Intelligent Information Management, 2009, 1, 65-72
doi:10.4236/iim.2009.12011 Published Online November 2009 (http://www.scirp.org/journal/iim)
The Specification of Agent Interaction in
Multi-Agent Systems
Dmitri CHEREMISINOV
United Institute of Informatics Problems, National Academy of Sciences of Belarus, Minsk, Belarus
Abstract: The problem of the description of interaction between agents in a multi-agent system (MAS) in the
form of dialogues of negotiations is considered. For formalization of the description of interaction at a level
of steps of the dialogue which is carried out in common by two spatially divided agents, the concept of syn-
chronization of processes is analyzed. The approach to formalization of the description of conditions of syn-
chronization when both the independent behaviour, and the communications of agents can be presented at a
level of logic is offered. It is shown, that the collective behavior of agents can be described by the synthetic
temporal logic that unite linear and branching time temporal logics.
Keywords: interaction protocol, temporal logic, parallel algorithm
1. Introduction
A multi-agent system [1] consists of set of agents that
operate together in order to achieve some goals. Such
system can be considered as the organization of agents
(by analogy to the human organization) or, in other
words, as some artificial society. Protocols play the cen-
tral role in the organization of this society. The protocol
of interaction can be stipulated by the designer of inves-
tigated system, or the agents who are taking part in in-
formation interchange agree about the application of a
protocol before interaction took place.
The interaction protocol of agents defines the rules
that govern the dialogue between agents in multi-agent
system. The central problem of the interactions that took
place in open systems and not being cooperative (dia-
logues of negotiations) is the problem of conformity
check between agent behavior and interaction protocol.
The implementation of conformity check encounters the
trouble what is the identification of steps of dialogue.
Recognition of the step which is carried out by two spa-
tially divided agents jointly, require analyzing the con-
cept of interaction of processes.
The basis of formal models of protocols is cooperating
sequential processes. Fundamental features these models
differ are the degree of synchronization of behaviour of
participants of interaction. This paper is the attempt to ana-
lyze by logic the concept of synchronization in these
frameworks.
2. Formalization of Concept of Interaction
Event
Usually collective behaviour of system of agents is de-
scribed as dialogue of agents which communicate by
means of sending and receiving messages. On each step
of activity the agent carries out some action depending
on the internal state and the received message. As a result
the action changes the internal state and sends messages
to other agents. The collaboration of agents emphasise
autonomy and cooperation (with other agents) in order to
perform tasks for their owners. Collaboration behaviour
of system of agents is unreachable when the agent
doesn’t know anything about individual behaviour of
other agents. Particularly because the agents are autono-
mous and cannot be assumed to be benevolent, agents
must know that others must do to act in certain ways
without requiring that one examine the internal reasoning
(or the source code) of the agents. Speaking informally,
the protocol is formal representation of knowledge of the
agent about individual behaviour of other agents into the
scope of joint task. There is still a need for a proper for-
malism for protocols that is suitable for automated im-
plementation. Suppose we are given a protocol specifica-
tion,
PS . One way of obtaining a concrete agent program
from
PS is to treat it as an executable specification, and
interpret the specification directly in order to generate
the agent’s behavior. If models for the specification lan-
guage can be given a computational interpretation, then
model building can be viewed as executing the specifica-
tion (Figure 1).
This knowledge is inexpedient to treat as parameter of
an agent program from speed consideration. This know-
ledge must be realized by programmer as the agent pro-
gram. In this scheme, we take our abstract representation
of the knowledge, and transform it into a concrete pro-
gram via some synthesis process.

D. CHEREMISINOV
66
Figure 1. Parameters of universal agent
For the specification of agent independent behaviour
are widely used formalisms of high level abstractness,
for example, such as temporal logic. At the same time the
communications between agents is specified by means of
concepts of a realization level, such as mail boxes and
messages. One of problems of such segregated approach
to interactions consists that it is extremely difficult to
model the interactions between agents though the inde-
pendent behaviour of the agent is described completely.
This problem arises due to absence of agent model uni-
fying aspects of independent behaviour and the commu-
nications. The main reason of absence of the general
model is the lack of conceptual basis unifying all ab-
straction, connected with collective behaviour of agents.
The independent behaviour of multi-agent system
agents are characterized by processes. Process is defined
by the full description of potential behaviour of the agent.
The behaviour of process consists of events. Thus, suit-
able axiomatization of concept of event is required for
the analysis of concept of interaction of processes.
The event serves as the concept to abstract from
physical time at the description of behaviour of system.
Widely widespread axiomatization of event is connected
with the assumption, that events have no duration [2].
The behaviour multi-agent system consists of events –
steps of dialogue between agents – and is consecutive in
this sense. For recognition of the step which is carried
out by two spatially divided agents jointly, it is impossi-
ble to bypass the concept of parallelism.
The models of parallelism known in the literature is
possible roughly divided into two classes: 1) models,
in which concurrent execution of two processes de-
scribed by interleaving of (atomic) events of those
processes; 2) models in which causal dependencies
between events are set explicitly. Interleaving models
are focused on systems with events are considered
instant and indivisible. In this case the act of interaction
is complete event which describe participation of all
processes cooperating in this act [2]. This act as the step
of dialogue are carried by two spatially divided agents
represent event which should have duration and
structure.
There is popular opinion the concept of the event hav-
ing duration is reduced to concept of instant event. The
following formulation of these assumptions is taken from
Hoare [3] “The actual occurrence of each event in the
life of an object should be regarded as an instantaneous
or an atomic action without duration. Extended or time-
consuming actions should be represented by a pair of
events the first denoting its start and the second denoting
its finish.”
Now it is known that this opinion is erroneous, and
behaviour in the events having duration is not reduced to
the behaviour expressed through instant events. Mutual
irreducibility the concept of the event having duration to
concept of instant event is proved formally and construc-
tively [4]. The formal proof is based on incomparability
of formalism describing event systems [5]. Systems of
the events having duration are described by the causal
relation (branching-time temporal logic), systems of in-
stant events – relation of consequence and parallelism
(linear-time temporal logic).
3. Structure of Interaction Event
The elementary structure of durational event that is a step
of dialogue is pair of durational events which constitute a
step densely without a time interval between. First event
can be interpreted as “pronouncing” of the message by
one agent; the second event can be interpreted as “per-
ception” of this message by other participant of dialogue.
The basic feature of this structure is the assumption of
density of an event composition and that constituting

D. CHEREMISINOV 67
events belong to behaviour of different agents (Figure 2).
Absence of a time interval between members of pair dur-
ational events designates instant event of synchronization
of processes.
3.1. The Event Model of Synchronization
Abstracting from function of agents, it is possible to con-
sider synchronization of their behaviour as the goal of
interaction. Thus, the step of dialogue is a composition
of th ree events, two events are durational events, and one
is instant event. However constituting event of interac-
tion still remains event which occur simultaneously in
different processes.
Agent 1 Agent 2
Inquiry
Inquiry
sending
Inquiry
reception
Figure 2. Structure of the communication event
Causality
• Waiting operation
• Acting operation
Event
y
Event E
Event E
Event y
Figure 3. Structure of operations
Agent 1 Agent 2
Inquir
y
Inquiry
Sending
Inquir
y
reception
Inquiry
waiting
Synchronization
Figure 4. Synchronization of behaviour of agents
On the one hand synchronization of agent behaviour
occurs during the rare moments. In the rest of the time
communicating agents behave independently from each
other. On the other hand, processes should interchange
information about current states to ensure synchroniza-
tion. Formally it can be reached by splitting of all events
constituting agent behaviour on internal and external
events. Only external events of the agent can be “visible”
to other agents. In this case the specification of the agent
behaviour is the causal relation on set of possible events,
in particular, this relation describe the reasons of occur-
rence of external and internal events.
Let composition durational internal event Е and instant
external event у is operation. A composition у  Е dur-
ational and instant events is waiting operation that wait
external event у, and a composition E  y is acting op-
eration which effect is realization of external event у
(Figure 3). It is necessary to note, that order of events in
both operations is the same: the first goes durational
event, then goes instant event. These compositions allow
to consider dependences between events of a composi-
tion as cause and effect because from physical reasons
event-consequence occurs behind event-reason without
overlapping on time. Waiting operation is durational ev-
ent end reason of its termination is y. Acting operation is
durational the event and the reason of y is its termination.
The symbol “” we interpret as cause and effect de-
pendence between events. Such treatment of waiting and
acting operations is a basis of formal semantics PRALU
language [6] in which conjunction of Boolean variables
describe external event of operations.
PRALU language in this interpretation represents the
synthetic temporal logic uniting linear and branching
time temporal logics supplied by the assumption of den-
sity of time [7]. Temporal formulas of this logic are in-
terpreted as the statement concerning order of events of
two sorts: instant and durational.
The composition considered above allows to describe
independent behaviour of agents. Parallel execution of
waiting operation by one agent and acting operation by
other agent leads to synchronization of behaviour of
agents during the moment of instant event y (Figure 4).
By definition the effect of waiting operation is its termi-
nation at moment of instant external event.
The line of “life” of the agent consists of pairs waiting
and acting operations. The border between them serves
as the synchronization event. Here the action consists
from “perception” of the accepted message and “pro-
nouncing” new message. Obviously, the occurrence of
synchronization depends on duration of acting opera-
tions.
3.2. The Interaction as an Event of an Environment
The step of dialogue can be considered as the other
composition of three events; one of which is durational,

D. CHEREMISINOV
68
and others two are instant (Figure 5). In this model of a
dialogue step the durational event is directly interaction.
This event, having duration, should have a physical basis.
Without loss of a generality it is possible to consider that
event of interaction occurs in an environment of agents.
In this model event of interaction becomes not distrib-
uted, but this event is local in an environment.
4. Concept of an Environment
From consideration of physical realizations of the dis-
tributed systems follows that the synchronization achieve
by the special organization of system of cooperating
agents. Two general types of the system organization for
achievement of synchronization are known: synchronous
and asynchronous systems. The standard definition of
distinction of these types of systems consists that syn-
chronous systems have shared “clock”, and it is said to
be asynchronous if each agent has its own independent
clock. It is obvious, that these shared “clock” are an ac-
cessory of an environment of agents.
In traditional interaction theories CCS [3] or CSP [8]
concept of an environment is used implicitly, hence it is
not formalized. CCS and CSP use on concept of an en-
vironment which consists in the following. The environ-
ment is considered simply other agent. Other words, the
environment for the given agent includes all other agents
of the system operating in parallel with this agent. In this
case the agent and an environment are objects of identi-
cal nature. It is obvious, that this assumption of proper-
ties of an environment is not well from the point of view
to specify the interaction for achievement of synchroni-
zation. Such approach is justified by following. It is con-
sidered that the concept of an environment concern with
realization of system and is not representable at a level of
behaviour.
Our purpose consists in offering formal model of inter-
action which is not concern with realization of system. We
consider an environment essentially distinct from agents.
The basis of this approach is the representation about in-
teraction as the communication act consisting from
Agent 1 Agent 2
Inquiry
Inquiry
sending
Inquiry
recept i on
Figure 5. Synchronization event as environment event
sending and receiving of the messages. This formalization
of interaction originates from Shannon’s paper about the
theory of communication [9] in which interaction is con-
sidered as a way of transfer of the message from sender to
a receiver via a medium also called transfer environment.
Physical realization of an environment can be the computer
program, the device or the physical environment.
Obviously, synchronization of agent behaviour is im-
possible without fixing data which are transferred during
their interaction [10] by an environment. Thus, environ-
ment serves as model of transport system for delivery of
messages. Other words environment represents the me-
mory that is shared of all agents. This memory is known
as a global state of multi-agent system. In its most simple
form, the communications can be based on the fixed set
of differing signals. In case of binary signals the repre-
sentation of a global state is the set of the boolean vari-
ables which values are possible signals. In case of struc-
tural signals the environment of agents usually refers as
message passing system. The concept of an environment
is closely concern with autonomy of agents. Autonomy
has its focus on freely choosing between actions and on
acting independently. Autonomy means that the agents
receive the information only through an environment.
System, in which the behaviour of an environment is
deterministic, refers to closed system. In case of closed
system it is supposed, that the reasons of all events are
inside of system and its behaviour is self controlled
completely. If the behaviour of an environment is non-
deterministic, system refers to opened system. Unlike the
memory considered in the theory of automatic devices,
the behaviour of memory of an environment of the open
system can depend on uncontrollable conditions.
The specification of interaction in the form of the de-
scription of message passing system does the description
of autonomous behaviour of the separate agent not
closed because this description is not enough for under-
standing of the complete behaviour of the agent. Obvi-
ously, most important property of the message passing
system is restriction on length of durational events, im-
posed by this system.
5. Time as Logic Concept
In the previous part of this paper the time was considered
as the logic concept expressed by relations between
events through sequence and order of events. Time is
discrete, because there is an observable time quantization
by the events that fixed in behaviour of an environment.
If we do not impose restrictions on duration of events in
all components of multi-agent system, the time is not
measured. The measured time means, that each event in
history of system behaviour is accompanied with number
that express either duration of event, or specifying the
moment of time when it occur. Synchronization of be-

D. CHEREMISINOV 69
haviour of agents means the measured time.
Measured time can be realized, if we assume, that du-
ration of all simultaneously executed acting operations in
a multi-agent system is identical. This duration is natural
for accepting for the unit of time. In this case in the
closed systems duration of waiting operations are ex-
pressed by an integer i  1. The assumption that duration
of all simultaneously executed acting operations is iden-
tical holds in synchronous system. Obviously, this as-
sumption defines the pairs of interacting waiting and
acting operations by number of a step of time. Synchro-
nous system keeps the assumption that time is discrete,
dense and measured.
Other assumption to realize measured time is that any
operation was carried out in parallel to itself is illegal. In
this case realization of any operation in history of func-
tioning of the agent is accompanied with counter number
of this realization. The formal proof of this statement is
in [7]. The function which calculate a counter number of
operation realization (from the start of system) when this
operation starts can be used for measurement of time.
Interaction occurs only in pairs of waiting and acting
operations which have the same count number. This is
known as a rendezvous condition. Asynchronous system
keeps the assumption that time is discrete and measured,
but removes the assumption that duration of all simulta-
neously executed acting operations is identical. They
measuring time principle is differ from synchronous type
system.
6. Programming of Agents in the PRALU
Language
The central problem in a multiagent system is that of
coordinating the work of the agents, a process that may
be understood as that of assuring that the sequences of
actions performed by the agents is consistent and coor-
dinated.
The specification of a conversation in a multiagent
system is determined by two components, messages and
protocols. The former are described in communication
languages, such as Knowledge Query and Manipulation
Language (KQML) [11], Foundation for Intelligent
Physical Agents (FIPA) ACL [12], and others. A diction-
ary and messages which may be exchanged by agents are
described in the communication languages.
A protocol is a set of interaction rules that serve to co-
ordinate the work of several agents. We consider protocol
as common knowledge by which agents achieve some
goals. Formal models of protocols have been studied
within the context of the theory of distributed computa-
tions. The fundamental feature that serves to distinguish
these models is the degree of synchronization of behav-
ior of the participants in an interaction. If we abstract
from the function of the agents, the objective of interac-
tion turns out to be synchronization of the behavior of
the interacting agents, since excessive synchronization
entirely undermines the feasibility of joint operation of
the agents. Achievement of synchronization requires
specialized organization of interacting processes.
The sequences consisting of action and waiting opera-
tions are linear algorithms in PRALU. For instance, the
following expression means: wait for p and execute A,
execute B, then wait for q and execute C: “–pAB
–qC ”.
In general, a PRALU algorithm can be presented as an
unordered set of chains 
j in the form

j:–pjLj

j, where
Lj is a linear algorithm, 
j and

j denote the initial and
the terminal chain labels represented by some subsets of
integers from the set M= {1,2,...,m}: 
j,

j  M and the
expression “i“ presents the transition operation: to the
chains with labels from

j.
Chains can be fulfilled both serially and in parallel.
The order in which they should be fulfilled is determined
by the variable starting set Nt  M (its initial value N0 =
{1} as a rule): a chain 
j=

j:–pjLj

j (that was passive)
is activated if

jNt and pj= 1. After executing the opera-
tions of the algorithm Lj, Nt gets a new value Nt+1= (Nt \

j) 

j.
6.1. Representing Agent Interaction Protocols in
PRALU
For an example of an interaction protocol, consider an
English auction [12]. The auctioneer seeks to find the
market price of a good by initially proposing a price be-
low that of the supposed market value and then gradually
raising the price. Each time the price is announced, the
auctioneer waits to see if any buyers will signal their
willingness to pay the proposed price. As soon as one
buyer indicates that it will accept the price, the auction-
eer issues a new call for bids with an incremented price
and continues until no buyers are prepared to pay the
proposed price. If the last price that was accepted by a
buyer exceeds the auctioneer’s (privately known) reser-
vation price, the good is sold to that buyer for the agreed
price. If the last accepted price is less than the reserva-
tion price, the good is not sold.
In the case of the auction there are participants of two
types: the Auctioneer and Buyers. So, we have two kinds
of interaction protocols – those of Auctioneer and of
Buyers. The last participants are peer and should be de-
scribed with identical interaction protocols.
Interaction protocol as a whole can be represented in
PRALU as three complex acting operations – blocks.
Each block has some sets of inputs and outputs that are
enumerated in brackets following the block name (the
other variables of a block are its internal). Initialization
of a complex acting operation is depicted by the frag-
ment such as “Buyer”. The operation Buyer exists in
as many copies as the number of participants of the auc-

D. CHEREMISINOV
70
tion, so the copies of the operation differ in their indexes
only.
The modeling of the process of auction begins with the
execution of “Main_process” triggering event that initi-
ates the interaction protocol execution. Here the proc-
esses Auctioneer and Buyerns are executed concurrently.
For the sake of simplicity we limit the number of buyers
to two. The process Auctioneer starts with sending the
first message (start_auction) that is waited by others par-
ticipants to continue communication. Below PRALU
description of the auction interaction protocol is shown.
Main_process ()
1:  2.3.4
2: Auctioneer 5
3: Buyer1 6
4: Buyer2 7
5.6.7: .
Buyern (start_auction, price_proposed, end_auction /
accept_pricen, not_understand)
1: – start_auction 2
2: – price_proposed Decide(/ decision_accept,
decision_reject) 3
– end_auction .
3: –decision_accept  accept_pricen 4
– decision_reject accept_pricen 4
– not_understand 4
4: – timeout 2
Auctioneer (accept_price1, accept_price2, not_under-
stand / start_auction, price_proposed, end_auction)
1:  start_auction 2
2:accept_price1.accept_price1.not_understand
 Price_propose(/price_proposed) 3
3:– not_understand 2
– accept_ price1 4
– accept_ price2 4
–not_understand.accept_price1.accept_price2
 end_auction  Is_reservation_price_exceeded
( / is_exceeded)6
4: price_propo sed.win1.win2 5
5: – accept_ price1 win1 2
– accept_ price2 win2 2
6: – is_exceeded good_sold 7
– is_exceeded good_sold 7
7: .
It is assumed that all unformalized operations are re-
ferred to as acting operations that set values of logical
variables assigned to them. For example, Buyer’s opera-
tion “Decide” decides for accepting or rejecting the an-
nounced price. Depending on adopted decision, it outputs
true value of logical variable “decision_accept” or “deci-
sion_reject”. In a similar, Auctioneers operation “Price_
propose” proposes an initial price or increments the
charged price outputting true value of logical variable
“price_proposed”; the operation “Is_reservation_price_
exceeded” verifies if the price accepted by a buyer ex-
ceeds the auctioneer’s reservation price outputting true or
false value of logical variable “is_exceeded”.
The operation “–timeout” (where timeout is integer
number) means waiting for timeout unit times before
doing something followed it. The operation “.” is in-
terpreted as the transition to an end of a process de-
scribed by the block. When the processes of Auctioneer
and all Buyers reach their end in the Main_process the
transition to its end is executed.
Within the BDI architecture [13] agents are associated
with beliefs (typically about the environment and other
agents), desires or goals to achieve, and intentions or
plans to act upon to achieve its desires. BDI agent con-
sists of the sets of beliefs B, plans P, situations E, actions
A and intentions I. When the agent notes a change in its
environment, it decides, that there an event takes place
representing some situation from E. Registration of the
event consists in changing a state of the agents “mind”: a
choice of some belief from B. According to it and the
desire (defined by some plan from P) the agent intends to
execute some intention representing some sequence of
actions from A to achieve the goal chosen from I. Thus,
planned actions are defined by the chosen plan from P.
After they are carried out, the current situation of the
environment will be changed.
In traditional parallel programming languages the ba-
sic concepts are data and control of data calculation.
Data are represented by values of variables, and the con-
trol is specified by a set of processes which transform
local memory states defining variable values. The
PRALU program of a BDI agent is a set of plans defin-
ing actions by means of which the agent should reach a
goal of its functioning. The plan consists of head labels, a
body and tail labels. The body of the plan is a sequence
of actions, by means of which the agent should reach a
goal of its functioning, and conditions which the agent
should check up. The head and tail labels of the plan
symbolize intentions. Critical concept for the behaviour
of the agent is the concept of active intention. The plan
will be carried out only when all intentions from its head
are active. After executing the plan all intentions from
the head become inactive and intentions from the tail
quite the contrary become active. The current set of ac-
tive intentions always is not empty, the body of a plan
and a set of tail intentions can be empty.
6.2. The Programming Methodology
We suggest the natural methodology of designing agent
program. It supposes splitting the program into two parts:
a synchronization block and a functional block (Figure 6).
The first block coordinates plan execution of the agent
program, that is, it controls the agent behavior. The syn-
chronization block should be described in PRALU

D. CHEREMISINOV
71
*Decide
accept_price
n
accept_price
n
End
Sstart_auction
price_proposed
decision_reject
decision_accept
not_understand
end_auction
timeout
S
y
nchronization block
–
PRALU-descri
p
tion
If Decide = 1,
compare the announced price
with maximal agents price
and set values of
decision_accept;
decision_reject.
Functional block –
p
redicates descri
p
tion
Figure 6. The program of the agent buyer in English auction
language. The functional block operates data and carries
out calculations. This block is realized in procedural lan-
guage.
The functional part is presented by predicates. The
predicate is the conditions describing memory states of
the agent program and the external environment or the
order directing performance of some actions. The appro-
priate logic variable is introduced for each predicate in
synchronization block.
Such an approach allows separating development of a
synchronizing part of the PRALU-description from the
functional one. When designing MAS, the implementa-
tion of the functional part can be delayed concentrating
designer’s attention on working out the synchronization
block implementing interaction protocol on PRALU.
The PRALU-description compiled by PRALU com-
piler on the intermediate language applied in the simula-
tion program [7] too. The program generated by the
PRALU compiler consists of two interacting blocks–
1) calculation of reactions, 2) control of sensors and ac-
tuating mechanisms of the system. The heart of the con-
trol structure of the program of reactions calculation is an
infinite loop; it consists of entering input signals into
computer memory, calculating reactions and outputting
signals to actuating mechanisms. The predicates of a
functional part are considered as “the additional equip-
ment” of MAS software in such model of the program
organization. The program compiled from PRALU has
semantics of measured time with of a rendezvous condi-
tion [5].
The majority of known systems for logic agent pro-
gramming use model of calculations of Prolog. Prolog to
find set of all decisions of a question, traverse a tree of
search, tries many variants, which is not included into the
decision, and comes back to earlier state in case of fail-
ure, trying other branch. This process is very expensive
of space and time. Computing efficiency offered meth-
odology is comparable to efficiency of the programs
written in C.
7. Conclusions
The independent behaviour of agent in the majority of
multi-agent system models is described by a formalism
of high level abstractness, but the communications is
specified by the concepts that close to realization. The
difference of levels of the description does not allow to
model the communications between agents at that level
in which their independent behaviour is described. This
problem arises because of absence of agent models that
unify aspects of local behaviour and the communica-
tions.
In the present work we suggest to describe the syn-
chronization conditions by specification of event proper-
ties which have been not concerned with the realization
of these events. Our approach allows to specify both the
independent behaviour and the communications at a level
of logic. It is shown, that the collective behaviour of
agents can be described by the synthetic temporal logic
that unity the linear and branching time temporal logics.
Such synthetic logic is an interpretation of PRALU lan-
guage.
The suggested agent programming methodology en-
sures structuring the process of MAS designing by
means of separating calculation part of MAS specifica-
tion from control part. That allows the designer to con-
centrate on more complex stage of MAS designing – its
interaction protocol. It is shown that language PRALU is
very suitable for specifying interaction protocols of MAS
and implementation of suggested methodology. Powerful
theory and software has been developed that provides
correctness verifying, simulation, hardware and software
PRALU-description’s implementation [6].
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