# On the Feasibility of Learning Bipolar Gradual Argumentation Semantics Using Neural Architectures

Caren Al Anaissy, Sandeep Suntwal, Mihai Surdeanu, Srdjan Vesic

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Caren Al Anaissy, Sandeep Suntwal, Mihai Surdeanu, Srdjan Vesic. On the Feasibility of Learning Bipolar Gradual Argumentation Semantics Using Neural Architectures. Agents and Artificial Intelligence. 16th International Conference, ICAART 2024, Ana Paula Rocha; Luc Steels; Jaap van den Herik, Feb 2024, Rome, Italy. pp.176-190, 10.1007/978-3-031-87330-0_9. hal-05468473

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# On the Feasibility of Learning Bipolar Gradual Argumentation Semantics Using Neural Architectures

Caren Al Anaissy¹[0000-0002-8750-1849], Sandeep Suntwal²[0000-0002-7746-7114], Mihai Surdeanu³[0000-0001-6956-8030], and Srdjan Vesic⁴[0000-0002-4382-0928]

¹ CRIL Université d'Artois & CNRS, Lens, France alanaissy@cril.fr

² University of Colorado, Colorado Springs, United States ssuntwal@uccs.edu

³ University of Arizona, Tucson, United States msurdeanu@arizona.edu

⁴ CRIL CNRS Univ. Artois, Lens, France {vesic}@cril.fr

**Abstract.** Computational argumentation has emerged as a crucial domain within artificial intelligence, offering insights into reasoning, decision-making, and communication processes. Its applications span various real-world scenarios, from legal argumentation to intelligence analysis. In this framework, arguments are represented as nodes in a graph, with edges depicting the relationships (support or attack) between them. This study explores the capacity of neural network approaches to learn bipolar gradual argumentation semantics, which incorporates both supportive and oppositional relationships. We initiate our approach by deriving acceptability degrees for graph nodes using the Quantitative Argumentation Debate (QuAD) semantics. We then apply this method to two benchmark datasets: Twelve Angry Men and Debatepedia. Utilizing this data, we train and assess three neural network architectures: Multilayer Perceptron (MLP), Graph Convolution Network (GCN), and Graph Attention Network (GAT), evaluating their ability to learn the acceptability degrees generated by QuAD semantics. Our findings demonstrate that these neural network methods can learn bipolar gradual argumentation semantics. Notably, models based on the GCN architecture outperform the other two, highlighting the significance of explicitly modeling argumentation graphs. Our software is publicly available at: https://github.com/clulab/icaart24-argumentation.

**Keywords:** Argumentation Semantics · Bipolar Weighted Argumentation Graphs · Neural Networks.

## 1 Introduction

*Computational argumentation theory (CAT)*[15, 9, 28, 7, 4–6] has evolved into a fundamental area of artificial intelligence (AI), finding applications in diverse tasks such as reasoning with inconsistent information, decision making[4], and classification [5] across various domains including legal and medical [6].

The primary focus of CAT lies in formalizing and automating the process of argumentation. This is achieved through the construction of argumentation graphs, where arguments and counter-arguments are interconnected via attack or support edges. Within

The first and the second authors contributed equally.
<figure><img src="image_2.png" /><figcaption>Fig. 1: An illustration of a bipolar argumentation graph.</figcaption></figure>

this framework, semantics plays a crucial role as a formal method for evaluating the
strength of each argument in the graph, taking into account its interactions with other
arguments. Recently, several bipolar gradual semantics have been proposed, includ-
ing QuAD [8], DF-QuAD [27], Exponent-based [2], and Quadratic Energy Model
(QEM) [24]. These semantics share two key properties: they model both attack and
support edges, and they compute acceptability degrees for the nodes in the graph, quan-
tifying the strength of individual arguments. This approach allows for a more nuanced
representation of argumentation, where arguments can be both opposed (attacked) and
reinforced (supported). Figure 1 illustrates a simple bipolar argumentation graph. To
capture the intricate nature of real-world discourse, our work focuses on bipolar grad-
ual argumentation semantics. While these semantics provide a final acceptability degree
for each node in the graph, they face a challenge in that convergence is not guaranteed in
the case of cyclic graphs. Neural networks, known for their convergence properties [31],
offer a potential solution to this issue. However, their ability to learn argumentation se-
mantics remains an open question, which we address in this study. In parallel, recent
advancements in machine learning, particularly in large language models (LLMs) like
GPT-4 [23], have sparked discussions about Artificial General Intelligence (AGI)[10,
33]. These claims are often supported by observations that LLMs can tackle novel tasks
across various domains without specific training. However, it's worth noting that these
claims are not universally accepted due to concerns about potential data contamina-
tion [29]. Our research is motivated by a crucial observation linking these two areas: for
any claims of machine reasoning or AGI to be valid, it is essential that the underlying
neural networks comprehend argumentation theory semantics. Given that argumenta-
tion is fundamental to human thinking, decision-making, and communication, it follows
that true machine reasoning would necessitate an understanding of these processes. To
investigate whether neural networks can model CAT semantics, we train and evaluate
multiple neural architectures on their ability to capture QuAD semantics. Our paper
makes three primary contributions:

1. We develop a dataset of argument graphs that embodies QuAD semantics. We utilize argument graphs from two existing datasets: Twelve Angry Men and Debatepedia, provided by the NoDE benchmark [11, 13]. We generate multiple versions of these graphs, assigning initial weights to arguments from four different distributions (Beta, Normal, Poisson, Uniform), and compute the corresponding acceptability degrees using QuAD semantics.
2. We implement three distinct neural architectures designed to learn and predict QuAD semantics acceptability degrees given a graph with initial weights. These architectures are based on Multilayer Perceptrons (MLP), Graph Convolution Networks (GCN) [18], and Graph Attention Networks (GAT) [32]. To effectively capture the argument graph structure, all architectures incorporate node features including node in-degree, total degree, and initial node weight. The graph-based architectures additionally utilize initial node weights, edge information, and edge weights (+1 for supports, -1 for attacks) as features.

3. We conduct a thorough evaluation of these architectures' capacity to predict accurate acceptability degrees. Our results indicate that their predictions closely approximate the true QuAD semantics acceptability degree, with mean squared errors as low as 0.05. However, it's important to note that this level of performance is achieved only when the argument graph is explicitly modeled using a graph-based neural architecture.

Note that this paper builds upon the work presented in [1], highlighting the problem in more detail and providing more details about the data and experiments.

## 2 Related Work

The exploration of neural networks in learning argumentation semantics has been previously undertaken by Kuhlmann and Thimm [19] and Craandijk and Bex [14], who focused on extension-based argumentation semantics. Kuhlmann and Thimm employed a conventional single forward pass classifier to approximate credulous acceptance under the preferred semantics. Craandijk and Bex proposed an argumentation Graph Neural Network (GNN) capable of predicting both credulous and sceptical acceptance of arguments under four well-established extension-based argumentation semantics. While our work shares the overarching goal of training neural networks to learn argumentation semantics, it extends these previous efforts in several significant ways. Firstly, we focus on gradual semantics rather than extension-based semantics, which presents a greater challenge for neural networks due to the continuous nature of acceptability degrees. Secondly, our method addresses both attack and support edges, whereas previous works considered only attack edges. Lastly, we investigate three different neural architectures to gain a more comprehensive understanding of the most effective representation for argumentation semantics.

In the realm of Computational Argumentation Theory (CAT), bipolar gradual semantics have been extensively studied. These semantics model both attack and support edges and compute argument acceptability degrees. The QuAD semantics was proposed by Baroni et al. [8] to evaluate the strength of answers in decision-support systems. However, this semantics suffers from two problems. The first problem is the saturation problem, where the supporters' (respectively attackers') aggregated strength is saturated to 0 (resp. 1) when an attacker (resp. supporter) has an acceptability degree of 1. To illustrate, suppose an argument *a* has an attacker (resp. supporter) of acceptability degree = 1. The other attackers (resp. supporters) become irrelevant for the attackers' (resp. supporters') aggregated strength since they make no difference on
this strength that has been already saturated to 0 (resp. 1). The second problem is the discontinuous behaviour of QuAD. For example, suppose that an unsupported argument *a* is attacked by very strong attackers, the acceptability degree of *a* is very low and can even reach 0. Now suppose we add a supporter for *a* that has a low acceptability degree, *a*'s acceptability degree can jump very easily from 0 to a high value, while *a*'s supporter is weak. We can have the same kind of discontinuity where the acceptability degree of an argument *a* that has very strong supporters, can jump from a high value (possibly = 1) to a low value, only because we added one weak attacker for *a*. One advantage of using the QuAD semantics is that it induces a symmetrical impact for attacks and supports when an argument *a* has a symmetric configuration of attackers and supporters, meaning when the number of *a*'s attackers and *a*'s supporters is the same and they have pairwise equal acceptability degree. More precisely, the distance of *a*'s initial weight is reduced from 0 by the value of *a*'s attackers' aggregated strength in the same proportion as the reduced distance of *a*'s initial weight from 1 by *a*'s supporters' aggregated strength. The DF-QuAD semantics was proposed by Rago et al. [27] to fix this discontinuity problem. However, this semantics also suffers from the saturation problem. Amgoud and Ben-Naim [3] introduce a set of twelve principles for bipolar weighted argumentation frameworks. They propose the Euler-based restricted semantics that satisfies these twelve principles. Then Amgoud and Ben-Naim [2] propose the Exponent-based restricted semantics, and they introduce the inertia principle in addition to the twelve existing principles, note that the Exponent-based restricted semantics satisfies all thirteen principles. In their work, Amgoud and Ben-Naim [3, 2] explain that both the QuAD and the DF-QuAD semantics do not satisfy some of these principles. This can be explained by the saturation problem from which the QuAD and the DF-QuAD semantics both suffer. Although the Exponent-based semantics satisfies the thirteen principles, Potyka [24] explains that this semantics violates the duality principle, meaning that it treats the attack relation and the support relation in an asymmetrical manner. Potyka [25] also explains that this semantics does not satisfy “open-mindedness,” i.e., its ability to change the initial weights is very limited. For this purpose, Potyka [24] proposes the Quadratic Energy Model (QEM) and proves that this semantics satisfies the twelve principles by Amgoud and Ben-Naim [3], the duality and the open-mindedness principles. The MLP-Based semantics [26] consists of viewing a multilayer perceptron (MLP), which is a feed-forward neural network, as a bipolar gradual argumentation framework. This semantics satisfies the same properties as the QEM, except that the MLP-Based semantics satisfies the open-mindedness property excluding the cases where the arguments' initial 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 investigate other semantics in future work.

It's important to note that QuAD and most subsequent semantics are only defined for acyclic graphs. The DF-QuAD [27] and Exponent-based [2] semantics share this limitation. Other proposed semantics either lack guaranteed convergence for all cyclic graphs [22] or have unproven convergence for cyclic graphs [24]. While some semantics converge for all graphs, they may lack practical applicability due to not satisfying open-mindedness [25]. Given these considerations, our work focuses on acyclic graphs using
QuAD semantics. We acknowledge this limitation and discuss potential future work on
cyclic graphs in the conclusion.

This section details our approach, focusing on the datasets used and the methods
employed to prepare them for our experiments.

3 Background Knowledge

In this section we provide the background knowledge for bipolar gradual semantics for
weighted bipolar argumentation frameworks, namely for the QuAD semantics.

A weighted bipolar argumentation framework WBAF consists of arguments with relation of support and attack between them. Weights which are scores ranging between 0 and 1, can be assigned either to arguments or to the attack and support relations. In this work we consider weighted argumentation frameworks where an initial weight is assigned to each argument to represent its intrinsic strength independently of its interactions with the other arguments. Bipolar gradual semantics compute the final strength of each argument by taking into consideration its initial weight and the strengths of its supporters and attackers. The final strengths values computed by such semantics are called acceptability degrees. Most of the bipolar gradual semantics use an iterative procedure to evaluate the acceptability of the arguments in a WBAF. This iterative procedure updates simultaneously, for all arguments in a WBAF, their strengths, until reaching an iteration *i* where all the strengths of the arguments converge to their final strengths. Many bipolar gradual semantics have been defined in the literature, most of them are defined for acyclic graphs, where the convergence of these semantics is guaranteed. When having acyclic graphs, arguments can be ordered in a topological way, and the acceptability degrees of the arguments can be calculated successively, based on their initial weights and the acceptability degrees of their parents.

**Definition 1 (Weighted Bipolar Argumentation Framework).** A weighted bipolar argumentation framework WBAF is a quadruple $\langle Ar, att, sup, w \rangle$ where Ar is a finite set called arguments, and $att, sup \subseteq Ar \times Ar$ are binary relations over Ar called attack and support respectively, and $w$ is a weighting function $w: Ar \to [0, 1]$, that associates for each argument $a \in Ar$ a value $w(a) \in [0, 1]$, called initial weight.

**Definition 2 (Bipolar Gradual Semantics).** A bipolar gradual semantics $\sigma$ for WBAFs is a function that maps a WBAF $\mathcal{F} = \langle Ar, att, sup, w \rangle$ into a weighting on $Ar$, $\sigma_{\mathcal{F}}: Ar \to [0, 1]$. $\text{Deg}^{\sigma_{\mathcal{F}}}(a)$ stands for the weight assigned by $\sigma_{\mathcal{F}}$, called acceptability degree of a calculated by $\sigma_{\mathcal{F}}$. Note that we also $\text{Deg}(a)$ and $\text{Deg}^{\sigma_{\mathcal{F}}}(a)$ interchangeably.

$\text{Sup}(a)$ (resp. $\text{Att}(a)$) denote the set of supporters (resp. attackers) of an argument $a$. Let $\text{SEQ}_{\text{Deg}}(\text{Att}(b)) = (\text{Deg}(a_1), \text{Deg}(a_2), \dots, \text{Deg}(a_p))$ and $\text{SEQ}_{\text{Deg}}(\text{Sup}(b)) = (\text{Deg}(s_1), \text{Deg}(s_2), \dots, \text{Deg}(s_q))$ be the sequences of the acceptability degrees of $b$'s attackers and supporters, respectively. A sequence $\text{SEQ}_{\text{Deg}}(\text{Att}(b))$ (resp. $\text{SEQ}_{\text{Deg}}(\text{Sup}(b))$) is called ineffective if the sequence is empty, meaning that $b$ has no attackers (resp. supporters), or if the sequence contains only zeros, meaning that all of $b$'s attackers (resp. supporters) have null acceptability degrees.
## 3.1 Quantitative Argumentation Debate QuAD Semantics

Baroni et al. [8] propose the QuAD semantics to evaluate the strengths of alternative design solutions for Issue-Based Information System (IBIS) [20] style debates. Note that Baroni et al. use the term quantitative to refer to the fact an initial weight is assigned to each argument. To calculate the acceptability degree of an argument *b*, Baroni et al. define a generic score function that aggregates *b*'s initial weight with two independent aggregation functions, that aggregate the strength of *b*'s attackers (resp. supporters) with *b*'s initial weight. The functions $f_a(b)$ and $f_s(b)$ recursively aggregate the strengths of an argument *b*'s attackers and supporters respectively with *b*'s initial weight. Figure 2 illustrates the QuAD semantics applied on a bipolar argumentation graph.

The acceptability degree of an argument *b* calculated by the QuAD semantics is defined as follows:

**Definition 3 (QuAD semantics).** Let $\mathcal{F} = \langle Ar, att, sup, w \rangle$ be a WBAF. The acceptability degree of an argument *a* in $\mathcal{F}$, calculated by the QuAD semantics is defined as:

$$ \text{Deg}(b) = \begin{cases} f_a(b) & \text{if } \text{SEQ}_{\text{Deg}}(\text{Sup}(b)) \text{ is ineffective and } \text{SEQ}_{\text{Deg}}(\text{Att}(b)) \text{ is non ineffective} \\ f_s(b) & \text{if } \text{SEQ}_{\text{Deg}}(\text{Att}(b)) \text{ is ineffective and } \text{SEQ}_{\text{Deg}}(\text{Sup}(b)) \text{ is non ineffective} \\ w(b) & \text{if } \text{SEQ}_{\text{Deg}}(\text{Sup}(b)) \text{ and } \text{SEQ}_{\text{Deg}}(\text{Att}(b)) \text{ are both ineffective sequences.} \\ \frac{f_a(b)+f_s(b)}{2} & \text{otherwise} \end{cases} \tag{1} $$

where

$$ f_a(b) = w(b) \cdot \prod_{a \in \text{Att}(b)} (1 - \text{Deg}(a)) $$

and

$$ f_s(b) = 1 - (1 - w(b)) \cdot \prod_{s \in \text{Sup}(b)} (1 - \text{Deg}(s)) $$

# 4 Approach

## 4.1 Data

We conducted our experiments using datasets derived from argument graphs sourced from two established benchmarks: Twelve Angry Men and Debatepedia, both provided by the NoDE benchmark [11, 13]. It's important to note that all graphs in these datasets are acyclic, which aligns with the requirements of the QuAD semantics we are using in this study. The following subsections describe each dataset in detail.

**Twelve Angry Men Dataset** The script of "Twelve Angry Men" serves as our first natural language argument benchmark. This dataset is particularly interesting as it represents a structured dialogue with clear argumentative elements. The dataset is divided into three acts (Act 1, Act 2, and Act 3), each containing a series of arguments presented by the characters in the play. In this dataset, every argument within each act is linked to at
<figure><img src="image_3.png" /><figcaption>Fig. 2: Example of a bipolar argumentation graph [1] extracted from the Debatepedia dataset [12], 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 numbers represent their acceptability degrees calculated using the QuAD semantics.</figcaption></figure>

least one other argument through either a support or attack relation. This interconnect-
edness reflects the nature of real-world debates, where arguments are rarely isolated but
instead form a complex web of supporting and opposing ideas. We transformed these
arguments into three distinct graphs, one for each act. In these graphs, each node rep-
resents an individual argument, and the edges between nodes represent the support or
attack relations between arguments. This transformation allows us to capture the struc-
ture of the debate in a format suitable for our neural network architectures. The resulting
graphs contain a total of 80 edges and 83 nodes across all three acts. To facilitate our
machine learning approach, we divided the dataset as follows:

- Training and Validation Set: Graphs from Act 1 and Act 2, containing 72 nodes in total.

- Test Set: Graph from Act 3, containing 11 nodes.

This division allows us to train and validate our models on a substantial portion of the
data while reserving a separate section for testing, ensuring a fair evaluation of our
models’ performance.

*Debatepedia and ProCon Dataset* Our second dataset is derived from Debatepedia and ProCon, two online encyclopedias of pro and con arguments covering a wide range of topics. This dataset provides a broader and more diverse set of arguments compared to the Twelve Angry Men dataset, allowing us to test our models on a variety of debate structures and topics. The dataset was carefully constructed through a manual selection process, focusing on a set of topics from Debatepedia and ProCon debates. Each debate in the dataset represents a distinct topic, and within each topic, individual arguments are constructed by extracting user opinions from the original sources. A key feature of this dataset is the representation of attack and support edges as binary relations. Arguments are connected either to the initial argument of the debate or to another argument within the same topic to which the new argument directly responds. This structure maintains a
chronological order, ensuring that the resulting graphs preserve the dialogue structure of the original debates. To prepare this dataset for our experiments, we transformed each debate into a graph structure similar to the Twelve Angry Men dataset. Each argument becomes a node in the graph, with edges representing the support or attack relations between arguments. The complete dataset contains 20 debates covering a diverse range of topics. For our machine learning approach, we divided these debates into the following partitions:

- Training and Validation Set: 14 graphs

- Test Set: 6 graphs

This division ensures that we have a substantial amount of data for training and validation while reserving a significant portion for testing, allowing us to assess how well our models generalize to unseen debate structures. In both datasets, we carefully preserved the original structure and relationships between arguments during the transformation process. This attention to detail ensures that our graph representations accurately reflect the complex nature of real-world debates, providing a solid foundation for training our neural network models to understand and predict argumentation semantics.

## 4.2 Method

Our approach to investigating the ability of neural networks to learn QuAD semantics involves several key steps, which we detail in this section.

**Data Preparation** The QuAD semantics requires each argument to have an initial weight that captures its intrinsic value. However, the datasets we used do not provide this information. To address this limitation, we developed a systematic approach to generate and assign initial weights to each node in our dataset. We used four different probability distributions to generate these initial weights:

- Beta Distribution: This distribution is particularly useful for modeling values that are constrained to intervals of finite length. It allows for a variety of shapes, making it suitable for representing different types of argument strength distributions.

- Normal Distribution: Also known as the Gaussian distribution, this symmetric distribution is often used to model natural phenomena. In our context, it represents a scenario where most arguments have moderate strength, with fewer extremely weak or strong arguments.

- Poisson Distribution: This discrete probability distribution expresses the probability of a given number of events occurring in a fixed interval. In our case, it models scenarios where argument strengths are more clustered around certain values.

- Uniform Distribution: This distribution assigns equal probability to all values within a given range. It represents a scenario where all initial argument strengths are equally likely.

By using these diverse distributions, we aimed to test the robustness of our neural network models across different potential distributions of argument strengths.
**Generating Argumentation Theory-based Baselines** After assigning initial weights, we computed the acceptability degree for each node using the QuAD semantics [8]. This step is crucial as it provides us with the 'gold standard' against which we can evaluate our neural network models.

**Neural Network Architectures** To investigate the capacity of neural networks to learn QuAD semantics, we implemented and evaluated three distinct neural network architectures:

1. Multilayer Perceptron (MLP): A feed-forward neural network that serves as our baseline model. While not specifically designed for graph-structured data, we adapted it to handle our argument graphs by incorporating relevant features.

2. Graph Convolution Network (GCN) [18]: This architecture extends the concept of convolution to graph-structured data. It's particularly well-suited for our task as it can directly operate on the graph structure of our argument networks.

3. Graph Attention Network (GAT) [32]: This architecture introduces attention mechanisms to graph neural networks, allowing the model to assign different importance to different neighboring nodes when aggregating information.

For all three architectures, we designed node features to capture the graph structure. These features include:

- Node in-degree: The number of edges pointing to the node

- Total degree: The total number of edges connected to the node

- Initial node weight: The weight assigned from our probability distributions

For the graph-based architectures (GCN and GAT), we additionally used:

- Edge information: The presence and direction of edges between nodes

- Edge weights: +1 for support edges and -1 for attack edges

These features allow our models to capture the complex relationships between arguments in the graph structure.

**Training and Evaluation Process** We used the acceptability degrees computed by the QuAD semantics as the gold standard to train, validate, and test our neural network architectures. The training process was conducted using the mean squared error (MSE) loss function, which measures the average squared difference between the predicted and true acceptability degrees. To ensure robustness of our results, we repeated this process for 100 different sets of initial weights for each graph and each initial weight distribution. This extensive experimentation allows us to account for potential variability in the initial weight assignments and provides a more comprehensive evaluation of our models' performance. In the next section, we present and discuss the results of these experiments, providing insights into the ability of neural networks to learn and replicate QuAD semantics across different graph structures and initial weight distributions. Figure 3 illustrates the overall training and evaluation methodology.
<figure><img src="image_4.png" /><figcaption>Fig. 3: Overview of the methodology for learning argumentation semantics with neural networks.</figcaption></figure>

**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 structured 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 process them using conventional data structures such as adjacency matrices [32]. In addition, adjacency matrices are dependent on the order in which the nodes appear, so they are not node invariant. To avoid the limitations of existing algorithms, we transform the arguments and debates into neural network graph structures, and learn the semantics using Graph Neural Networks (GNNs) [16, 30]. GNNs aim to utilize conventional 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 operations. The equation for this operation is as follows:

$$ \mathbf{n}_{i}^{(k)} = \gamma^{(k)} \left( \mathbf{n}_{i}^{(k-1)}, f_{j \in \mathcal{N}(i)} \phi^{(k)} \left( \mathbf{n}_{i}^{(k-1)}, \mathbf{n}_{j}^{(k-1)}, \mathbf{e}_{j,i} \right) \right) \quad (2) $$

where $\mathbf{n}^{(k-1)} \in \mathbb{R}^P$ represents node i's node features in layer k-1, $\mathbf{e}_{j,i} \in \mathbb{R}^Q$ 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, $\phi$ denotes a neural network that constructs the message to node i for each edge j, i, and $\gamma$ denotes a neural network that takes the output of this aggregation to update the acceptability degree for node i. The final output produces the updated acceptability degrees for each node in the graph. We conducted experiments using three architectures: MLP, GCN, and GAT. MLP is a feed-forward neural network architecture suitable for some structure data but not graphs. This architecture serves as our first baseline. GCNs [18] extend the concept of convolution, which is widely used in
convolutional neural networks (CNNs) [21] 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. Similarly, in GCNs, a convolutional layer processes nodes and their neighboring nodes to aggregate information. GATs, our third architecture, use more complex attention-based architectures to explore the *entire* neighborhood of a node in an order invariant way [32]. 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 features 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 partition.

<table><caption>Table 1: Results for Twelve Angry Men and Debatepedia datasets using QuAD [1]. 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 (lower is better). R-MSE represents the relative MSE. Bold MSE results indicate the best among the three neural networks. Kendall's τ measures the correlation between node ranks produced by neural networks and QuAD semantics. *, **, *** indicate statistical significance (≤.05, <.005, ≤.0005).</caption><thead><tr><th rowspan="2">Model</th><th colspan="3">MLP</th><th colspan="3">GCN</th><th colspan="3">GNN-GAT</th></tr><tr><th>MSE</th><th>R-MSE</th><th>K. Tau</th><th>MSE</th><th>R-MSE</th><th>K. Tau</th><th>MSE</th><th>R-MSE</th><th>K. Tau</th></tr></thead><tbody><tr><td colspan="10"><strong>Twelve Angry Men Dataset</strong></td></tr><tr><td>Beta</td><td>0.18</td><td>3.33</td><td>-0.23</td><td><strong>0.09</strong></td><td>1.67</td><td>0.48</td><td>0.14</td><td>2.55</td><td>0.23</td></tr><tr><td>Normal</td><td>0.15</td><td>2.84</td><td>-0.18</td><td><strong>0.09</strong></td><td>1.64</td><td>0.41</td><td>0.11</td><td>2.08</td><td>0.26</td></tr><tr><td>Poisson</td><td>0.20</td><td>inf</td><td>-0.44</td><td><strong>0.14</strong></td><td>inf</td><td>0.39</td><td>0.18</td><td>inf</td><td>0.25</td></tr><tr><td>Uniform</td><td>0.14</td><td>2.48</td><td>-0.19</td><td><strong>0.07</strong></td><td>1.23</td><td>0.47</td><td>0.10</td><td>1.78</td><td>0.22</td></tr><tr><td colspan="10"><strong>Debatepedia Dataset</strong></td></tr><tr><td>Beta</td><td>0.36</td><td>0.67</td><td>0.36</td><td><strong>0.07</strong></td><td>0.12</td><td>0.72***</td><td>0.10</td><td>0.19</td><td>0.69</td></tr><tr><td>Normal</td><td>0.34</td><td>0.64</td><td>0.39</td><td><strong>0.06</strong></td><td>0.11</td><td>0.73***</td><td>0.08</td><td>0.16</td><td>0.65</td></tr><tr><td>Poisson</td><td>0.29</td><td>1.06</td><td>0.20</td><td><strong>0.08</strong></td><td>0.27</td><td>0.62***</td><td>0.14</td><td>0.50</td><td>0.76</td></tr><tr><td>Uniform</td><td>0.32</td><td>0.56</td><td>0.33</td><td><strong>0.05</strong></td><td>0.08</td><td>0.76***</td><td>0.07</td><td>0.12</td><td>0.64</td></tr></tbody></table>

# 5 Results and Discussion

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 initial argument weights. To evaluate the performance of the neural architectures we used mean squared error (MSE) between the predicted
and the gold acceptability degrees. We also used the Kendall rank correlation coefficient metric (also referred as Kendall's $\tau$) [17], to measure the correlation between the node ranks produced by a given neural network 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 observation 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 $\le$.05 and $\tau$ value > 0 signifies a statistically significant similarity between the two rankings. Here, a statistically significant Kendall's $\tau$ score indicates that the acceptability degree rankings produced by QuAD semantics have a high correlation with the acceptability degrees produced by the neural networks. Formally, Kendall's $\tau$ is calculated as follows:

$$ \tau = \frac{2}{k(k-1)} \sum_{i<j} \operatorname{sgn}(x_i - x_j) \operatorname{sgn}(y_i - y_j) $$

where $k$ is the number of observations, $x_i$ and $y_i$ are the rankings of the $i^{th}$ observation for the two variables being compared, and $\operatorname{sgn}$ is the sign function that returns 1 if the argument is positive, -1 if negative, and 0 if zero. We draw the following observations from this experiment:

- First, our experiments indicate that neural networks can indeed approximate to predict the acceptability degrees computed by QuAD semantics. To our knowledge, this is the first work to show that neural networks can learn to replicate bipolar gradual CAT semantics. This is an exciting result considering 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 importance of modelling argument interactions. For example, the MSEs measured for GCN range between 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 considerably 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 approximately twice that ranging from 0.08 to 0.14. We consider this another positive result, which indicates that, as long as the neural architectures capture 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 calculated between the ranking produced by GCN and the ranking produced by QuAD semantics, we can observe a moderate positive correlation between the two rankings for the Twelve Angry Men dataset. We can also observe a strong positive correlation between the two rankings for the Debatepedia 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 ranking. These results are
particularly valuable since they give us insights about the capability of GCN to ef-
fectively predict the ranking among the nodes in a bipolar gradual argumentation
graph.

# 6 Conclusion and Future Work

Argumentation is becoming increasingly significant in AI for tasks requiring decision-
making and communication. We contend that comprehending argumentation should be
essential for neural networks implementing machine reasoning.

This research explored neural networks’ capacity to acquire gradual bipolar argu-
mentation semantics. We performed various experiments to train and assess neural net-
works’ ability to learn QuAD argumentation semantics. Our results suggest that neural
networks can successfully learn argumentation semantics. A noteworthy observation
is that GCNs, a graph-based neural architecture, consistently yield the best outcomes,
highlighting the necessity of explicitly modeling the argument graph structure.

Overall, this study is the first to demonstrate that neural architectures can acquire
gradual bipolar argumentation semantics. A limitation of this research is that all data
used for training and testing the proposed neural architectures comprised only acyclic
graphs, where QuAD semantics is guaranteed to converge. In future work, we plan to
extend our research to include cyclic graphs where QuAD (or other) semantics con-
verge. To our knowledge, no dataset or benchmark exists containing a substantial num-
ber of real-world bipolar weighted cyclic graphs. We are presently gathering cyclic
graphs from online debates and verifying instances where QuAD semantics converges.
Additional future work will involve training neural networks on other bipolar weighted
semantics, based on the desired behavior in a specified context.

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