On Learning Bipolar Gradual Argumentation Semantics
with Neural Networks
Caren Al Anaissy
1 a
, Sandeep Suntwal
2 b
, Mihai Surdeanu
3 c
and Srdjan Vesic
4 d
CRIL Universit
e d’Artois & CNRS, Lens, France
University of Colorado, Colorado Springs, U.S.A.
University of Arizona, Tucson, U.S.A.
CRIL CNRS Univ. Artois, Lens, France
Argumentation Semantics, Bipolar Gradual Argumentation Graphs, Neural Networks.
Computational argumentation has evolved as a key area in artificial intelligence, used to analyze aspects of
thinking, making decisions, and conversing. As a result, it is currently employed in a variety of real-world
contexts, from legal reasoning to intelligence analysis. An argumentation framework is modelled as a graph
where the nodes represent arguments and the edges of the graph represent relations (i.e., supports, attacks)
between nodes. In this work, we investigate the ability of neural network methods to learn a gradual bipolar
argumentation semantics, which allows for both supports and attacks. We begin by calculating the acceptabil-
ity degrees for graph nodes. These scores are generated using Quantitative Argumentation Debate (QuAD)
argumentation semantics. We apply this approach to two benchmark datasets: Twelve Angry Men and Debate-
pedia. Using this data, we train and evaluate the performance of three benchmark architectures: Multilayer
Perceptron (MLP), Graph Convolution Network (GCN), and Graph Attention Network (GAT) to learn the
acceptability degree scores produced by the QuAD semantics. Our results show that these neural network
methods can learn bipolar gradual argumentation semantics. The models trained on GCN architecture per-
form better than the other two architectures underscoring the importance of modelling argumentation graphs
explicitly. Our software is publicly available at: https://github.com/clulab/icaart24-argumentation.
Computational argumentation theory (CAT) (Dung,
1995; Besnard and Hunter, 2008; Rahwan and Simari,
2009; Baroni et al., 2018; Amgoud and Prade,
2009; Amgoud and Serrurier, 2008; Atkinson et al.,
2017) has emerged as a fundamental area of artifi-
cial intelligence (AI) and is used in many tasks such
as reasoning with inconsistent information, decision
making (Amgoud and Prade, 2009), and classifica-
tion (Amgoud and Serrurier, 2008) across domains
such as legal and medical (Atkinson et al., 2017).
CAT focuses on formalising and automating the
process of argumentation. It accomplishes this
by constructing argumentation graphs in which ar-
The first and the second authors contributed equally.
guments and counter-arguments are interconnected
through either attack or support edges. Within CAT,
semantics serves as a formal method for evaluating
the strength of each argument in the graph considering
its interactions with other arguments. Several bipo-
lar gradual semantics have been proposed recently:
QuAD (Baroni et al., 2015), DF-QuAD (Rago et al.,
2016), Exponent-based (Amgoud and Ben-Naim,
2018), and Quadratic Energy Model (QEM) (Potyka,
2018). This class of semantics have two key proper-
ties: (a) they model both attacks and supports edges,
and (b) they compute acceptability degrees for the
nodes in the graph, which quantify the strength of in-
dividual arguments in the argument graph. That is,
arguments are not only met with opposition (attack),
but also with reinforcement (support). For example,
QuAD semantics (Baroni et al., 2015), a state-of-the-
art semantics, enables the joint analysis and treatment
of both attack and support relations between argu-
ments. That is, it considers the initial weights of the
arguments as well as the attack and support relations
Al Anaissy, C., Suntwal, S., Surdeanu, M. and Vesic, S.
On Learning Bipolar Gradual Argumentation Semantics with Neural Networks.
DOI: 10.5220/0012448300003636
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 16th International Conference on Agents and Artificial Intelligence (ICAART 2024) - Volume 2, pages 493-499
ISBN: 978-989-758-680-4; ISSN: 2184-433X
Proceedings Copyright © 2024 by SCITEPRESS Science and Technology Publications, Lda.
between them in order to calculate the final accept-
ability degree for each argument.
To capture the complex landscape of real-world
discourse, in this work we focus on bipolar gradual
argumentation semantics. While bipolar gradual ar-
gumentation semantics provide the final acceptabil-
ity degree for each node in the graph, there is still
no solution to the fact that they are not guaranteed
to converge in case of cycles. This issue can be re-
solved using neural networks. Neural networks are
known for converging (Smith and Topin, 2019) how-
ever, their ability to learn argumentation semantics is
still unknown. In this work, we focus on the latter
In the space of deep learning, recent developments
in machine learning and especially in large language
models (LLMs) such as GPT-4 (OpenAI, 2023) have
generated claims of (sparks of) Artificial General In-
telligence (AGI) (Bubeck et al., 2023; Zhang et al.,
2023). These claims seem to be supported by the
observation that LLMs can solve new tasks that they
have not been exposed to during their training such as
mathematics, coding, vision, medicine, law, psychol-
ogy, without needing any domain-specific prompting
(Bubeck et al., 2023).
Our paper is motivated by an important observa-
tion that connects the two threads above: a crucial
prerequisite for claims of machine reasoning or AGI
is that the underlying neural networks understand ar-
gumentation theory semantics. Given that argumenta-
tion is an integral part of thinking, making decisions,
and conversing, how else would a machine truly rea-
son? To verify if neural networks can model CAT
semantics, in this work we train and evaluate multi-
ple neural architectures on their capacity to capture
QuAD semantics. In particular, our paper makes three
1. We construct a dataset of argument graphs that
captures QuAD semantics. In particular, we
used the argument graphs from two datasets:
Twelve Angry Men and Debatepedia provided by
the NoDE benchmark (Cabrio and Villata, 2013;
Cabrio et al., 2013). We generated multiple ver-
sions of these graphs, where the arguments’ ini-
tial weights are drawn from four different distribu-
tions (Beta, Normal, Poisson, Uniform), and the
corresponding acceptability degrees are computed
using QuAD semantics.
2. We implement three distinct neural architectures
It is important to note that these claims are not widely
accepted due to suspicions of “contamination,” i.e., the data
used to train these LLMs often contains the tasks used dur-
ing testing (Sainz et al., 2023), which invalidates the bold
claims of AGI.
that learn to predict QuAD semantics acceptabil-
ity degrees given a graph with initial weights.
Our architectures are based on: Multilayer Per-
ceptrons (MLP), Graph Convolution Networks
(GCN) (Kipf and Welling, 2016), and Graph At-
tention Networks (GAT) (Veli
c et al., 2017).
To capture the argument graph structure, all these
architectures have access to node features that in-
clude: (a) node in-degree, (b) total degree, and
(c) the initial node weight. In addition, the two
graph-based architectures use as features: the ini-
tial node weights, edge information, and edge
weights (+1 for supports and -1 for attacks edges).
3. We evaluate the capacity of these architectures
to predict correct acceptability degrees. We con-
clude that their predictions indeed come close
to the true QuAD semantics acceptability degree
(with a mean squared error as low as 0.05). How-
ever, this conclusion has an important caveat: this
performance is only achieved when the argument
graph is explicitly modelled using a graph-based
neural architecture.
Kuhlmann and Thimm (Kuhlmann and Thimm, 2019)
and Craandijk and Bex (Craandijk and Bex, 2020)
trained neural networks to learn extension-based ar-
gumentation semantics. Kuhlmann and Thimm em-
ployed a conventional single forward pass classifier
to approximate credulous acceptance under the pre-
ferred semantics. Craandijk and Bex proposed an
argumentation Graph Neural Network (GNN) that
learns to predict both credulous and sceptical accep-
tance of arguments under four well-known extension-
based argumentation semantics. Our effort operates
under the same goal, i.e., training a neural network to
learn an argumentation semantics, but it extends these
works considerably. First, these two papers focused
on extension-based semantics, whereas ours focuses
on gradual semantics. This, in principle, is harder
to replicate using neural networks due to the contin-
uous values of acceptability degrees. Second, both
these papers take into account only attacks edges; our
method addresses both attacks and supports edges.
Lastly, we explore three different neural architectures
to better understand the best representation for argu-
mentation semantics.
Within CAT, bipolar gradual semantics, which
model both attacks and supports edges and com-
pute argument acceptability degrees, are well stud-
ied. The QuAD semantics was proposed by Baroni
et al. (Baroni et al., 2015) to evaluate the strength of
ICAART 2024 - 16th International Conference on Agents and Artificial Intelligence
answers in decision-support systems. However, this
semantics can sometimes behaviour discontinuously.
The DF-QuAD semantics was proposed by Rago et
al. (Rago et al., 2016) to fix this discontinuity prob-
lem. Amgoud and Ben-Naim (Amgoud and Ben-
Naim, 2018) introduce a set of thirteen principles for
bipolar weighted argumentation semantics. In their
work, the authors explain that both the QuAD and
the DF-QuAD semantics do not satisfy some of these
principles. This is because, as Potyka explains (Po-
tyka, 2018; Potyka, 2019), the QuAD and the DF-
QuAD semantics both have a saturation problem.
That means that once an argument has an attacker
(supporter) with a degree of 1, it becomes meaning-
less to take all the other attackers (supporters) into
account in the aggregation function. To fix this sat-
uration problem, Amgoud and Ben-Naim (Amgoud
and Ben-Naim, 2018) propose the Exponent-based
semantics that satisfies the thirteen principles pro-
posed. However, Potyka (Potyka, 2018) explains
that the Exponent-based semantics violates the dual-
ity principle, meaning that this semantics treats the at-
tack relation and the support relation in an asymmetri-
cal manner. Potyka (Potyka, 2019) also explains that
the Exponent-based semantics do not satisfy “open-
mindedness, i.e., its ability to change the initial
weights is very limited. The Quadratic Energy Model
(QEM) proposed by Potyka (Potyka, 2018) satisfies
twelve properties among the thirteen properties pro-
posed by Amgoud and Ben-Naim (Amgoud and Ben-
Naim, 2018), the duality and the open-mindedness
properties. The MLP-Based semantics (Potyka, 2021)
consists of viewing a multilayer perceptron (MLP),
which is a feed-forward neural network, as a bipo-
lar gradual argumentation framework. This seman-
tics satisfies the same properties as the QEM, ex-
cept that the MLP-Based semantics satisfies the open-
mindedness property excluding the cases where the
arguments’ intial weight is 0 or 1. However, in this
work we focus on the QuAD semantics because it is
widely known and easily explainable. We plan to in-
vestigate other semantics in future work.
Unfortunately, QuAD and most of the followup
semantics are only defined for acyclic graphs. To de-
tail, the DF-QuAD semantics (Rago et al., 2016) and
the Exponent-based semantics (Amgoud and Ben-
Naim, 2018) are also defined for acyclic graphs.
For the semantics proposed by Mossakowski and
Neuhaus (Mossakowski and Neuhaus, 2016), the con-
vergence is not guaranteed for all cyclic graphs. The
convergence of the Quadratic Energy Model proposed
by Potyka (Potyka, 2018) for cyclic graphs is not
proven. Mossakowski and Neuhaus (Mossakowski
and Neuhaus, 2018) show that twenty-five different
semantics can be obtained by combining five aggrega-
tion functions with five influence functions. However,
only three of these semantics converge for all graphs.
Potyka (Potyka, 2019) shows that these three se-
mantics do not satisfy open-mindednes, which makes
them unsuitable for any practical application. Po-
tyka shows also that continuizing discrete models can
solve divergence problems. However, there is cur-
rently no proof of convergence for continuous models
in cyclic graphs. The MLP-Based semantics (Potyka,
2021) is fully-defined for all acyclic graphs and for
cyclic graphs with convergence conditions.
Since we use QuAD, we also focus only on acyclic
graphs in this work. We acknowledge this limitation,
and discuss future work on cyclic graphs in Section 5.
3.1 Data
We performed experiments using datasets created us-
ing argument graphs from two benchmarks: Twelve
Angry Men and Debatepedia provided by the NoDE
benchmark (Cabrio and Villata, 2013; Cabrio et al.,
2013). Note that all the graphs in those datasets are
acyclic. The two datasets used in our study are de-
scribed next.
Twelve Angry Men Dataset. The script of “Twelve
Angry Men” is the first natural language argument
benchmark in our experiments. This dataset contains
three acts (Act 1, Act 2 and Act 3). Every argument
in each act links to at least another dialogue argument
it supports or attacks within the act. The benchmark
contains three graphs (one for each act), where each
argument represents a node and is connected to other
nodes that it supports or attacks. The three graphs
contain 80 edges and 83 nodes in total. We split the
dataset as follows: the graphs from Act 1 and Act 2
(72 nodes) were the training and validation partitions,
while the graph in Act 3 (11 nodes) was the test par-
Debatepedia and ProCon Dataset. This dataset
consists of two encyclopedia of pro and con argu-
ments. The dataset was manually constructed by
selecting a set of topics of Debatepedia/ProCon de-
bates. Here, each debate represents one topic. Within
each topic, an argument is constructed by extract-
ing user opinion. In this dataset, as the attack and
support edges are represented as binary relations,
On Learning Bipolar Gradual Argumentation Semantics with Neural Networks
the arguments are connected with the starting argu-
ment or another argument within the same topic to
which the newest argument refers. A chronologi-
cal order is maintained to ensure a dialogue struc-
ture. This dataset contains 20 debates across differ-
ent topics.The train and validation partition contain
14 graphs; the test partition contains six graphs.
3.2 Method
The QuAD semantics requires each argument to have
an initial weight that captures its intrinsic value. How-
ever, the datasets do not provide such information. To
address this limitation, we generated initial weights
for each node in our dataset using four probabil-
ity distributions: Beta, Normal, Poisson, and Uni-
form. Next, we computed the acceptability degree
score for each node using the QuAD semantics (Ba-
roni et al., 2015). Finally, we used the acceptability
degree scores as the gold degrees to train, validate,
and test three neural network architectures: a multi-
layer perceptron (MLP), a graph convolution network
(GCN) (Kipf and Welling, 2016), and a graph atten-
tion network (GAT) (Veli
c et al., 2017). These
steps were repeated for 100 different initial weights
for each graph and initial weight distribution.
3.2.1 Generating Argumentation Theory-Based
The notation Sup(a) (resp. Att(a)) stands for the set
of supporters (resp. attackers) of argument a, and the
notation w(a) stands for the initial weight of a. deg(a)
stands for the acceptability degree of a. We provide a
short explanation of how the QuAD semantics works.
Quantitative Argumentation Debate. The QuAD
semantics determines the strength, i.e., the acceptabil-
ity degree of each argument, by considering its initial
weight and the aggregated strengths of its attackers
and supporters. The functions f
(a) and f
(a) re-
cursively aggregate the strengths of an argument as
attackers and supporters respectively with as initial
weight. Figure 1 illustrates the QuAD semantics ap-
plied on a bipolar argumentation graph.
Then, the acceptability degree of a is defined as:
deg(a) =
(a) if Sup(a) =
0, Att(a) ̸=
(a) if Sup(a) ̸=
0, Att(a) =
w(a) if Sup(a) =
0, Att(a) =
(a)+ f
(a) = w(a) ·
(1 deg(b))
(a) = 1 (1 w(a)) ·
(1 deg(b))
Figure 1: Example of a bipolar argumentation graph ex-
tracted from the Debatepedia dataset (Cabrio and Villata,
2014), for the debate called Sobrietytest. The red arrows
represent attacks while the green arrows represent supports.
The first row of numbers next to the arguments represent
their initial weights which are assigned randomly (drawn
from a given distribution), while the second row of num-
bers represent their acceptability degrees calculated using
the QuAD semantics.
3.2.2 Learning Argumentation Semantics
To investigate the capacity of neural networks to learn
QuAD semantics, we explore three different neural
network architectures. Note that the neural network
architectures typically employed for learning struc-
tured data are not suited for resolving non-euclidean
input data such as graphs. Due to the variable size
and shape of the input graphs, it is difficult to pro-
cess them using conventional data structures such as
adjacency matrices (Veli
c et al., 2017). In addi-
tion, adjacency matrices are dependent on the order in
which the nodes appear, so they are not node invari-
ant. To avoid the limitations of existing algorithms,
we transform the arguments and debates into neu-
ral network graph structures, and learn the semantics
using Graph Neural Networks (GNNs) (Gori et al.,
2005; Scarselli et al., 2008). GNNs aim to utilize con-
ventional deep learning principles for non-euclidean
data. GNNs achieve this by allowing for message
passing between nodes (which represent arguments)
and edges (which represent relations such as support
or attack, and have a weight) through convolution op-
erations. The equation for this operation is as follows:
= γ
, f
jN (i)
, n
, e
ICAART 2024 - 16th International Conference on Agents and Artificial Intelligence
Table 1: Results for Twelve Angry Men and Debatepedia datasets using QuAD. The top row indicates the neural network
architecture. The first column represents the distribution from which the initial random weights were assigned. These results
are means across 100 different initial weights for each node. MSE represents the final mean squared error. Since MSE is an
error based statistic, a lower value is better. RMSE represents the relative MSE. The MSE results highlighted in bold indicate
the best MSE results among the three neural networks.The Kendall Tau correlation metric measures the correlation between
the node ranks produced by a given neural network and the ranks produced by QuAD semantics. A statistically significant
Kendall’s τ represents that rankings produced by NNs and QuAD semantics were similar. *, **, *** indicate statistical
significance (.05, .005, .0005).
MSE RMSE Kendall Tau MSE RMSE Kendall Tau MSE RMSE Kendall Tau
Twelve Angry Men Dataset
Beta 0.18 3.33 -0.23 0.09 1.67 0.48 0.14 2.55 0.23
Normal 0.15 2.84 -0.18 0.09 1.64 0.41 0.11 2.08 0.26
Poisson 0.2 inf -0.44 0.14 inf 0.39 0.18 inf 0.25
Uniform 0.14 2.48 -0.19 0.07 1.23 0.47 0.1 1.78 0.22
Debatepedia Dataset
Beta 0.36 0.67 0.36 0.07 0.12 0.72*** 0.1 0.19 0.69
Normal 0.34 0.64 0.39 0.06 0.11 0.73*** 0.08 0.16 0.65
Poisson 0.29 1.06 0.2 0.08 0.27 0.62*** 0.14 0.5 0.76
Uniform 0.32 0.56 0.33 0.05 0.08 0.76*** 0.07 0.12 0.64
where n
represents node i
s node features
in layer k 1, e
represents edge features from
node j to node i, informing us about the importance
of each neighbor. f represents a permutation invariant
function (e.g., sum, avg) to ensure that the methods
make no assumptions about the spatial relationships
between node features during convolutions, φ denotes
a neural network that constructs the message to node i
for each edge j, i, and γ denotes a neural network that
takes the output of this aggregation to update the ac-
ceptability degree scores for node i. The final output
produces the updated acceptability degree scores for
each node in the graph.
We conducted experiments using three architec-
tures: MLP, GCN, and GAT. MLP is a feed-forward
neural network architecture suitable for some struc-
ture data but not graphs. This architecture serves as
our first baseline. GCNs (Kipf and Welling, 2016)
extend the concept of convolution, which is widely
used in convolutional neural networks (CNNs) (Le-
Cun et al., 1998) for image or text processing, to
the graph domain. In CNNs, a convolutional layer
applies filters over local patches of an input image
(or local textual context) to extract features. Simi-
larly, in GCNs, a convolutional layer processes nodes
and their neighboring nodes to aggregate informa-
tion. GATs, our third architecture, use more com-
plex attention-based architectures to explore the en-
tire neighborhood of a node in an order invariant
way (Veli
c et al., 2017). To capture the graph
structure for the MLP architecture, we created node
features that contain: (a) node in-degree, (b) total
degree, and (c) the initial node weight. These fea-
tures help overcome some limitations such as uniform
structure for each input. For the two graph-based
architectures, we used as features: the initial node
weights, edge information, and edge weights (+1 for
supports and -1 for attacks edges). All neural methods
were trained using the mean-squared error (MSE) loss
on the corresponding training partitions. We tuned the
early stopping hyperparameter on the validation par-
Table 1 presents the results from our study, in which
we evaluate the three proposed neural architectures
on the graphs introduced in previous section. This
table lists results across the four distributions for ini-
tial argument weights. To evaluate the performance
of the neural architectures we used mean squared er-
ror (MSE) between the predicted and the gold accept-
ability degrees. We also used the Kendall rank cor-
relation coefficient metric (also referred as Kendall’s
τ) (Kendall, 1938), to measure the correlation be-
tween the node ranks produced by a given neural net-
work and the ranks produced by QuAD semantics.
Kendall’s tau computes the difference between the
number of matching and non-matching observation
pairs and divides it by the total number of observa-
tion pairs. A value of 1 indicates complete negative
association, 1 indicates complete positive association,
and 0 indicates no association between the variables.
The underlying hypothesis tests if the two lists are
identical. A p-value .05 and τ value > 0 signifies
a statistically significant similarity between the two
rankings. Here, a statistically significant Kendall’s τ
score indicates that the acceptability score rankings
produced by QuAD semantics have a high correlation
with the acceptability degree scores produced by the
neural networks.
On Learning Bipolar Gradual Argumentation Semantics with Neural Networks
Formally, Kendall’s τ is calculated as follows:
τ =
k(k 1)
i< j
where k is the number of observations, x
and y
the rankings of the i
observation for the two vari-
ables being compared, and sgn is the sign function
that returns 1 if the argument is positive, -1 if nega-
tive, and 0 if zero. We draw the following observa-
tions from this experiment:
First, our experiments indicate that neural net-
works can indeed learn to predict the acceptabil-
ity degrees computed by QuAD semantics. To our
knowledge, this is the first work to show that neu-
ral networks can learn to replicate bipolar gradual
CAT semantics. This is an exciting result consid-
ering the complexity of the task.
Second, the best results by far are obtained by
neural architectures that model graphs explicitly
(GCN and GNN-GAT), which highlights the im-
portance of modelling argument interactions. For
example, the MSEs measured for GCN range be-
tween 0.05 and 0.09 for the two datasets and
the four probability distributions used for initial
weights. In contrast, the MSEs measured for the
MLP, which uses a limited number of features to
summarize the graph structure, range from 0.14
to 0.36 depending on the dataset and probability
distribution. The latter results are not only con-
siderably worse, but also show extreme variation
between datasets.
Third, between the two graph-based architectures,
GCN performs consistently better than GNN-
GAT. For example, for the Debatepedia Dataset,
the MSE measured for GCN ranges from 0.05 to
0.08, whereas the MSE for GNN-GAT is approx-
imately twice that ranging from 0.08 to 0.14. We
consider this another positive result, which indi-
cates that, as long as the neural architectures cap-
ture the argument graph structures, simplicity is
better. This is an important observation for the
deployment of these neural architectures in real-
world software applications.
Lastly, if we consider the Kendall Tau scores cal-
culated between the ranking produced by GCN
and the ranking produced by QuAD semantics, we
can observe a moderate positive correlation be-
tween the two rankings for the Twelve Angry Men
dataset. We can also observe a strong positive cor-
relation between the two rankings for the Debate-
pedia dataset, which is statistically significant at a
very low p-value threshold. These results show
us that GCN is not only capturing the general
trends in the data (as indicated by low MSE) but
is also performing well in maintaining the ranking
of the values, therefore producing consistent rank-
ing. These results are particularly valuable since
they give us insights about the capability of GCN
to effectively predict the ranking among the nodes
in a bipolar gradual argumentation graph.
Argumentation continues to grow as a key area in
AI for several tasks that require decision-making and
communication. As such, we argue that understand-
ing argumentation should be a requirement for neural
networks that implement machine reasoning. In this
study, we investigated the ability of neural networks
to learn gradual bipolar argumentation semantics. We
conducted several experiments to train and evaluate
neural networks’ ability to learn the QuAD argumen-
tation semantics. Our findings indicate that argu-
mentation semantics can be learned by neural net-
works successfully. One important observation is that
the best results are consistently produced by GCNs,
a graph-based neural architecture, which underlines
that the argument graph structure must be explicitly
modelled. All in all, this paper is the first to show
that neural architectures can learn gradual bipolar ar-
gumentation semantics.
One limitation of this work is that all the data used
for training and testing the proposed neural architec-
tures consisted only of acyclic graphs, where QuAD
semantics is guaranteed to converge. In the future, we
will expand our work to include cyclic graphs where
the QuAD (or other) semantics converge. To the best
of our knowledge, there does not exist a dataset or
benchmark that contains a significant number of real-
world bipolar weighted cyclic graphs. We are cur-
rently working on collecting cyclic graphs from real
online debates and verify in which situations QuAD
semantics converges. Other future work will include
training neural networks on other bipolar weighted se-
mantics, based on the behaviour desired in a specified
This work was supported by the International Emerg-
ing Action (IEA) project RHAPSSODY and joint
PhD Program SURFING, both funded by the French
National Center for Scientific Research (CNRS) and
ICAART 2024 - 16th International Conference on Agents and Artificial Intelligence
the University of Arizona. Caren Al Anaissy and
Srdjan Vesic were also supported by the project AG-
GREEY ANR22-CE23-0005 from the French Na-
tional Research Agency (ANR).
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