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m
sent
by adding it to
MEM
ego
together with the last received message
m
received
as well
as when receiving a message
m
received
by adding it to
MEM
alter
together with the last
message
m
sent
the agent sent itself. Each time, a tuple of messages is memorized, if this
would lead to a memory size
n
the oldest entry is removed from the memory.
This way to model an agent's memory is an important modification of that by Dittrich
et al. [3], differing in alter not only being considered one single agent, but the whole
community of agents other than ego. This reflects Luhmann's understanding of double
contingency as a phenomenon not restricted to an encounter of two individuals, but oc-
curring between systems in a generalized manner [11, pp. 105-106]. Thus, expectations
may well be established regarding the behavior of the whole MAS, considering it as a
social system. The entries in its memory, therefore, reflect an agent's observations of its
interactions with any of its fellow agents.
Moreover, this interpretation of double contingency between an agent and the whole
agent community allows not only for the content of a message to be selected according
to memorized experience from former agent interactions. In fact, it also enables the
agent to determine a message's receivers (i.e., the interaction partners) in the selection
process. Hence, the advantages of the dyadic model by Dittrich et al. [3] regarding
structural emergence are retained while avoiding the aforementioned drawbacks of its
extension for an arbitrary number of agents.
In order to calculate expectations from an agent's memory
MEM
, the memory access
function
lookup
:
MEM
∗
×
>
1] (with
MEM
∗
denoting the set of all possible
agent memories
MEM
) estimates the probability of one message being observed as the
response to another:
M
×
M
−→
[0
,
l
m
received
,
m
sent
m
j
∈
M
l
m
received
,
m
j
lookup
(
MEM
,
m
received
,
m
sent
)
=
(1)
where
⎩
n
c
M
|
n
+
i
n
·
1
−
1 f
m
received
,
m
sent
≡
mem
i
∈
MEM
l
m
received
,
m
sent
=
|
+
(2)
M
0 e
i
=
1
Here,
≡
is an equivalence relation on the message tuples
M
,
M
×
M
,
M
. Therefore,
mem
i
denotes the pairwise equality of the received and sent mes-
sages, compared to those in memory entry
mem
i
, with regard to their performatives,
sets of receivers, and contents. This is the second major modification of the original
model, allowing for considering advanced message semantics (in contrast to the very
abstract message representation by Dittrich et al. [3]). Especially the content of mes-
sages depends on the application domain. Thus, domain dependent equality measures
(e.g., the distinction of orders for different product types) are required. The constant
c
M
is used to avoid message combinations to be regarded completely impossible in case of
missing observations [3, sec. 9.4]. With
mem
1
∈
m
received
,
m
sent
≡
MEM
being the most recent observa-
tion, this function uses a linear discount model to reflect the agent gradually forgetting
past observations.
Two kinds of expectations are subsequently calculated for selecting an agent's next
message. On the one hand, the
expectation certainty
(EC) denotes an agent's assured-
ness about which reaction to expect from the MAS following its own message. On the
