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Formal Constructs
Several formal constructs are needed in the following. Let
Act
=
{
α
1
,..,
α
n
}
be a set of
a
d
,
actions
, and
Agt
=
{
Ag
1
,..,Ag
m
}
a set of
agents
.The
general plan library
is
=
∪
a
is the abstraction hierarchy rule set and
d
is the decomposition hierarchy rule set.
where
α
∈
α
is the
An action
Act
is called
elementary action
in
if there is no rule
r
in
such that
left part of
r
. We will call
BAct
(
Basic Actions
) the set of elementary actions in
and
CAct
(
Complex Actions
) the remaining actions in
Act
.
Given
α
1
,
α
2
and
d
, we introduce the
Dom-c(
α
1
α
2
)
operator to say that
α
1
dominates
α
2
α
2
is dominated by
α
1
)in
d
:
Dom-c(
α
1
α
2
)
=
(or
True
if there is a set of rules
(r
1
,..,r
m
)
in
d
, such that:
(
α
1
=
Lr
1
)
∧
(
α
2
∈
Rr
m
)
∧
(Lr
i
∈
Rr
i-1
)
, where:
Lr
j
and
Rr
j
are, respectively, the left
part and the right part of the rule
r
j
and
2
≤
i
≤
m
(in the same way it is possible to define the
a
). We denote
Dom-a(
Agx
as the
Ag
x
's plan library, and
Act
Agx
, the set of actions known by
Ag
x
. The set of irreducible
actions (through decomposition or specification rules) included in
α
1
α
2
)
operator considering the abstraction hierarchy rule set
Agx
is composed of two
subsets: the set of actions that
Ag
x
believes to be elementary actions (
BAct
Agx
) and the set of
actions that
Ag
x
believes to be complex but for which it has no reduction rules (
NRAct
Agx
:
Non Reduced actions
). Then
BAct
Agx
is included in
Act
and possibly
BAct
Agx
is included or
coincides with
BAct
. In fact, given an elementary action, an agent may (or may not) know the
body of that action. We define
S
Agx
as the
skill set
of
Ag
x
, the actions in
BAct
Agx
whose body
is known by
Ag
x
(action repertoire of
Ag
x
).
20
We call
R
the operator that, when applied to an
action
α
, returns the set of the
results
produced by
α
.
Definition of Delegation and Adoption
The domain of MAS, collaboration (Haddadi, 1996), and teamwork are already familiar with
the notion of delegation. However, our analysis is grounded on more basic notions (Hexmoor,
2000). In addition, our delegation theory is not limited to explaining and modeling interpersonal
relationships; the basic concepts of our definition also apply to (and are necessary even if not
sufficient for) other important concepts such as:
institutional delegation
, in which the delegator transfers to the delegee not just some task
but also some right, obligation, responsibility, power and so on (Jones and Sergot, 1996).
Of course, this notion is richer than our basic concept (see below).
roles and prescriptions in organizations
, roles can be analyzed also as sets of delegated tasks
(Castelfranchi and Falcone, 1997).
In our model,
delegation and goal adoption are characterized in terms of the particular set
of mental states (cognitive ingredients) of the agents involved in the interaction
. Informally,
in
20
In sum, an agent
Ag
x
has its own plan library,
Agx
, in which some actions (
CAct
Agx
and
NRAct
Agx
) are complex
actions (and it knows the reduction rules of
CAct
Agx
) while some other actions (
BAct
Agx
) are elementary actions (and
it knows the body of a subset -
S
Agx
-ofthem).
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