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.
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Conclusions
Weattempted to show that:
i) There are several levels of cooperation - more or less
"deep"midhelpful- mid several levels of lask delegation.
8