that are able to do then also B is able to do x; if A belongs to a class of agents that have the motivation g then also A has such a goal g). We will not examine how the agent models the "willingness"of file contractor[1 1 ]. A modeling x It is possible to predict different needs of agent-modeling, from the two different structural positions in the contract relationship: ¯ Basically, the client should modelabilities and reliability of the contractor; he will only exceptionally use plan and intention recognition. ¯ Indeed, the contractor, in general does not need to model client’s capabilities, while (in deep cooperation) he needs modelingquite well client’s plans and goals; thus he will apply PR and Intention Recognition. This asymmetryhas, of course, someexception: - sometimesthe contractor should modelclient’s abilities to better realize his help (consider overhelp due to the necessity of realizing tasks that the client did not delegate but is not really able to do, (example:ravioli); consider underhelpdue to the fact that the client is able to do part of x, and B leaves her to do i0; - sometimesfor the client is useful to apply PR on the contractor activity, for examplefor monitoring his task execution whenshe did not delegate also the control (we do not consider monitoring problem here [12]). PR is also necessary in weak delegation, where A must exploit B’s autonomousactivity and intentions without any agreement. A modelin~ B ix~ SB^ (Delegates B C ix) CEK(B,IX)go CEK(B,IX)=0A 03 reduces-and-execu~x(part-of ix))A(DelegatesB C (rest-of with ix=(pm~-ofix)U(rest-of (ixje SB)A((r~,.,rm)~CEK(B,Ix)) (ixi~ SB)A (r~,.,rm)~ CEK(B,IX)(with l<i<n) But there are other different reductions in CEK(Brc0 (ixe Sn)^ (ix~ CAct~)A(gc Ga(B,ix)A (gCGa(B,ot)) CEK03,IX’)=0A (Delegates B C ix’)) with ix’=(part-of ix) nonexecutable from B (3ix~ SBI (3cq e CActB)A(gCGa(B,IX,)A (gCG~l(B,cq)) CEK(B,cc’)=0A(DelegatesB C ix’)) with ix’=(part-of ix~) non executable fi’om B (Delegates B C g) (3ctl(ae SB)^ (3al(ixe CActB)A(gCGa(B,cz)A (g CGa(B,ct)) CEK(B,c0=0A(DelegatesB C to’)) with ix’=(part-of ix) nonexecutable from B Table 1 ixE Sn x=ix;r, .... , r mare the reductions rules for ix in ixt ..... ixn with (ix~ CACtA)^ ((0~E SA)v(oqeBActa)) x=g with (3ixe ACtAI (gCGa(A,ix)) l’c=g with (Vote ACtAI (not (gCGa(A,c~))) ((ix~ SB)v(ix~SB))^ (Delegates B C ix) ((CEK(B,IX)go)v (CEK03,IX)=0))A (Delegates B C ix) (DelegatesB C ix;r,,.,rm) (ix~ CActB)A (gCGa03,ix)^ CEK(B,ct)go) (3ix~ CActB)A (gCGa(B,ixl)^ CEK(B,IX,)go) (3ixl(ixe CActB)A (g CGa(B,ix)A CEK03,IX)gO) motivations of the client wouldbe possible on the basis of the true plan library of the client herself. Lackingthis, the contractor works on his ownplan library to recognize the plans of the other! In other words,the contractor practically and by default assumesthat his plan library is shared. The contractor is normally supposed to be more expert about the delegated task (to have a richer or more correct plan-library) than the client (how/why to delegate othe~vcise?)or to have more"local" mid specific knowledge. This is in general true for the plans dominatedby x, not for plans whichdominatex. It follows that in certain cases the contractor could have expertise-problems in understanding the client’s higher plans (for ex. soldier-general relationships); and, viceversa, that the client could have some problems in monitoring the executive plans of a Modeling the "client" For "simple adoption" the contractor does not need modeling the client: he must just to understand the task (request). Indeed, as we said, deeper levels of cooperation require to go beyond the request. Thus modelingclient’s plans, goals, motivations, interests, is necessary. Above, the various adoptionlevels wereillustrated; at each level it was already apparent what aspects of the client the contractor should model: if he has to ascribe her certain goals or interests, and recognizeher pl,’ms, in order to adopt them. A very important problem is the following: how can the contractor recognize client’s plans in which delegation (~) is inserted? The ideal recognition of the active plan and 6 more expert or "local" contractor. In a complete theory of delegation types, one should distinguish betweendelegation of tasks in whichthe client is as expert as (or moreexpert than) the contractor, and delegation of tasks to an expert agent. Modeling the "contractor": trust Client’s modelof the contractor has mainly to do with his competenceand willingness [11]. In particular, the model of competencies is relative to domaincompetencies, meta or planning-competencies, control capabilities and capabilities for sub-delegation; instead, the modelof the willingness is in relation with goals, commitments,and reliability. WhenA attributes to B the capability to sub-delegate to the agent C, A attributes (and delegates) to B also the capability of modeling C. Given (Delegates A B x), A should believes about B that: a) when x=a: - either CEK(B,a)~’O - CEK(B,a)=0, but B can sub-delegate to an agent C the part of the task he is unable to execute or decomposeor - in both cases - CEK(B,a)¢0or CEK(B,o0=0 - B can subdelegate to an agent C; b) when x=g: - either there is in ActBan action ot such that gC R(a) [to go back case a) about a]; - or there is not in ActBan action ot such that gCR(a)but (Delegates B C g) - in both cases - such an a exists or not - B can delegate g toC. For a moredetailed analysis see table 1. In this table for each raw, the first columnindicates the modelingof x by A, the following columns indicate the corresponding possibilities of the modelingof B. Cases with x=(a,g) are omitted becausetheir results are just the combinationof the cases with x=a and x=g. Competeneies and abilities As we said a fundamentalrole is played by the modelingof abilities and expertise of the other agent. In particular, in our approachit is critical the knowledgeof the plan library of the other agent. In our model knowledgeabout actions and rules (plans) can be distributed mnongthe agent, in hierarchical way. Wemean that there are plans and/or actions that can be ascribed to any agent (universal competence); others that can be ascribed to sub classes or categories of agents (like roles in organizations) that have specialized expertise or skills (class competence);others that pertain only to certain agents (personal competence). This is classical approach to the User Modeling[10] that can be applied to actions and plan libraries in agent modeling. Notice that such a plan-ascription is fund~unelmdboth for modelingthe contractor’s competenciesand for recognizing the client’s plans. Conflicts between delegation adoption and In this section we do not consider the possible conflicts arising from the delegation of Control action. Delegation and Entitlement Postulate: If A delegates B the task r, then A, implicitly or explicitly, entitles B to r. Wewill say that B is entitled by A to "t through the delegation (Delegates A B x), when Iherc is common(to and B) knowledgethat A is committed to not oppose, to not be astonished, etc., if B pursues x [2]. An agent B can be entitled beyonddelegation. Let us define over-entitlement the case in whichan agent A (or the role or the organizationof B) entitles lhe agent B an overhelp, or to a critical help or to a critical overhelpor, at last, to an hypercritical help. The over-entitlement can be: - explicit (explicit request from Ato B to care of morethan the delegatedtask); - implicit: in r (for example, the task delegated is obviously incomplete or inadequate); in role of B (the delegation implies a completionin the role of B). Discrepancy and Conflict There is correspondence between delegation and adoption when: (Delegates A B x)^(Adopts B A x) and the agents A and B have the same interpretation of x. Whenthere is discrepancy (that is to say the above correspondenceis not true) there could be present delegation conflicts. There is delegation conflict each time: - B interprets the delegation in different way from A’s interpretation (misunderstanding)or - there is discrepancy and B adopt beyondthe entitlement. Howeverwe are considering only "cooperative conflicts": conflicts starting from the cooperation between A and B; conflicts that B could produce because of his owngoals are neglected. Also, conflicts that rise because A believes B non cooperative about the task, are neglected. Correspondence between delegation and adoption is not always the best help by B to A, neither, sometimes, the wantedhelp. In the great majority of cases a good help needs planning ability and overhelpor critical help. It is a general case that A delegates B to x but entitles B beyondx itself, and A has the expectation that B will do it. Starting from the different cases of delegation, we will describe the mainconflict classes: - conflict on the kind of task: the client thinks to delegate a certain kind of task (for example, pure executive task) on the contrary she is delegating a different kind of task (for ex,’unple an opentask); - conflict on the possibility to sub-delegate x (or a subpart of x); - conflict on fl~e metaleveldelegated competencies; - conflict on the contractor’s entitlenl¢lll: this conflict is present when the client thinks to have entitled the contractor more (or less) than it is deducible from delegation or from explicit or implicit entitlement. client’s pov correspondin~contractor’s point of view "c=cxwith 0t~ SBA(0teCActB) ot~ SBA(OteNRActe)^ (ae SA) (not 3CI Conflict on the task (Delegates B C a) Error o[delegation x=a with ae SB^(ae CActB) ~ Ss^(ot~ NRActQA (cte BActA) (not 3CI Conflict on the task (Delegates B C or) Errorof delegation "c=otwith 0rE SB (aa NRActA) Conflict on the task Table 2 ii) Theselevels are related to the hierarchical structure of plans or tasks. iii) There is a non-arbitrary correspondencebetweenlevels of delegation and levels of adoption; we called "contract" this relation. iv) A "deep" cooperation needs understanding of plans, goals, and interests of the oilier agent or user. v) A task delegation needs a representation of practical and cognitive abilities (and resources) of the delegate; wecalled this representation:"trust". vi) There is a fundamental distinction between the delegation/adoptionof: a domaintask (practical action), or planning or problemsolving action or a control action. vii) There could be several conflicts due either to some misunderstanding of the delegation, or to mismatch betweendelegation and help, and viceversa. In table 2 are considered the conficts on the tasks (pov means point of view). Wewill consider nowthe different kinds of conflict on the basis of various cases of adoption shown above. cl: P_~, this is the conflict rising in the subhelp case where the client delegates a task and the contractor adopts a subpart of the task. In the overhelp several possibilities of conflicts can rise; starting from (Delegates A B x) [intending that the delegate of x is in the context of a wider task x’, with (dominatescz o~’): wewill call this situation (DelegatesAB "c (in x x’))]: c2: There is conflict when (Adopt B A x~ (in x x~)) A (not-dominates x’ (dominatesxl x) A (~’~l X’) A (CEK(B,0q)¢:0) either because of a misunderstanding (for exmnple, the contractor supposes that in some interaction the client communicatedit information about x~, or in the client’s modelby the contractor it is supposedthat g~ is a client’s goal, that is to say gle G^, etc.) or becauseof ~lifference of knowledge(for exmnple,in the plan libr,’u’y of the contractor there is not the reductionrule froma’ in c~, etc.). In this case the "over-part" of the plan that B adopt could be superfluousor quite deleterious. Superfluous,if the over-part is not useful in ct’, but it does not lose any useful result of cz for ct’, more formally: Pr(cz, a’,g’)CR(cq). For example: A says B: "Whattime is it?" and B answers A: "Quiet, it is 17.00 o’clock, the conference will start at 19.00 then we will arrive in due time". But, actually A asked B the time because it had a telephone appointment. Deleterious, whenthe over-part not only it is not useful in c~’, but it loses someuseful result of cz for cz’, more formally: Pr(ct,o~’,g’)~R((x~) and because Pr(0t,o~’,g’) Rr0x,ct’,g) U TRr((x,ct’,g) then 3r I (re Rr(ct,cz’,g)[it relevant result of o~ in cz’ towardsg]) v (re TRa’(cz,(x’,g) is a transitory result of (x in cz’ tow,’u’ds g]) A r~ R(ct,). Thenr is a temporaryresult of ct in cq: re Tr((x,cq). For example: A asks B to make-pesto; B (believing that wants to realize the plan make-spaghetti-pesto) makes spaghetti-pesto. Actually A wants make-tagliatelle-pesto. Anothercase is whenin c2, also action ot is changed. c3: In the overhelpevenif there is not conflict like in c2, it is possible an entitlement conflict. c4: A special misunderstandingwithout conflict is: (Adopt B A xl (in x xl) A (in Xi X2)) A (not-dominates x’ (dominates x2 x~ x) ^ (dominates z’ "r~ x) A (CEK(B,cq)*0). In this case, the contractor (B) adoptsan overplanof ct, (xi, that he considers useful for an extra overplan (z2 not considered by the client (A). In this operation B adopts the overplancq that is useful in the overplanct’ too. c5: In the case of critical help there is a conflict whenRB(ct) not correspond with g; then whenthe contractor changes ct in (Zl this substitution is chosenstarting fromthe results of (x, RB(ot), instead of g. B is finding an action cz~ in ActB such as: CEK(B,cz~),:0,with RB(a)CRB(fz~). c6: In the hypercritical help there is conflict whenthe A’s preferences are different from the preferences A must have according to B. Given gl~ GA,g2~ GA,then A prefers g, to g2, and B thinks that g2 must be preferred to g~ by A. Acknowledgements Wewouldlike to thank Fiorella De Rosis for her precious remarques. References [1] Cohen, Ph. & Levesque, H., Intention is Choice with Commitment. Artificial Intelligence, 42(3), 1990. [2] Castelfranchi, C., Commitment: from intentions to groups and organizations. In Proceedings of ICMAS’96, S.Francisco, June 1996, AAAI-MIT Press [3] Falcone, R., Castelfranchi, C., CHAPLIN:A Chart based Plan Recognizer, Proceedings of the Thirteenth International Conference of Avignon, Avignon, France, 2428 May, 1993. [4] Vilain, M., Getting Serious about Parsing Plans: A GrammaticalAnalysis of Plan recognition. In Proc. of the 1JCAI, 190-197, Boston, 1990. [5] Kautz, H. A. (1987). A Formal Theory of Plan recognition. PhDthesis, l~hfiversity of Rochester, 87. [6] Pollack, M., Plans as complex mental attitudes in Cohen, P.R., Morgan,J. and Pollack, M.E. (eds), Intentions in Communication, MITpress, USA, pp 77-103, 1990. [7] Conte,R. & Castelfranchi, C. Cognitive and Social Action, UCLPress, London, 1995 [8] Chu-Carroll J., Carberry, S., A Plan-Based Modelfor Response Generation in Collaborative Task-Oriented Dialogues in Proceeedings of AAAI-94. 1994. [9] Poggi, I., Castelfranchi, C., Parisi, D., Answers,replies and reactions. In H. Parret. M. Sbisa’, J. Verschueren (eds.)Possibilities and Limitations of Pragmatics.Studies in Language Companion Series (Vol. 7), Amsterdam:J. Benjamins, 1981. [10] Rich, E. User Modeling via stereotypes. Cognitive Sciences, 3:329-354, 1984. [11] Miceli, M., Cesta, A., Strategic Social Planning Looking for Willingness in Multi-Agent Domains. In Proceedings of the F~fleenth Annual Conference of the Cognitive Science Society (pp. 741-746). 1993. [12] Castelfranchi, C., Falcone, R. (1995), "To say and do" virtual actions in the structure and recognition of discourse plans with regard to practical plans, INTERACT ’95, Lillehammer, Norway,27-29 June, 1~)5. Conclusions Weattempted to show that: i) There are several levels of cooperation - more or less "deep"midhelpful- mid several levels of lask delegation. 8