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a fully autonomous action of Y . For a more complete discussion on the mental ingredients of
the weak delegation see (Castelfranchi and Falcone, 1998).
The expression W-Delegates(X Y
τ
) represents the following necessary mental ingredients:
and its result g )isa goal of X .
b) X believes that there exists another agent Y that has the power of (Castelfranchi, 1991)
achieving
a) The achievement of
τ
(the execution of
α
.
c) X believes that Y will achieve
τ
in time and by itself (without any X 's intervention).
c-bis) X believes that Y intends (in the case that Y is a cognitive agent) to achieve
τ
τ
in time
and by itself, and that will do this in time and without any intervention of X .
d) Xprefers 3 to achieve
τ
through Y .
e) The achievement of
through Y is the choice (goal) of X .
f) X has the goal ( relativized (Cohen and Levesque, 1987) to (e)) of not achieving
τ
τ
by itself.
We consider ( a , b , c , and d ) what the agent X views as a ' Potential for relying on ' the agent
Y , its trust in Y ; and ( e and f ) what X views as the ' Decision to rely on ' Y . We consider
'Potential for relying on' and 'Decision to rely on' as two constructs temporally and logically
related to each other.
We hypothesize that in weak delegation (as in any delegation) there needs to be a decision
made based on trust and in particular there are two specific beliefs of X :
belief1 X :if Y makes the action then Y has a successful performance;
belief2 X : Y intends to do the action.
For example, X sees Y waiting at the bus stop, and - while running to catch the bus - she
counts on Y to stop it.
As shown in Section 6.2, the trustworthiness of Y is evaluated by X using the formula (6.4).
For the sake of simplicity we assume that :
DoT X , Y ,τ,
trustworthiness ( Y
τ
)
(6.9)
In other words: X has a perfect perception of Y 's trustworthiness: X believes/knows Y 's real
trustworthiness.
The interesting stage in weak delegation is when:
)) 4
Bel ( X
¬
Bel ( YW - Delegates ( X
,
Y
)))
Bel ( YW - Delegates ( X
,
Y
(6.10)
in other words: there is a weak delegation by X on Y, but actually Y is aware of it (while X
believes that Y is not).
The first belief ( belief1 X ) is very often true in weak delegation, while the second one
( belief2 X ) is necessary in the case we are going to consider. If Bel(Y W-Delegates(X Y
τ
)), this
3 This means that, either relative to the achievement of τ or relative to a broader goal g that includes the achievement
of τ ,X believes herself to be dependent on Y (see (Jennings, 1993), (Sichman et al. , 1994) and Section 2.9.1 on 'weak
dependence').
4 Other possible alternative hypoteses are:
¬ Bel ( XBel ( YW - Delegates ( X , Y ))) Bel ( YW - Delegates ( X , Y )) or
Bel ( XBel ( Y ¬ W - Delegates ( X , Y ))) Bel ( YW - Delegates ( X , Y ))
 
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