https://doi.or g/10.31449/inf.v48i9.3448 Informatica 48 (2024) 107–1 12 107
Argumentation-based Machine Learning for In consistent Knowledge Bases
Nguyen Thi Hong Khanh
Electric Power University , Hanoi, V ietnam
E-mail: khanhnth@epu.edu.vn
Keywords: belief mer ging, ar gumentation
Received: February 19, 2021
In this paper , we intr oduce a new ar gumentation framework for belief mer ging. T o this end, a constructive
model to mer ge possiblistic belief bases built based on the general ar gumentation framework is pr oposed.
An axiomatic model, including a set of rational and intuitive postulates to characterize the mer ging r esult
is intr oduced and several logical pr operties ar e mentioned and discussed. Belief mer ging is one of active
r esear ch fields with a lar ge range of applications i n Artificial Intelligence. Most of the work in this r esear ch
field is in the centralized appr oach, however , it is difficult to apply to interactive systems such as multi-agent
systems.
Povzetek: Vpeljan je ar gumentacijski okvir za združevanje pr epričanj, ki uporablja konstruktivni model
za združevanje baz pr epričanj in vključuje nabor racionalnih in intuitivnih postulatov za karakterizacijo
r ezultatov združevanja.
1 Intr oduction
In recent years, Belief Mer ging, a research field study on
the integration of the knowledge bases, has become an at-
tractive research area in Artificial Intelligence. It is applied
in a lar ge range of a reas such as Information Systems, Mul-
tiagent Systems, Data Retrieval, and Distributed Systems.
The advantage of belief mer ging approach is the richness
of information we can obtain but its trade-of f is the incon-
sistencies that we have to solve. In literature, there are
two main approaches to deal with the inconsistencies arisen
when we combine multiple information sources.
In the first approach, we will try to adopt the incon-
sistency in obtaining information source by improving the
classical reasoning methods. One of typical instances of
this idea is the family of paraconsistent logics [16, 9, 8].
This approach needs a simple operation to collect and store
information from source, but it requires a highly computa-
tional complexity reasoning operation. Unfortunately , the
reasoning operation is more frequently used than another ,
thus this approach is only suitable for a specific class of ap-
plications.
In the second approach is using b elief mer ging in which
we try to build a consistent information system from mul-
tiple information sources. Precisely , from the given belief
bases{ K
1
,...,K
n
} we build a consistent belief baseK
∗ which best represents for these belief bases.There are two
settings in this approach, the centralized and distributed
ones. In centralized setting, belief mer ging is considered
as an arbitration in which all belief bases are submitted to
a mediator , and this mediator will decide which is the com-
mon belief base. This is the main trend in belief mer ging
with a lar ge range of works such as [20, 21]. Obviously ,
in this setting the mer ging result is depend on the mediator ,
the participating agents have to expose all their own beliefs
and they are omitted in mer ging process. Therefore, it is
dif ficult to apply to high interactive systems such as multi-
agent systems.
In the second setting, each mer ging process is consid-
ered as a game in which participants step by step give their
proposals until an agreement is reached. The first direc-
tion in this setting is belief mer ging by negotiation with
some typical works are as follows: a family of game-based
mer ging operators[17], a two-stage belief mer ging process
[10, 1 1], a bar gaining game solution [27] and a game model
for mer ging stratified belief bases [19, 22, 23, 25, 26].
The second direction is belief mer ging by ar gumentation
in which mer ging process is or ganized as a debate and par -
ticipants uses their own beliefs and manipulates ar gumenta-
tion skills to reach the agreement. T ypically , an ar gumenta-
tion framework for mer ging weighted belief bases [15] and
other framework for mer ging the belief bases in possibilis-
tic logic by Amgoud et al. [3]. In [24], a general framework
for mer ging belief bases by ar gumentation is introduced,
however , the semantics of ar gumentation extensions are not
mentioned and discussed.
In this work, we propose a new ar gumentation frame-
work for mer ging possibilistic logic bases. The contribu-
tion of this paper is two-fold. First, we introduce a frame-
work to mer ge possibilistic belief bases in which a general
ar gumentation framework is applied in possibilistic belief
bases to obtain meaningful results in comparison to other
belief mer ging techniques for belief mer ging in possibilistic
logic such as [3, 5, 4, 7, 18]. Second, an axiomatic model in-
cluding rational and intuitive postulates for mer ging results
is introduced and several logical properties are discussed.
The rest of this paper is or ganized as follows: W e review
about possibilistic logic in Section II . Belief mer ging for

108 Informatica 48 (2024) 107–1 12 N.T .H. Khanh
prioritized belief bases by possibilistic logic framework is
presented in Section III . Section IV and Section V introduce
a general ar gumentation framework and a model to mer ge
belief bases by this framework. Postulates for belief mer g-
ing by ar gumentation and logical properties is introduced an
discussed in Section VI . Some conclusions and future work
are presented in Section VII .
For the sake of representation, we consider the follow-
ing example: A terrible environmental crisis, which cause
mass fish deaths (a ), happened in the seabed in Middle of
V ietnam. There are some opinions ordered in time series as
follows:
The public and scientists: The mass fish deaths (a ) are
caused by the toxic spill disaster of a steel factory (b ):
(b→ a ).
Steel factory: W e have a modern waste water treatment
system (c ), thus the water was cleaned before it was dis-
char ged: (c,c →¬ b ).
Communication agencies: The steel factory has imported
hundreds of tons of chemical toxic (d ) and its under ground
tube is put at wrong position (f ): (d,f ).
The public and scientists: A diver has died (g ) with the
symptom caused by toxin from water (b ): (g,b → g ).
Steel factory: W e have imported chemical material to de-
ter gent our tubes (d ) however the water was cleaned before
it was dischar ged: (¬ (d→ b) ). Our under ground tube is in
the right position and it has not been completed, thus it can
dischar ge now: (¬ f ).
Official A uthorities: There are two causes of mass fish
deaths. It may be from chemical toxin (d ) or it may cause
by algae bloom phenomenon (e ): (d→ a)∨ (e→ a ). W e
have not yet had any clue about the relation between mass
fish deaths and the dischar ge of steel factory .
The public and scientists: The mass fish deaths cannot
cause by the algae bloom phenomenon because there is no
body of algae, water did not change color and fishes died at
the bottom: (¬ e ).
From the progression of events as above, we have the sets
of beliefs as follows:
K
1
: { b→ a,g,b → g, ¬ e} ,
K
2
: { c,c →¬ b, ¬ (d→ b), ¬ f} ,
K
3
: { d,f } ,
K
4
: { (d→ a)∨ (e→ a)} .
2 Possibilistic logic
In this work, we consider a propositional languageL built
on a finite alphabetP and common logic connectives in-
cluding¬ , ∧ , ∨ , and→ . The classical consequence relation
is⊢ . W e useΩ to denote a finite set of interpretations ofL .
Givenω ∈ Ω ,ω |= ψ represents thatω is a model of the
formulaψ .
A possibilistic formula(ψ,α ) includes a propositional for -
mula ψ and a weight α ∈ [0, 1] . A possibilistic be-
lief base is a finite set of possibilistic formulas K =
(ψ i
,α i
)|i = 1,...,n . W e denoteK
∗ an associated belief
base w .r .tK defined as follows:K
∗ ={ ψ i
| (ψ i
,α i
)∈ K} .
Obviously , a possibilistic belief baseK is consistent ifK
∗ is consistent and vice verse . W e also denoteK andK
∗ set
of all possibilistic belief bases and their associated belief
bases, respectively .
For each possibilistic belief baseK , the possibility dis-
tribution ofK , denoted byπ K
as follows: [13]∀ ω ∈ Ω π K
(ω ) =
   1 if∀ (ψ i
,α i
)∈ K,ω |=ψ i
1− max{ α i
: (ψ i
,α i
)∈ K andω ⊭ ψ i
} otherwise
(1)
Continuing Example 1.
Suppose that K = { (a, 0. 8), (¬ c;0. 7), (b → a, 0. 6), (c;0. 5), (c→¬ b;0. 4)} .
According to Definition 2, we can determine the possibility
distribution forK as follows:π K
(a¬ b¬ c) = 1,π K
(abc) =
0. 6,π K
(ab¬ c) = 0. 5,π K
(a¬ bc) = 0. 3 , andπ K
(¬ abc) =
π K
(¬ ab¬ c) = π K
(¬ a¬ bc) = π K
(¬ a¬ b¬ c) = 0. 2
Given a possibilistic belief base K and α ∈ [0, 1] , the
α − cut ofK is denoted byK
≥ α and defined as follows:
(K
≥ α = { ψ ∈ K
∗ | (ψ,β ) ∈ K,β ≥ α } ) . Similarly , a
strict α − cut of K is denoted by K
>α
and defined as
follows: (K
>α
={ ψ ∈ K
∗ | (ψ,β )∈ K,β >α } ) .
Possibilistic belief baseK
1
is equivalent to possibilistic
belief baseK
2
, written asK
1
≡ K
2
if and only ifπ K1
=
π K2
. It is easy to prove thatK
1
≡ K
2
if f for allα ∈ [0, 1]
(K
1
)
≥ α ≡ (K
2
)
≥ α )
2.1 Possibilistic infer ence
The inconsistency degr ee of possibilistic belief baseK is
as follows:
Inc(K) =max{ α i
:K
≥ α i
is inconsistent} (2)
The inconsistency degree of possibilistic belief base K
is the maximal value α i
such that the α i
− cut of K
is inconsistent. Conventionaly , if K is consistent, then
Inc(K) = 0 . Given a possibilistic belief base K and
(ψ,α )∈ K ,(ψ,α ) is a subsumption inK if:
(K\{ (ψ,α )} )
≥ α ⊢ ψ (3)
Respectively ,(ψ,α ) is a strict subsumption inK ifK
>α
⊢ ψ . W e have the following lemma [6]: If (ψ,α ) is a sub-
sumption inK thenK ≡ (K\{ (ψ,α )} ) . Given a possi-
bilistic belief baseK , formulaψ is a plausible consequence
ofK if:
K
>Inc(K)
⊢ ψ (4)
Given a possibilistic belief base K , formula (ψ,α ) is a
possibilistic consequence ofK , denotedK⊢ π (ψ,α ) , if:
- K
>Inc(K)
⊢ ψ - α>Inc (K) and∀ β >α,K
>β
⊬ ψ

Ar gumentation-based Machine Learning… Informatica 48 (2024) 107–1 12 109
In any inconsistent possibilistic belief baseK , all formulas
with certainty degrees smaller than or equal toInc(K) will
be omitted in the inference process. Continuing Example
2, obviouslyK is equivalent to
K
′ ={ (a, 0. 8), (¬ c, 0. 7), (b→ a, 0. 6), (c, 0. 5)} .
Formula (c → ¬ b, 0. 4) is omitted because of Inc(K) =
0. 5 .
W e have:
- Plausible inferences ofK are¬ a,c → a,b → a,... - Possibilistic consequences ofK are(c→ a, 0. 7), (b→ a, 0. 6),... .
3 Belief merging by argumentation
in possibilistic logic
In this section, we consider an implementation of general
framework above in order to solve the inconsistencies oc-
cur when we combine belief bases (K
1
,...,K
n
) . Let us
start with the concept of ar gument. Each ar gument is pre-
sented as a double⟨ S,s⟩ , wheres is a formula andS is set
of formulas such that:
(1) S ⊆K
∗ ,
(2) S ⊢ s ,
(3) S is consistent andS is minimal w .r .t. set inclusion.
S is the support ands is the conclusion of this ar gument.
W e denoteA(K) the set of all ar guments built fromK .
W e recall an ar gumentation framework in [2], it is ex-
tended from the famous one proposed by Dung in [14]. An
ar gumentation framework is a triple⟨A , R, ⪰⟩ in whichA
is a finite set of ar guments, R is a binary relation repre-
sented the relationship among the ar guments inA , and⪰ is
a preorder onA×A . W e also use≻ to represent the strict
order w .r .t⪰ . LetX,Y be two ar guments inX .
- Y attacksX ifY ⪰ X andY RX .
- IfY RX butX ≻ Y thenX can defend itself .
- X set of ar gumentsA defendsX ifY attacksX then there
always existsZ ∈A andZ attacksY .
A set of ar guments A is conflict-free if ∄ X,Y ∈ A such thatXRY
The attack relations among ar guments include undercut
and rebut. They are defined as follows: Let ⟨ S,s⟩ and
⟨ S
′ ,s
′ ⟩ be ar guments ofA(K) . ⟨ S,s⟩ undercuts⟨ S
′ ,s
′ ⟩ if
there exists p ∈ S
′ such that s ≡ ¬ p . Namely , an ar -
gument is under undercut attack if there exists at least one
ar gument in its support is attacked. Let⟨ S,s⟩ and⟨ S
′ ,s
′ ⟩ be ar guments ofA(K) . ⟨ S,s⟩ rebuts⟨ S
′ ,s
′ ⟩ if s ≡ ¬ s
′ .
Informally , two ar guments rebut each other if their conclu-
sions are conflict.
In [1], the authors ar gued that each ar gument has a degree
of influence. It allows us to compare ar guments to choose
the best one. When the priorities of ar guments are explicit,
the higher certain beliefs support, the stronger the ar gument
is. The strength of the ar gument is defined as follows: The
force of an ar gumentA = ⟨ S,s⟩ , denoted byforce(A) is
determined as follows:
force(A) =min{ α i
:ψ i
∈ S and(ψ i
,α i
)∈K} . (5)
W e consider any aggregation operator⊕ satisfied the fol-
lowing properties:
(1) ⊕ (0,... 0) = 0 ,
(2) Ifα ≥ β then for alli = 1,...,n , then
⊕ (x
1
,...,x
i− 1
,α,x
i+1
,...,x
n
) ≥ ⊕ (x
1
,...,x
i− 1
,β,x
i+1
,...,x
n
) .
Several common aggregation operators considered in liter -
ature are maximum (Max ), sum (Σ ) and lexicographical
order(GMax ). LetK = { K
1
,...,K
n
} be a set ofn pos-
sibilistic belief bases and A = ⟨ S,s⟩ be an ar gument in
A(K) , then
- ∀ ψ i
∈ S,K
i
⊢ (ψ j
,a
ji
),i = 1,...,n.
- force(A) =min{⊕ (a
j1
,...,a
jn
)} . By the force of ar gument, we can compare ar guments as
follows: Ar gumentX is preferred to ar gumentY , denoted
byX ≻ Y ifforce(X)>force(Y) . GivenK ={ (¬ b∨ a, 0. 9), (b, 0. 7), (¬ d∨ a, 0. 6), (d, 0. 5)} , we have:
K ={ (¬ b∨ a, 0. 9), (b, 0. 7), (¬ d∨ a, 0. 6), (d, 0. 5)} .
W e have two ar guments related toa :
- A
1
=<{¬ b∨ a,b} ,a>,
- A
2
=<{¬ d∨ a,d} ,a>. However ,A
1
is preferred toA
2
becauseforce(A
1
) = 0. 7
andforce(A
2
) = 0. 5 .
The inconsistence of a possibilistic belief base K
i
can
be calculated from the force of inconsistent ar guments
as follows: Let K be a possibilistic belief base and
⟨A (K),Undercut, ≻⟩ be an ar gumentation framework.
Inc
att
(K) =max{ min(force(X),force (Y))| α i
attA
j
} . (6)
where att ∈ { undercut,rebut} . Let
K
1
= { (a ∨ ¬ b;0. 9), (f;0. 9), (g;0. 8), (¬ d ∨ ¬ e;0. 5), (¬ e;0. 5), (d;0. 5) ,
(a ∨ ¬ d;0. 4), (¬ b ∨ g;0. 3), (a ∨ ¬ e;0. 3), (a;0. 2), (a ∨ ¬ d∨¬ e;0. 1)} ,
K
2
= { (c;0. 8), (¬ f;0. 8), (¬ b∨¬ c;0. 2), (¬ b∧ d;0. 3)} ,
and ⊕ be an aggregation function defined as follows:
⊕ (α,β ) =α +β − α.β . W e have:
K
⊕ = { (a ∨ ¬ b ∨ c;0. 98), (c ∨ f;0. 98), (a ∨ ¬ b ∨ ¬ f;0. 98), (c∨ g;0. 96), (¬ f ∨ g;0. 96), ((a∨¬ b)∧ (a∨ ¬ b ∨ d);0. 93), ((¬ b ∨ f) ∧ (d ∨ f);0. 93), (a ∨ ¬ b ∨ ¬ c;0. 92), (¬ b∨¬ c∨ f;0. 92), (a∨¬ b;0. 9), (f;0. 9), (c∨ ¬ d ∨ ¬ e;0. 9), (c ∨ ¬ e;0. 9), (c ∨ d;0. 9), (¬ d ∨ ¬ e ∨ ¬ f;0. 9), (¬ e ∨ ¬ f;0. 9), (d ∨ ¬ f;0. 9), (a ∨ c ∨ ¬ d;0. 88), (¬ b∨ c∨ g;0. 88), (a∨¬ d∨¬ f;0. 88), (¬ b∨

1 10 Informatica 48 (2024) 107–1 12 N.T .H. Khanh
¬ f ∨ g;0. 88), (a ∨ c ∨ ¬ e;0. 86), ((g ∨ ¬ b) ∧ (g ∨ d);0. 86), (a∨¬ e∨¬ f;0. 86), (a∨ c;0. 84), (¬ b∨¬ c∨ g;0. 84), (a ∨ ¬ f;0. 84), (a ∨ c ∨ ¬ d ∨ ¬ e;0. 82), (a ∨ ¬ d ∨ ¬ e ∨ ¬ f;0. 82), (g;0. 8), (c;0. 8), (¬ f;0. 8), ((¬ b ∨ ¬ e) ∧ (d ∨ ¬ e);0. 65), ((¬ b ∨ d) ∧ (d);0. 65), (¬ b ∨ ¬ c ∨ ¬ d ∨ ¬ e;0. 6), (¬ b ∨ ¬ c ∨ ¬ e;0. 6), (¬ b ∨ ¬ c ∨ d;0. 6), (a∨¬ b∨¬ c∨¬ d;0. 52), ((¬ b∨ g)∧ (¬ b∨ g∨ d);0. 51), ((a ∨ ¬ b ∨ ¬ e) ∧ (a ∨ d ∨ ¬ e);0. 51), (¬ d ∨ ¬ e;0. 5), (¬ e;0. 5), (d;0. 5), (¬ b∨¬ c∨ g;0. 44), (a∨¬ b∨ ¬ c∨¬ e;0. 44), ((a∨¬ b)∧ (a∨ d);0. 44), (a∨¬ d;0. 4), (¬ b∨ g;0. 3), (a∨¬ e;0. 3), (¬ b∧ d;0. 3), (a∨¬ b∨¬ c∨¬ d∨ ¬ e;0. 28), (a;0. 2), (¬ b∨¬ c;0. 2), (a∨¬ d∨¬ e;0. 1)} .
W e have:
Undercut = (A
11
,A
32
), (A
11
,A
33
), (A
32
,A
11
), (A
32
,A
12
), (A
32
,A
16
), (A
32
,A
17
) ,
(A
32
,A
18
), (A
32
,A
19
), (A
32
,A
21
), (A
32
,A
22
), (A
32
,A
25
), (A
32
,A
28
), (A
32
,A
29
) ,
(A
32
,A
30
) .
W e have:
Inc
undercut
(K
⊕ ) =max{ min(0. 9, 0. 8),min (0. 9, 0. 8), min(0. 8, 0. 9),min (0. 8, 0. 9), min(0. 8, 0. 9),min (0. 8, 0. 9), min(0. 8, 0. 9),min (0. 8, 0. 88), min(0. 8, 0. 88),min (0. 8, 0. 88), min(0. 8, 0. 86),min (0. 8, 0. 84), min(0. 8, 0. 82),min (0. 8, 0. 82)} = 0. 8 .
Therefore, the inconsistency degree ofK
⊕ is 0.8.
Now , we can define the belief mer ging by ar gumentation
as follows:
Let K = { K
1
,...,K
n
} be a set of possibilistic belief
bases. Belief mer ging operator is defined as follows:
∆ att
⊕ (K) = { ψ | (ψ,a ) ∈ K
⊕ ,a > Inc
att
(K
⊕ )} where
att ∈ { indercut,rebut} . W e call ∆ att
⊕ the family of
BMA ( Belief Mer ging by Ar gumentation ) operators. Con-
tinuing Example 3, withatt = undercut and⊕ (α,β ) =
α +β − α.β we have:
∆ att
⊕ (K) = {{ (a∨¬ b∨ c), (c∨ f), (a∨¬ b∨¬ f), (c∨ g), (¬ f∨ g), ((a∨¬ b)∧ (a∨¬ b∨ d)), ((¬ b∨ f)∧ (d∨ f)), (a∨ ¬ b∨¬ c), (¬ b∨¬ c∨ f), (a∨¬ b), (f), (c∨¬ d∨¬ e), (c∨ ¬ e), (c∨ d), (¬ d∨¬ e∨¬ f), (¬ e∨¬ f), (d∨¬ f), (a∨ c∨ ¬ d), (¬ b∨ c∨ g), (a∨¬ d∨¬ f), (¬ b∨¬ f∨ g), (a∨ c∨ ¬ e), ((g∨¬ b)∧ (g∨ d)), (a∨¬ e∨¬ f), (a∨ c), (¬ b∨¬ c∨ g), (a∨¬ f), (a∨ c∨¬ d∨¬ e), (a∨¬ d∨¬ e∨¬ f)} .
4 Postulates and logical pr operties
W e recall thatK = { K
1
,...,K
n
} is a finite set of possi-
bilistic belief bases,AF
s
is an ar gumentation framework is
determined fromK . Aggregation functionK
⊕ is defined
as follows: K
⊕ :K
n
→ K
∗ . The set of postulates is intro-
duced as follows:
(SYM) K
⊕ ({ K
1
,...,K
n
} ) =K
⊕ ({ K
π (1)
,...,K
π (n)
} ) ,
whereπ is a permutation in{ 1,...,n } .
Postulate (SYM), sometimes called (ANON)[12], en-
sures the equity of participants. It states that the result
of an ar gumentation process should reflect the ar gu-
ments of the participants rather than their identity .
(CON) ∄ ψ ∈ L (K
⊕ ({ K
1
,...,K
n
} ) ⊢ ψ ) ∧ (K
⊕ ({ K
1
,...,K
n
} )⊢¬ ψ )
Postulate (CON) states that belief mer ging by ar gu-
mentation should return a consistent result.
(UNA) if K
∗ 1
≡ ... ≡ K
∗ n
then K
⊕ ({ K
1
,...,K
n
} ) ≡ K
∗ 1
.
Postulate (UNA) presents the assumption of unanim-
ity . It states that if all participants possess the same set
of beliefs, then this set of belief should be the result of
ar gumentation process. Clearly , Postulate (UNA) is
more general than postulate (IDN) and it also implies
(IDN) which is defined as follows:
(IDN) K
⊕ ({ K
i
,...,K
i
} )≡ K
∗ i
It states that if all participants have the same possibilis-
tic belief base, then after the ar gumentation process,
we should have the result as its associated belief base.
(CLO) ∪ n
i=1
B
∗ i
⊢K
⊕ ({ K
i
,...,K
i
} )
Postulate (CLO) requires the closure of the result of ar -
gumentation process. It states that any belief in ar gu-
mentation result should be in at least some input belief
base.
(MAJ) if |{ K
∗ i
⊢ ψ,i = 1...n }| >
n
2
then
K
⊕ ({ K
i
,...,K
i
} )⊢ ψ .
Postulate (MAJ) states that if a belief is supported by
the majority group of participants, it should be in the
result of ar gumentation process.
(COO) ifK
∗ i
⊢ ψ,i = 1...n thenK
⊕ ({ K
i
,...,K
i
} )⊢ ψ .
Postulate (COO) states that if a belief is supported by
all participants, it should be in the result of ar gumen-
tation process.
W e have the following lemma: It holds that:
- (UNA) implies (IDN);
- (MAJ) implies (COO).
Investigate the properties of belief mer ging operator de-
fined in the previous section we have:
Family of BMA operators satisfies the following postu-
lates (SYM) , (CON) , (UNA) , and (CLO) . It does not
satisfy(MAJ) .
5 Conclusion
In this paper , a framework for mer ging possibilistic belief
bases by ar gumentation is introduced and discussed. The
key idea in this work is using the inconsistent degree as a
measure together with the notion of undercut to construct an
ar gumentation framework for belief mer ging. A set of pos-
tulates is introduced and logical properties are mentioned

Ar gumentation-based Machine Learning… Informatica 48 (2024) 107–1 12 1 1 1
and discussed. They assure that the proposed model is
sound and complete. The deeper analysis on the set of pos-
tulates and logical properties, and the evaluation of com-
putational complexities of belief mer ging operators in this
framework are reserved as future work.
Acknowledgment
The authors would like to thank Professor Quang Thuy Ha,
T ran T rong Hieu and Knowledge T echnology Lab, Faculty
of Information T echnology , VNU University of Engineer -
ing and T echnology for expertise support.
Refer ences
[1] L. Amgoud and C. Cayrol. Inferring from incon-
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