ARGUMENTATION-BASED ONE-TO-MANY
NEGOTIATION MODEL
Guorui Jiang and Sheng Chen
School of Economics and Management, Beijing University of Technology, Chaoyang, Beijing, China
Keywords: Argumentation-based negotiation, Dialogue game protocols, Multi-agents.
Abstract: Today, within the field of multi-agent systems, the theory of argumentation has become instrumental in
designing rich interaction protocols and in providing agents with a means to manage and resolve conflicts.
However, to date much of the existing literature focuses argumentation models based on two agents and
tends to overlook the influence on knowledge base and the relationship between different negotiation
processes. To end this, this paper presents an argumentation-based one-to-many negotiation model. The
contributions are three points: First, we present an argumentation model based on knowledge set with
different influence. Second, we extend a protocol based on dialogue game to govern the agent interactions
and the update of knowledge bases in one-to-many negotiation. In doing so, our model can collect the
knowledge from other negotiating partners and use it in the negotiation with another negotiating partner.
1 INTRODUCTION
Argumentation-based negotiation (Rahwan et at.,
2004) which is gaining increasing popularity for
allows agents to exchange additional information, or
to challenge about their beliefs and other mental
attitudes during the negotiation process has potential
ability to overcome the limitations of more
conventional approaches to automated negotiation.
There are many frameworks of argumentation-based
negotiation having been proposed by many scholars,
such as Carles Sierra (Sierra et al., 1997), Amgoud
(Amgoud et al., 2000a), Sarit Kraus (Kraus et al.,
1998). The key elements of argumentation-based
framework contain communication and domain
languages, the negotiation protocol, and various
information stores, argument and proposal
evaluation, argument and proposal generation and
argument selection (Guorui & Xiaoyu, 2009).
However, to date much of the existing literature
focuses argumentation models based on two agents
and tends to overlook the influence on knowledge
base and the relationship between different
negotiation processes. Actually, how to arrange and
update the knowledge in database is an important
problem in argumentation negotiation. The agent can
collect the information from different negotiation
processes or different opponents. So, this paper
presents an one-to-many argumentation negotiation
model that focuses on the arranging and updating the
knowledge of agents during negotiating.
2 THE ARGUMENTATION
MODEL
The agent’s reasoning model is specified using
argumentation model. This work is inspired by the
work of Dung (Dung, 1995) and Leila Amgoud
(Amgoud et al., 2000b) but goes further in dealing
with influence between arguments which come from
different knowledge base in a set of knowledge
bases.
An agent has many knowledge bases during one-
to-many negotiation. Let
0
Γ be the private
knowledge base of the agent, and
12
, ,...,
n
ΓΓ Γbe the
knowledge bases that store the knowledge comes
from the negotiating agents
12
, ,...,
n
Ag Ag Ag
respectively. We can organize the set of knowledge
bases in the form of a tree. Each base is supposed to
be consistent. We assume knowledge bases contain
formulas of a propositional language
ζ
.  stands
for classical inference and
≡
for logical equivalence
during negotiation.
268
Chen S. and Jiang G.
ARGUMENTATION-BASED ONE-TO-MANY NEGOTIATION MODEL.
DOI: 10.5220/0003270402680274
In Proceedings of the Twelfth International Conference on Informatics and Semiotics in Organisations (ICISO 2010), page
ISBN: 978-989-8425-26-3
Copyright
c
 2010 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

Definition 1(Argument) An argument is a pair
(
)
,
H
h
where
h is a formula of
ζ
and
H
is a subset of
Γ
such that 1)
H
is consistent, 2)
H
h and 3)
H
is
minimal, so no subset of
H
satisfying both 1) and 2)
exists.
H
is called the support of the argument and
h is its conclusion.
We use the notation:
(,)
H
Support Ag h= to
indicate that agent
A
g
has a support
H
for the
conclusion h.
Definition 2 (Attack Relation) Attack is a binary
relation between two arguments. Let
()
11
,
H
h and
()
22
,
H
h be two arguments over
1
Γ and
2
Γ
respectively.
()
11
,
H
h attacks
()
22
,
H
h is denoted by
() ( )
11 2 2
,,
attack
H
hHh⎯⎯⎯→ .
(
)
(
)
11 2 2
,,
attack
H
hHh⎯⎯⎯→
2
iff h H∃∈ such that
1
hh≡¬ .In other words, an
argument is attacked
iff there exists an argument
for the negation of an element of its support.
To capture the fact that some facts are more
strongly believed (Guorui et al., 2009) (maybe
because of different honesty and capability degree of
different agents) we assume that any set of
knowledge bases has an influence order over it. We
suppose that this ordering derives from the fact that
the knowledge bases set
12
, ,...,
n
ΓΓ Γcome from
different agents
12
, ,...,
n
A
gAg Ag respectively such
that facts in
i
Γ have the same influence order and
have more influence than those in
j
Γ
where
ij≠
.The influence level of a nonempty subset
H
of
i
Γ ,()level H .
Definition 3 (Influence) Let
()
11
,
H
h and
(
)
22
,
H
h
be two arguments over
1
Γ
and
2
Γ respectively.
()
11
,
H
h has more influence than
(
)
22
,
H
h
according to
I
nflu iff
12
() ( )levelH levelH≥ .
Definition 4(Argumentation Model) An argumentat-
ion model (AM) is a triple
(), ,A Attack InfluΓ
such that
01
( ) ( ) ( ) ... ( )
n
AA A AΓ= Γ + Γ + + Γ is a set
of the arguments built from
01
, ,...,
n
ΓΓ Γ
respectively.
A
ttack is a binary relation representing
defeat relationship between arguments,
() ()
Attack A A⊆Γ×Γ, and
I
nflu is a (partial or
complete) pre-ordering on ( ) ( )
AAΓ× Γ.
Influ
 stands
for the strict pre-order associated with
I
nflu .
Definition 5 (Strongly Attack) Let ,
A
B be two
arguments of
()A
Γ
,
B
strongly attacks A iff
B
attacks
A and it is not the case that
Influ
A
B .
Definition 6 (Legal Argument Rule) An argument
A from AM is legal iff there is not any argument
from AM which strongly attacks
A . And a legal
argument that come from AM can be denoted as
()
A
AM Ag .
3 DIALOGUE GAME
FOR ONE-TO-MANY
NEGOTIATION
3.1 Dialogue Game
Formal dialogue games (Maudet et al., 1998) are
games in which two or more participants “move” by
uttering locutions, according to certain pre-defined
rules. In recent years, they have found application as
the basis for communications protocols between
autonomous software agents, including for agents
engaged in: persuasion dialogues, where one agent
seeks to persuade another to endorse some claim;
information-seeking dialogues, where one agent
seeks the answer to some question from another
(Amgoud et al., 2006c).
3.2 Dialogue Move Rules
A social commitment SC is an engagement made by
an agent that some fact is true or that something will
be done. This commitment is directed to a set of
agents. A commitment is an obligation in the sense
that the sender must respect and behave in
accordance with this commitment. The paper
uses
12
(, ,)SC Ag Ag p which will be denoted in the
rest of this paper ( )
SC p to indicate the social
commitment that
1
A
g sends to
2
A
g .
The paper uses ( )
i
SCS Ag storing the social
commitment that presented by
i
A
g . When
i
A
g
create a new social commitment, ( )
i
SCS Ag will
update itself by adding the new commitment,
1
() () ()
ii i i
SCS Ag SCS Ag SC p
−
=∪. Each Agent has
access to the other Agent’s
SCS to get the social
commitments which are sent to it. The knowledge
retrieves from the social commitments from the
other Agent
i
A
g constitute the new knowledge of
ARGUMENTATION-BASED ONE-TO-MANY NEGOTIATION MODEL
269

Agent
A
g
. So
A
g
can get knowledge from the
SCS of other Agents to build the knowledge set.
A speech act
SA is an act performed on a
commitment or its content. The action that an agent
can perform on a commitment is
Create and
Withdraw . Create means that making an offer.
When the agent(speaker) accept the other agent’s SC
and the content of other agent’s SC is the opposition
of speaker’s SC, the speaker will withdraw the SC
that its sent. And the actions that an agent can
perform on commitment content are: Act-Arg:
,Re , , , ,Accept fuse Challenge Defend Attack Justfiy .
A propositional formula p, which is accord with
legal argument rule, can be generated from an
agent’s argumentation system, if this Agent can find
an argument supporting p. The paper uses the
notation _ ( )
p
Arg Sys Ag to denote the fact that a
propositional formula p can be generated from the
argumentation system of
A
g
(()
A
MAg).
The paper uses
12
_(,(,,))S Create Support Ag SC Ag Ag p=
which will be denoted in the rest of this paper
(,())
S Support Ag SC p= to indicate the set of
commitments
S created by agent to support the
content of
12
(, ,)SC Ag Ag p . Act-Arg(Ag,[S],SC(p))
means the argumentation-related action that
Ag
performs on the content of SC(p) using the
contents of S as support.
'
Act-Arg(Ag,[S],S )
indicates that Agent performs an argumentation-
related action on the content of a set of commitment
'
S using the content of S as support.
As the dialogue move rules presented by Jamal
Bentahar and Jihad Labban (Bentahar & Labban,
2009) he paper distinguish five types of dialogue
games: entry, defense, challenge, justification and
attack. Based on the five types of dialogue games,
this paper extends the protocol by adding the rules of
updating knowledge database of each agent.
3.2.1 A Entry Game
1
(,())Create Ag SC p (1)
Rationality:
1
_()
p
Arg Sys Ag
Dialogue: the other player can respond with
1.
21 1 2
(,[],()) _(),Accept Ag S SC p a p Arg Sys Ag= ,
12
(,())S Support Ag SC p= ,
1
a is the condition to
accept ( )
SC p ,
1
S is the support of ( )SC p in the
argumentation model of
2
A
g .
2.
21 2
Re ( , ( )), _ ( )
f
use Ag SC p b p Arg Sys Ag=¬ 
,
1
b is the condition.
3.
21 2
( , ( )), ( _ ( ))Challenge Ag SC p c p Arg Sys Ag=¬ ∧
2
(_())
p
Arg Sys Ag¬¬  ,
1
c is the condition.
Update:
111
() (){()}
ii
SCS Ag SCS Ag SC p
−
=∪,
1
A
g
will update its social commitment store by adding
the new commitment ( )
SC p .
2121
() (){}
ii
SCS Ag SCS Ag S
−
=∪
,when
2
A
g respond
by
21
(,[],())
A
ccept Ag S SC p ,
2
A
g will update its
commitment store by adding
1
S .
212
() ()
ii
SCS Ag SCS Ag
−
= ,when
2
Ag
respond by
Re
f
use or Challenge .
3.2.2 Defence Game
1
(,[],())
D
efend Ag S SC p (2)
Rationality: receive
2
Re ( , ( ))
f
use Ag SC p from
other player
Dialogue:
1.
2012 1 2
(,[],), ,() _(),
ii
Accept Ag S S a i SC p S p Ar g Sys Ag=∀ ∈ ⇒ 
01
()S Support S= As for every propositional formula
in
1
S , the AM of
2
A
g has a support of it. And the
support set is
0
S .
2.
22 2 2 2
(,), ,() (( _())
ii
Challenge Ag S b i SC p S p Arg Sys Ag=∀ ∈ ⇒ ¬ 
2
(_()))
i
pArgSysAg∧¬ ¬  .
3.
''
232 3
( ,[ '], ), , ( ) ,
ij
Attack Ag S S c i SC p S S S=∀ ∈ ⇒∃ ⊆
'
2
(,)
j
i
S Support Ag p=¬ As for every propositional
formula in
3
S , the AM of
2
A
g has a support of the
opposition of it. And the support set is '
S .
Where
{ ( ) | 0,..., }
i
SSCpi n==,
i
p
are propositional
formulas.
3
1
( ), , , 1,...,3&
ii i j
US S SCpS S ij i j
=
=
∪∩=Φ=≠
Update:
111
() (){}
ii
SCS Ag SCS Ag S
−
=∪ ,
1
A
g will
update its social commitment store by adding the
new commitment ( )
SC p .
2120
() (){}
ii
SCS Ag SCS Ag S
−
=∪,when
2
A
g respond
by
A
ccept
.
212
() ()
ii
SCS Ag SCS Ag
−
= ,when
2
A
g respond by
Challenge .
2123
() (){}
ii
SCS Ag SCS Ag S
−
=∪, when
2
A
g respond
by
A
ttack .
By definition,
1
(,[],())
D
efend Ag S SC p means
that
1
A
g creates S in order to defend the content of
()
SC p .Formally:
0
[] _ ( , ())S Create Support Ag SC p= .
3.2.3 Challenge Game
1
(,())Challenge Ag SC p (3)
ICISO 2010 - International Conference on Informatics and Semiotics in Organisations
270

Dm_1(Ag0,Ag1)
Dm_2(Ag0,Ag1)
Dm_n(Ag0,Ag1)
Dm_3(Ag0,Ag1)
Dms
KB_1
KB_1 KB_1 KB_1KB_1
Dm_1(Ag0,Ag2)
Dm_1(Ag0,Agn)
Dm_2(Ag0,Ag2)
Dm_2(Ag0,Agn)
Dm_3(Ag0,Ag2)
Dm_3(Ag0,Agn)
Dm_n(Ag0,Ag2)
Dm_n(Ag0,Agn)
Dialogue move rules
Dialogue move rules
Dialogue move rules
update of knowledge base
Figure 1: The protocol of one-to-many negotiation.
Rationality:
22 1
,() (( _( ))
ii
b i SC p S p Arg Sys Ag=∀ ∈ ⇒ ¬ 
1
(_()))
i
pArgSysAg∧¬ ¬  means
1
A
g does not has
knowledge about propositional formula p.
Dialogue:
2
(,[],())
J
ustify Ag S SC p
Update:
111
() ()
ii
SCS Ag SCS Ag
−
=
212
() (){}
ii
SCS Ag SCS Ag S
−
=∪,when
2
A
g respond
by
J
ustify .
3.2.4 Justification Game
Case1( ( )SC p S∉ )
1
(,[],())
J
ustify Ag S SC p (4)
Rationality: receive Challenge from other player,
then Agent should use
J
ustify to answer the question.
Dialogue: the respond rule is the same with
D
efend rules.
1.
2012 1
(,[],), ,() _
ii
Accept Ag S S a i SC p S p Arg=∀ ∈ ⇒ 
20 1
(), ()Sys Ag S Support S= .
2.
22 2 2 2
(,), ,() (( _())
ii
Chal l enge Ag S b i SC p S p Arg Sys Ag=∀ ∈ ⇒ ¬ 
2
(_()))
i
pArgSysAg∧¬ ¬  .
3.
''
232 3
( ,[ '], ), , ( ) ,
ij
Attack Ag S S c i SC p S S S=∀ ∈ ⇒∃ ⊆
'
2
(,)
j
i
S Support Ag p=¬.
Update: the updating rules are the same with
D
efend rules.
Case2( { ( )}
SC p S= )
1
(,[],())
J
ustify Ag S SC p (5)
Rationality: receive Challenge from other player,
Dialogue:
1.
2
( , ( )),( )
A
ccept Ag SC p Acceptence ,when
2
A
g
trusts
1
A
g
or the influence of
1
A
g
is higher than
2
A
g
.
2.
2
Re ( , ( ))( min )
f
use Ag SC p Ter ate ,when
2
A
g
does not trust
1
A
g
or the influence of
2
A
g
is higher
than
1
A
g
.
Update:
111
() ()
ii
SCS Ag SCS Ag
−
= and
212
() ()
ii
SCS Ag SCS Ag
−
=
{()}
SC p S
=
means that Agent justify p by itself and
Agent does not have any other knowledge to justify
p. At this situation,
2
A
g only can accept or reject it,
because
2
A
g has challenged it and it does not has
any argument about p.
3.2.5 Attack Game
1
(,[],())
A
ttack Ag S SC p (6)
Rationality:
1
(,)S Support Ag p
=
¬
Dialogue:
1.
21 5 2
Re ( ,), ,() ( ,())
i
f
use Ag S a i SC p Support Ag SC q=∃ ∈ ¬
Where
1
{()}SSCq=
.
2.
20 25 2
(,[],), ,()
ii
A
ccept Ag S S b i SC p S p=∀ ∈ ⇒
2
_( )
A
rg Sys Ag .
3.
23 5 3 2
(,), ,() (( _())
ii
Challenge Ag S c i SC p S p Arg Sys Ag=∀ ∈ ⇒ ¬ 
2
(_()))
i
pArgSysAg∧¬ ¬  .
4.
''
245 4
( ,[ '], ), , ( ) ,
ij
A
ttack Ag S S d i SC p S S S=∀ ∈ ⇒∃ ⊆
ARGUMENTATION-BASED ONE-TO-MANY NEGOTIATION MODEL
271

tanAccep ce
tanAccep ce
Step7
(, ,) 0.5
(, ,) 0.5
E
ntryGame
SC C M p
SC C F p
−
−
Re
(,, )
fuse
SC M C p¬
(,,)
Challenge
SC F C p
[ (,,), (,,), (,,)], (,,)0.5
Defence
SC C M t SC C M m SC C M g SC C M p −
[ ( , , ), ( , , ), ( , , )], ( , , ) 0.
5
Justify
SC C F t SC C F m SC C F g SC C F p
−
[(,,)],
(,, )0.8
Attack
SC M C s
SC M C m¬−
[ ( , , )],
(,,)0.8
Accept
SC M C x
SC M C t −
[ ( , , )],
(,,)0.8
Accept
SC M C g
SC M C g −
[ (, ,), (, ,)], (, , ) 0.9
Attack
SC C M b SC C M s SC C M m −
(,,)
Challenge
SC M C b (,,)
Accept
SC M C s
[ (,,)], (,,)0.9
Justify
SC C M b SC C M b −
(,,)
Challenge
SC F C g (,,)
Challenge
SC F C t
[ ( , , ), ( , , )],
(,,) 0.9
Accept
SC F C b SC F C s
SC F C m −
[(,,)],
(, ,) 0.8
Justify
SC C F g
SC C F g −
(,,)
Challenge
SC F C x
[(,,)],
(, ,) 0.8
Justify
SC C F x
SC C F t −
[ (,,)], (,,)0.8
Justify
SC C F x SC C F x −
Step1
Step2
Step3
Step4
Step5
Step6
tanAccep ce
Step0
Figure 2: The process of negotiation.
'
2
(,)
ji
S Support Ag p=¬where
{ ( ) | 0,..., }
i
SSCpi n==
,
i
p
is a propositional formula.
4
1
(),
iij
i
SSSCpSS
=
=∪ ∩ =∅
∪
， ,1,...,4ij= and ij
≠
.
Update:
111
() (){}
ii
SCS Ag SCS Ag S
−
=∪,
1
A
g will
update its social commitment store by adding the
new commitment set
S .
212
() ()
ii
SCS Ag SCS Ag
−
= , if
2
A
g responds with
Re
f
use or Challenge .
2120
() (){}
ii
SCS Ag SCS Ag S
−
=∪,when
2
A
g respond
by
A
ccept
.
'
212
() (){}
ii
SCS Ag SCS Ag S
−
=∪,when
2
A
g respond
by
A
ttack .
3.3 One-to-Many Protocol
In one-to-one negotiation, a negotiation process
between
12
,
A
gAgconstitutes by a sequence of
dialogue moves one after another and the update of
knowledge set between every two dialogue moves.
In one-to-many negotiation, every players are
equipped with an argumentation model of the kind
discussed above. Each has access to their own
private knowledge base
Γ
and social commitment
stores. The Agent can access to the social
commitment stores to search the social commitments
that sent to it. According the Agent which the social
commitment comes from, The Agent can store the
knowledge which is retrieved from social
commitment in the knowledge base set
12
, ,...,
n
ΓΓ Γ
respectively.
In the process of negotiation (Figure 1),
0
A
g negotiates with
12
, ,...,
n
A
gAg Agrespectively in
synchronization. Before the negotiation started,
0
A
g
only has private knowledge base
Γ .When
0
A
g starts
negotiation with
12
, ,...,
k
A
gAg Ag respectively in
synchronization,
0
A
g can retrieve knowledge from
social commitment that sent by
12
, ,...,
k
A
gAg Ag
and store it in
12
, ,...,
n
Γ
ΓΓrespectively.
i
Γ denotes
the knowledge that come from
i
A
g during
negotiation. Each knowledge base will grow with
the process of negotiation.
0
A
g can use the
opponents’ knowledge to negotiate with the other
opponents. Within the process of the negotiation, the
knowledge of
0
A
g will grow quickly.
ICISO 2010 - International Conference on Informatics and Semiotics in Organisations
272

4 AN DIALOGUE PROCESS
Let us consider the following dialogue to illustrate
the process of one-to-many argumentation
negotiation presented in this paper.
In the family, the child want to have a travel to
Sanya in Hainan province. The child should
persuade mother and father to travel to Sanya. Only
if father and mother all agree with child, the family
can go to have a travel to Sanya. Agent Child’s KB
contains ({ , , }, )tmg p,where t means the family has
enough time to have a travel, m means the family
has enough money to travel to Sanya, g is a brief
that Sanya is a good place to have a travel, p is the
suggest to travel to Sanya. And the expression mean
that p will be true if t, m and g are true. Agent
Father’s KB contains ({ , }, )bs m , b indicates bonus
that father receives yet, s indicate the deposit of the
family. Agent Mather’s KB contains ({ }, )xt ,
({ }, )
g
g , ({ }, )
s
m¬ ,({ }, )mp¬¬,where x means the
family has a plan to have a travel. Besides, Father
has the biggest influence and the child has the
smallest influence and father and mother trust each
other. If they can make an argument that is the
opposition of the brief, they should accept the brief
of each other. And the process of the dialogue is
presented as Figure 2. C indicates child,
M
indicates mother, and
F
indicates father.
If the child negotiate with his father in one-to-
one negotiation, the process will stop at step3
because of the luck of knowledge. Similarly, if the
child negotiate with his mother, the process will stop
at step3 because of the luck of knowledge.
But in one-to-many negotiation, the child can
have access to his father’ social commitment
store(SCS) and get the new knowledge ({ , }, )bs m at
step3.Then child can use it to persuade mother in
step4. Similarly, the child can have access to his
mother’s SCS and get the new knowledge
({ }, )xtand ({ }, )
g
g at step3. Because the father’s
influence is bigger than his mother, mother accept
the knowledge ({ , }, )bs m in the step5 and step7 .
Because father and mother trust each other, father
accept the knowledge ({ }, )xt and ({ }, )
g
g of
mother .
5 CONCLUSIONS
This paper presents an argumentation model based
on agent’s society influence and extends a protocol
based on dialogue game which makes agents can
collect and update the knowledge base in one-to-
many negotiation’s process. Much of the existing
literature overlooks the influence between different
negotiation processes, especially in the field of one-
to-many and many-to-many negotiation. Knowledge
is the basic element for argumentation systems to
build an argument supporting a conclusion. So an
interesting direction for future work is how to make
agents be equipped with capacity enabling them to
collect, update, manage and apply knowledge during
negotiating processes, especially in one-to-many and
many-to-many negotiation.
ACKNOWLEDGEMENTS
This work is supported by the National Natural
Foundation of China (No: 70940005).
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