to align with the users' needs, cities may introduce exceptions that make the rule unclear<sup>12</sup>. The LEZ definition problem emphasizes the necessity of conducting a more comprehensive analysis of travelers' decision-making processes to grasp the rule's impact on travelers and, consequently, assess its effectiveness.

Agent-based simulations focus on individual decision-making processes, making them valuable tools for analyzing the modal shift problem [1, 2]. However, these works often limit the traveler's context to their activities and locations, while the decision process of the agents is primarily guided by a single criterion, such as price impact [1] or the utilization of shared autonomous vehicles [2]. As a result, the diverse contexts of travelers are not adequately considered.

Modal shifting is determined by a whole range of factors that are interrelated to a larger or smaller extent. For instance, [3] conducted a study involving 205 Australian university students to examine the relative importance and correlation between psychological and situational factors in predicting commuter transport mode choices. The study's findings include: (1) individuals' values influence their commuting behavior through their corresponding beliefs regarding the environmental impact of cars, (2) factors such as cost, time, and accessibility contribute to individuals' choices of commuting mode, and (3) both situational and psychological factors jointly influence pro-environmental behavior. For a comprehensive review of the modal choice concept, interested readers can refer to [4].

To address this complexity, this article aims to propose a framework that captures the various contexts within which travelers make their travel decisions.

In this article, we argue that formal argumentation, such as the Dung framework [5], can be used to represent the decision-making context of travelers. Arguments and attacks pertain to specific situations for the traveler and elucidate the support or refutation of a modal choice. In this sense, argumentation seems particularly relevant to represent complex multi-criteria decisions structures, in opposition to numerical functions or simple logical rules. An additional benefit of argumentation is its similarity to how we, humans, reason, as it has been suggested by Mercier and Sperber [6], which makes it easier to understand and use for humans. Furthermore, argumentation gives us an explicit justification about the decision while it is not necessarily the case for other AI techniques, especially the numeric-based reward functions.

The contributions of this article are:

* An argumentation framework to represent context-based decisions,

* An application of argumentation to the problematic of the modal shift.

This paper is organized as followed: Firstly, Section 2 proposes a state of the art on argumentation-based decisions frameworks. Secondly, Section 3 introduces the case study dedicated to represent urban travelers behaviors within a simulator of multimodal transportation networks. Thirdly, Section 4 presents the formal framework and recalls basics notions. Finally, Section 5 presents the first results of the proof-of-concepts and Section 6 proposes conclusion and perspective of future work.

<footnote n="1">¹https://ec.europa.eu/transport.themes/urban/studies_cs</footnote>

<footnote n="2">²https://ec.europa.eu/transport/sites/default/files/uvar_final_report_january_28.pdf</footnote>
## 2. Agumentation-based decisions systems

Argumentation has been identified as an effective tool for decision-making and decision-support systems, particularly in situations where the recommended decisions need to be explained [7, 8]. Multiple studies [9, 10, 11, 12] have investigated the introduction of argumentation capabilities in decision-making and emphasized the importance of presenting arguments in favor or against possible choices to the user of a decision-support system. For instance, argumentation has been applied to justify a multiple criteria decision or represent decisions taken by a group of agents as in vote systems [13]. In a context of computer simulations, argumentation has been applied into agent-based simulations to model the opinion of agents [14], or [15] considers a case study in which argumentation is used to assess and compare cultural options available to farmers. However these approaches in agent-based models do not consider argumentation to make agent taking decisions. In [16], they use argumentation to represent knowledge of agents and their reasoning about alternatives in an automata framework, named as Action-based Alternating Transition Systems (AATS) framework. Some approaches in the literature in decision-support systems used argumentation to justify an option w.r.t. a goal. In [15], they consider a case study in which argumentation is used to assess and compare cultural options available to farmers. In their approach a system is a set of variables X and a set of states which is an instantiation of each variable of X, as e.g. $X = X_{out} \cup X_{in}$, where $X_{out}$ is the observation, and $X_{in}$ is human control values. An argument is a triplet $Arg = (option, goal, justification)$ which is associated with an option, a goal and a justification.

In this article, we are interested in the model proposed in [17]. They proposed an abstract argumentation model that defines an argumentation-based decision framework as tuple $(A, D, R, F_f, F_c)$ where $A$ is a set of arguments, $D$ is a set of decisions, $R$ is an attack relation, $F_f$ is a mapping (resp. $F_c$) between pros (resp. cons) arguments and their associated decisions. Their model has several advantages:

* The simplicity of the model for linking arguments and decisions without having to change the abstract structure of arguments

* It provides the possibility of extending it easily to other argumentation models like e.g. Value-based Argumentation Frameworks (VAF) [18]

## 3. The simulated environment

The proposal presented in this paper is evaluated using a multiagent simulator available in the *Plateforme Territoire*<fnref n="3" />. This simulator enables agent travelers to access multimodal shortest itineraries between their origin and destination and simulates their movement along the chosen itinerary at a speed corresponding to the selected transportation mode. Itineraries can be evaluated using pre-trip indicators that influence the itinerary choice of the traveler agents. These indicators can be based on factors such as distance or traffic-related aspects like noise, which depends on the number of vehicles along different parts of the itinerary. Additionally, the

<footnote n="3">³https://territoire.emse.fr</footnote>
simulator calculates global traffic indicators for each transportation mode to assess the system, such as the number of late travelers.

**Application.** Each agent has to decide about one alternative which corresponds to choose a particular transportation network. In this simulator, we consider the following set of alternatives *Alts* and *N* be a set of agents :

D1 p.t. := "go by public transport"

D2 bike := "go by bike"

D3 walk := "go by foot"

D4 car := "go by car"

Each agent decides based on indicators. For each agent $i \in \mathcal{N}$, we consider the following indicators *Inds*. We first define the indicators based on alternatives *Alts*:

• $t: \mathcal{Alts} \to \mathbb{D}^+$ for a given alternative, it returns the duration for this alternative

• $d: \mathcal{Alts} \to \mathbb{D}^+$ for a given alternative, it returns the distance for this alternative

• $pol: \mathcal{Alts} \to \mathbb{D}^+$ for a given alternative, it returns the pollution rate associated with this alternative

• $noi: \mathcal{Alts} \to \mathbb{D}^+$ for a given alternative, it returns the noise generated by this alternative

• $cos: \mathcal{Alts} \to \mathbb{D}^+$ for a given alternative, it returns the cost of this alternative

Indicators based on the agent state:

• $em: \mathcal{N} \to \{\top, \bot\}$ is a function that represents if one agent has a medical emergency

• $isOld, isFemale, isReadyToModalShift: \mathcal{N} \to \{\top, \bot\}$ are functions that represent if one agent is old, is female, or is ready to modal shift<fnref n="4" />

• $hasCar, hasECar, hasBike: \mathcal{N} \to \{\top, \bot\}$ are functions that represent if one agent has a car, or has an electric car, or has a bike and are s.t. for each agent $i \in \mathcal{N}$, if $hasCar(i) = \bot$ then $hasECar(i) = \bot$

Indicators based on the state of the environment:

• $isHealthCrisis, isRushHour, isTheNight \in \{\top, \bot\}$ translate if there is a health crisis, if this is the rush hour, or if it is the night

We formally define the state space (based on previously defined indicators) such as :

$$ SpInds = ((\mathbb{D}^+)^{Alts \times \mathcal{N}})^4 \times (\{\top, \bot\}^{Alts \times \mathcal{N}} \times (\{\top, \bot\}^N)^7 \times \{\top, \bot\}^3 $$

In the sequel we consider the following notation :

$$ \forall s \in SpInds, \forall ind \in Inds, s_{ind} = ind $$

This last notation translates for all $s \in SpInds$, $s_{[t]} = t$ i.e. we return the part of the value of the component of vector that assigns the function which evaluates the duration of each alternative.

<footnote n="4">⁴For a sake of simplicity, we reduce to a small set of characteristics of the agent.</footnote>
## 4. Argumentation-based framework for Decision Making

In this section we give the model of Amgoud and Prade [19] and their definitions of extensions w.r.t. their model. Secondly, we present our framework called ADP (Argumentation-based Decision Process) which extends their model. The main advantages of our framework are:

* The decision of an agent is contextualized w.r.t. the state thanks to its argumentation graph.

* The notion of arguments is abstract so that it can be easily extended to approaches that consider and explicit goals, or other argumentation approaches as e.g. logic-based argumentation [20].

### 4.1. Argumentation Framework for Decision Making

In order to map arguments to decisions, [17] extends the standard argumentation framework [5] to decisions. Arguments are mapped to supported decisions (i.e. pro arguments) and unsupported decisions (i.e. con arguments).

**Definition 1.** An Argumentation Framework for Decision Making (AFDM) is a tuplet $AFDM = (A, R, D, F_f, F_c)$ such that:

* $A$ is a set of arguments

* $R$ is a binary relation called *attack relation*

* $D$ is a set of decisions (or actions)

* $F_f : D \to 2^A$ is a function that assigns from $D$ the set of pro arguments

* $F_c : D \to 2^A$ is a function that assigns from $D$ the set of con arguments

We note $ADF(A, D) = 2^A \times 2^{A \times A} \times 2^D \times (2^A)^D \times (2^A)^D$ the set of Argumentation-based Decision Framework based on a set of arguments $A$ and a set of decisions $D$ and consider:

$$ \forall a \in A, \mathcal{F}_f^{-1}(a) := \{d \in D : a \in \mathcal{F}_f(d)\}, \mathcal{F}_c^{-1}(a) := \{d \in D : a \in \mathcal{F}_c(d)\} $$

A semantics of argumentation frameworks is given by the notion of extensions [5]. Extensions characterize which arguments are considered as admissible in regard to the argumentation graph.

**Definition 2 (Extensions).** Let $(A, R, D, F_f, F_c)$ be an AFDM, $S \subseteq A$ be a set of arguments.

* $S$ is an *admissible extension* iff $S$ is conflict-free and all arguments $A \in S$ are acceptable w.r.t. $S$.

* $S$ is a *complete extension* iff $S$ is admissible and contains all acceptable arguments wrt $S$.

* $S$ is a *grounded extension* iff $S$ is a minimal complete extension wrt $\subseteq$ i.e. $\exists S' \subseteq A$ s.t. $S' \subseteq S$, $S'$ is a complete extension.

* $S$ is a *preferred extension* iff $S$ is a maximal admissible extension wrt $\subseteq$.

* $S$ is a *stable extension* iff $S$ is conflict-free, and $\forall A \in A \setminus S, S \in A$.

* $S$ is an *ideal extension* iff $S$ is a maximal admissible extension wrt $\subseteq$ that is included in all preferred extensions.
Let us notice that in the general case there is no consensus about which extension semantics to use. However as suggested in [21] some extensions can be considered as more preferable due to their uniqueness, e. g. the grounded or the ideal extension.

## 4.2. Argumentation-based Decision Process

The Argumentation-based Decision Process (ADP) framework incorporates argumentation theory to model the decision-making process, enabling the selection of decisions based on argument extensions derived from the argumentation graph.

Thus, the system is fully described by a set of agents $\mathcal{N}$, a set of states $S$, a set of arguments $\mathcal{A}$ and a set of decisions $\mathcal{D}$ or actions that agents can do. In the sequel, we define an argumentation-based decision process for one agent $i \in \mathcal{N}$. A function $\sigma$ defines for each state $s \in S$, an instance of Amgoud and Prade's model i.e. a subset of possible decisions $\mathcal{D}' \subseteq \mathcal{D}$ that in $s$ the agent can do, a subset of arguments $\mathcal{A}' \subseteq \mathcal{A}$ which are verified in $s$, a set of (un)supported decisions $\mathcal{F}'_f(\mathcal{F}'_c)$, and a set of attacks $\mathcal{R}'$ that are generated by the semantics of each argument in $\mathcal{A}'$. Then, a function $\epsilon$ defines the extension semantics which is used by the agent to compute her stationary politics $\pi$. Since there is no consensus about how to compute the "winning" set of arguments based on a particular extension semantics (and so the decision), we let abstract and consider rather an heuristic function $h$ which defines the computation method to choose a decision based on an extension semantics. Thus, we assume that the politic of the agent (which is stationary) is fully defined by this heuristic function i.e. $\pi = h$. The stationary policy function ensures that a decision is chosen from the available options for each state in a consistent manner w.r.t. the set of admissible arguments.

**Definition 3.** An Argumentation-based Decision Process (ADP) is a tuple $(\mathcal{ADP} = (S, \mathcal{A}, \mathcal{D}, \sigma, \epsilon, \pi)$ such that:

* $S$ is a no-empty set of states

* $\mathcal{A}$ is a no-empty set of arguments

* $\mathcal{D}$ is a no-empty set of decisions (or actions)

* $\sigma: S \to \mathcal{ADF}(\mathcal{A}, \mathcal{D})$ is a function s.t.

$$ \forall s \in S, \sigma(s) = (\mathcal{A}', \mathcal{R}', \mathcal{D}', \mathcal{F}'_f, \mathcal{F}'_c) \text{ where:} $$

- $\mathcal{A}' \subseteq \mathcal{A}$ is a subset of arguments associated with state $s$ and we note $\sigma_{[\mathcal{A}]}(s) = \mathcal{A}'$

- $\mathcal{R}' \subseteq \mathcal{A}' \times \mathcal{A}'$ represents the set of attacks between arguments in $\mathcal{A}'$ and we note $\sigma_{[\mathcal{R}]}(s) = \mathcal{R}'$

- $\mathcal{D}' \subseteq \mathcal{D}$ is a subset of decisions associated in a state $s$ and we note $\sigma_{[\mathcal{D}]}(s) = \mathcal{D}'$

- $\mathcal{F}'_f: \mathcal{D}' \to 2^{\mathcal{A}'}$ and we note $\sigma_{[\mathcal{F}_f]}(s) = \mathcal{F}'_f$ and $\sigma_{[\mathcal{F}_f^{-1}]}(s) = \mathcal{F}'_f^{-1}$ is a function that assigns a set of pro arguments for each decision in $\mathcal{D}'$ in a state $s$

- $\mathcal{F}'_c: \mathcal{D}' \to 2^{\mathcal{A}'}$ and we note $\sigma_{[\mathcal{F}_c]}(s) = \mathcal{F}'_c$ and $\sigma_{[\mathcal{F}_c^{-1}]}(s) = \mathcal{F}'_c^{-1}$ is a function that assigns a set of con arguments for each decision in $\mathcal{D}'$

* $\epsilon: 2^{\mathcal{A} \times \mathcal{A}} \to 2^{2^\mathcal{A}}$ is a function that, from an argumentation graph, returns the set of extensions
* $\pi: S \to \mathcal{D}$ is a stationary politic s.t. $\forall s \in S, \pi(s) = h_s(\epsilon(\sigma_{[\mathcal{R}]}(s)))$ where $h_s: 2^{2^A} \to \mathcal{D}$ is a function s.t. each chosen decision belongs to the set of extensions given by the AFDM:

$$ \forall \mathcal{E} \subseteq 2^A, h_s(\mathcal{E}) \in \{d \in \mathcal{D} : d \in \sigma_{[\mathcal{D}]}(s)\} $$

We now present how this model is applied in our proof-of-concept. The implemented model has 22 arguments, and for a sake of readability, we do not present all of these arguments in this article but only 4 of them.

**Application.** Let consider the following ADP = ($S, A, D, \sigma, \epsilon, \pi$) where $S = SpInds$ and $D = Alts$. We consider a set of arguments $A$ and we assume in our study case that $\sigma$ is such that for all $s \in S$ and for each agent $i \in \mathcal{N}$:

* A. $hC := $ "agent i has no car"; C. $hB := $ "agent i has no bike",

**Activation** : $hC \in \sigma_{[A]}(s)$ iff $s_{[hasCar]}(i) = \perp$ and $hB \in \sigma_{[A]}(s)$ iff $s_{[hasBike]}(i) = \perp$

**Pros** : $\sigma_{[\mathcal{F}_f^{-1}]}(s)(hC) = \sigma_{[\mathcal{F}_f^{-1}]}(s)(hB) = \emptyset$

**Cons** : $\sigma_{[\mathcal{F}_c^{-1}]}(s)(hC) = \sigma_{[\mathcal{F}_c^{-1}]}(s)(hB) = \emptyset$

**Attacks** : $\{ (a, d) \in \{(hB, bike), (hC, car)\}, \{ (a, x) : x \in \sigma_{[\mathcal{F}_f]}(s)(d) \} \subseteq \sigma_{[\mathcal{R}]}(s) \}$

**Meaning** : If she has no car (resp. no bike), then $hC$ (resp. $hB$) is verified. It is not in favor, or against any alternative and attacks all verified arguments that supports one of these alternatives.

* $iAE := $ "it is a medical emergency"

**Activation** : $iAE \in \sigma_{[A]}(s)$ iff $s_{[em]}(i) = \top$

**Pros** : $\sigma_{[\mathcal{F}_f^{-1}]}(s)(iAE) = \{ d \in \sigma_{[D]}(s) : \neg \exists x \in \sigma_{[D]}(s), s_{[t]}(i)(x) > s_{[t]}(i)(d) \}$

**Cons** : $\sigma_{[\mathcal{F}_c^{-1}]}(s)(iAE) = \sigma_{[D]}(s) \setminus \sigma_{[\mathcal{F}_f^{-1}]}(s)(iAE)$

**Attacks** : $\{ (iAE, x) : x \in \sigma_{[A]}(s), \sigma_{[\mathcal{F}_f^{-1}]}(s)(x) \cap \sigma_{[\mathcal{F}_c^{-1}]}(s)(iAE) \neq \emptyset \} \subseteq \sigma_{[\mathcal{R}]}(s) $

**Meaning** : If there is a medical emergency, then $iAE$ is verified. It is in favor of all alternatives that are the quickest, against the others and attacks all verified arguments that are in favor of at least one alternative that is not the quickest.

* $cRA := $ "the car alternative crosses the regulated area"

**Activation** : $cRA \in \sigma_{[A]}(s)$ iff $s_{[reg]}(i)(car) = \top, s_{[hasCar]}(i) = \perp$ and $car \in \sigma_{[D]}(s)$

**Pros** : $\sigma_{[\mathcal{F}_f^{-1}]}(s)(cRA) = \emptyset$

**Cons** : $\sigma_{[\mathcal{F}_c^{-1}]}(s)(cRA) = \{ car \}$

**Attacks** : $\{ (cRA, x) : x \in \sigma_{[\mathcal{F}_f]}(s)(car) \} \subseteq \sigma_{[\mathcal{R}]}(s) $

**Meaning** : $cRA$ is verified when the alternative car crosses a regulated area while it should be forbidden. It attacks all arguments in favor of car.

* $iEx := $ "it is too much expensive for agent i when $s_{[cos]}(i)(d) > \theta_i^c(s)(d)$" with $d \in \mathcal{D}$ and $\theta_i^c(s) : \mathcal{D} \to \mathbb{D}^+$ a function to set a threshold for what the agent considers as too much expensive

**Activation** : $iEx \in \sigma_{[A]}(s)$ iff $\exists d \in \sigma_{[D]}(s)$ s.t. $\cos(i)(s)(d) > \theta_i^c(s)(d)$

**Pros** : $\sigma_{[\mathcal{F}_f^{-1}]}(s)(iEx) = \{ d \in \sigma_{[D]}(s) : \theta_i^c(s)(d) > s_{[cos]}(i)(d) \}$

**Cons** : $\sigma_{[\mathcal{F}_c^{-1}]}(s)(iEx) = \{ d \in \sigma_{[D]}(s) : s_{[cos]}(i)(d) > \theta_i^c(s)(d) \}$

**Attacks** : $\{ (iEx, x) : \exists d \in \sigma_{[\mathcal{F}_c^{-1}]}(s)(iEx), x \in \sigma_{[\mathcal{F}_f]}(s)(d) \} \subseteq \sigma_{[\mathcal{R}]}(s) $
**Meaning** : *iEx* is verified when at least one alternative is above the threshold of acceptability of agent *i* in regard to her budget. It attacks all arguments that supports one alternative which is not in the threshold of acceptability.

It is worth noting that attacks hold more weight in the decision-making process compared to simply considering a list of pros and cons. This is because a single attack can invalidate an argument and subsequently remove it from the extensions, thus impacting the agent's deliberation process for making choices.

Furthermore, this model could be easily extended to get a more realistic models by considering other arguments as e.g. "I'm relocating", "I'm the police", "I prefer biking", "There is no bicycle network", "There is no bus at this hour", etc.

# 5. Experimental results

In this section, we provide an application of the framework to simulate the modal shifting. We present the results obtained from our experiments, starting with an explanation of the various scenarios tested. Then, we provide an example of an argumentation graph generated for one agent. Finally, we demonstrate how decision-making based on argumentation can be utilized to evaluate the evolution of the overall transportation network.

## 5.1. Implemented scenarios

We aim to enhance the simulation of regulating a multimodal transportation networks, consisting of a car, bus, walk, and bicycle network, each with distinct characteristics such as average speed, environmental impact, financial cost, and noise level. Specifically, we focus on regulating the car network, which involves determining certain areas where cars are either allowed or prohibited from accessing. We present the parameters considered in two network configurations: namely, a configuration without regulated areas and another with regulated areas (LEZ). In both, we assume there are 5000 traveler agents, no health crisis, and it is rush hour. The objective of a traveler agent is to choose the most appropriate transportation mode. We also establish some thresholds based on these assumptions e.g. 90% have a bike and 100% a car, 30% of them have an electric car, 40% are ready to modal shift, 20% are senior, 10% are emergencies. The threshold for the acceptability w.r.t. time i.e. $\theta_i^t(s)(d)$ is set arbitrary as the following : if the travel time is greater than $1.2 \times t_{min}$ then it is unacceptable. The noise threshold $\theta_i^n(s)(d)$ should not exceed 1.0. The quantity of pollution, $\theta_i^p$, should not exceed 9.0, the cost becomes unacceptable when the cost is greater than $\theta_i^c(s)(d) = 0.2$ and the distance is unacceptable when it is greater than $\theta_i^l = 200.0$. We consider 6 scenarios:

* Without LEZ: the objective is to evaluate the impact of taking into account the context in the distribution of the travelers per networks considering a classical multimodal network.

- $s_1$: the traveler agents decide by considering the quickest alternative, i.e. a monocriteria decision process.

- $s_2$: the traveler agents decide with the proposed ADP.
* With LEZ: the objective is to evaluate if our model is efficient to understand the traveler decision process for the transportation modal shift.

- $s_3$: the traveler agents choose the quickest alternative. The comparison with $s_1$ will give information about the quality of the decision criteria to understand the consequences of the LEZ definition.

- $s_4$: the agents decide with an ADP. The comparison with $s_2$ will give information about the quality of the decision criteria to understand the consequences of the LEZ definition.

- $s_5$: the traveler agents decide with the ADP defined in $s_4$ but the distance acceptance has been reduced. The comparison with $s_4$ should show an increase of the modes with the shortest distance.

- $s_6$: the traveler agents decide with the ADP defined in $s_5$ but the pollution acceptance has been reduced. The comparison with $s_5$ should show an increase of the least polluting modes.

## 5.2. From the point of view of one agent

After running the scenario $s_4$ (ADP+LEZ), we illustrate an argumentation graph of one agent. Its characteristics are given by: $s_{[em]}(i) = \perp$, $s_{[isOld]}(i) = \perp$, $s_{[isRTMS]}(i) = \perp$, $s_{[hasCar]}(i) = \top$, $s_{[hasECar]}(i) = \perp$, $s_{[hasBike]}(i) = \top$.

**Application.** If $Grd(\sigma_{[R]}(s))$ is the computed grounded extension from the argumentation graph $\sigma_{[R]}(s)$ where $s$ represents the current state, then, we define the scoring function $scr_1: \sigma_{[D]}(s) \to \mathbb{R}$ such that for all decisions $d \in \sigma_{[D]}(s)$:

$$pros(d) = |Grd(\sigma_{[R]}(s)) \cap \sigma_{[F_f]}(s)(d)|$$

$$cons(d) = |Grd(\sigma_{[R]}(s)) \cap \sigma_{[F_c]}(s)(d)|$$

$$scr(d) = \begin{cases} \frac{pros(d)}{pros(d)+cons(d)} & \text{if } pros(d) + cons(d) \neq 0 \\ 0 & \text{otherwise} \end{cases}$$

We compute the scores by considering the argumentation model given in Application 4.2. The result of the computed argumentation graph is depicted in Table 2. Then, by computing the grounded extension, we get: $Grd(\sigma_{[R]}(s)) = \{\{5, 17\}\}$. To deal with equalities, we assume the following order for agent i: Bus > Bike > Walk > Car. For a sake of simplicity we decided to set this order arbitrary. In this setting, the agent chooses the car alternative by avoiding the regulated area since $scr(Car) = 1$ while for other alternatives $X$, we have $scr(X) = 0$.

## 5.3. From a global perspective: how individual explicit decision processes may be manipulated to influence the system

We analyze the impact of a LEZ on agents considering scenarios $s_1, s_2$ (ADP), $s_3$ (LEZ), $s_4$ (ADP+LEZ), $s_5$ (ADP+LEZ), $s_6$ (ADP+LEZ). The Table 1 presents the distribution of the travelers
between the transportation modes according to several scenarios. Here we compare the scenarios to illustrate three advantages of our approach. In each of them, travelers have to choose the transportation modes corresponding to their preferences with or without considering LEZ.

<table><caption>**Table 1**
Distribution of the travelers per transportation mode</caption><thead><tr><th>Scenario</th><th>Car</th><th>Bike</th><th>Walk</th><th>Bus</th></tr></thead><tbody><tr><td>s<sub>1</sub></td><td>1</td><td>0</td><td>0</td><td>0</td></tr><tr><td>s<sub>2</sub></td><td>0,4944</td><td>0,304</td><td>0,163</td><td>0,0386</td></tr><tr><td>s<sub>3</sub></td><td>0,9502</td><td>0,005</td><td>0</td><td>0,0448</td></tr><tr><td>s<sub>4</sub></td><td>0,4408</td><td>0,297</td><td>0,163</td><td>0,0992</td></tr><tr><td>s<sub>5</sub></td><td>0,48</td><td>0,2678</td><td>0,1632</td><td>0,089</td></tr><tr><td>s<sub>6</sub></td><td>0,4454</td><td>0,2348</td><td>0,1742</td><td>0,1456</td></tr></tbody></table>

**Is our approach adapted to reproduce the diversity of travelers' modal choices?** The scenario $s_1$ considers that travelers choose the quickest trip without other parameters while the travelers in $s_2$ decide according to the argumentation model presented in section 5.1. Here, the result shows that with the only decision criteria based on time it is not possible in this example to have a real multimodal system, the car alternative is always the fastest transportation mode. The argumentation model is closer to the reality.

**Is our approach efficient to understand the consequences of the network regulation on multimodal travelers' modal choices?** The scenarios $s_3$ and $s_4$ are respectively similar to $s_1$ and $s_2$ expected that a LEZ is deployed. We can observe for both the same evolution with the transfer of around 5% of travelers from the car mode to the bus mode. The advantage of our proposal is that this transfer being based on a more realistic initial distribution we observe a multimodal traffic that is more balanced between modes.

**Is our approach adapted to understand the consequences of traveler behaviors on the transportation system?** The scenario $s_5$ is based on $s_4$ (LEZ deployed and ADP) with the modification of the distance constraint argument ($\theta_i^l$) which is reduced to 0. It means that travelers prefer the shortest trips. We observe that there is a shift of travelers towards the car mode to reach a value close to that of $s_2$. This illustrates that the decision is the result of a compromise, as the majority of travelers do not shift.

The scenario $s_6$ is based on $s_5$ with the reduction of the tolerance of the pollution ($\theta_i^p$). This argument counter balances partially the one of the distance. The result is a percentage of travelers choosing the car mode that is similar to $s_4$ and an increase of the traveler choosing the bus mode. This last mode is a good compromise between the distance and pollution arguments.
# 6. Conclusion

In this article, we have presented an argumentation-based decision process framework for modeling the decision-making process of urban travelers. To demonstrate the feasibility of our framework, we have provided a proof-of-concept by instantiating the model with arguments that could be considered in a modal shifting.

It is important to highlight that our current model lacks of realistic data on real behavior of urban travelers, and we acknowledge that it represents a preliminary effort in this direction. In future research, we plan to enhance our framework by incorporating e.g. web-based data and considering more statistical data. We believe that it will provide more accurate insights into the decision-making process of agents and will provide more realistic results.

By combining our framework with comprehensive and up-to-date web data, we anticipate that our model will offer a deeper understanding of urban travelers’ decision processes, ultimately leading to more effective strategies for promoting responsible modal choices in transportation.

# 7. Acknowledgement

We thank the 3IA Côte d'Azur ANR-19-P3IA-0002, the HyperAgents project ANR-19-CE23-0030 and the Acceler-AI project Projet-ANR-22-CE23-0028 for their support.

# References

[1] I. Kaddoura, G. Leich, K. Nagel, The impact of pricing and service area design on the modal shift towards demand responsive transit, Procedia Computer Science 170 (2020) 807-812.

[2] J. Kamel, R. Vosooghi, J. Puchinger, F. Ksontini, G. Sirin, Exploring the impact of user preferences on shared autonomous vehicle modal split: A multi-agent simulation approach, Transportation Research Procedia 37 (2019) 115-122.

[3] C. M. Collins, S. M. Chambers, Psychological and situational influences on commuter-transport-mode choice, Environment and behavior 37 (2005) 640-661.

[4] A. De Witte, J. Hollevoet, F. Dobruszkes, M. Hubert, C. Macharis, Linking modal choice to motility: A comprehensive review, Transportation Research Part A: Policy and Practice 49 (2013) 329-341.

[5] P. M. Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artificial intelligence 77 (1995) 321-357.

[6] H. Mercier, D. Sperber, Why do humans reason? arguments for an argumentative theory., Behavioral and brain sciences 34 (2011) 57-74.

[7] J. Fox, D. Glasspool, V. Patkar, M. Austin, L. Black, M. South, D. Robertson, C. Vincent, Delivering clinical decision support services: there is nothing as practical as a good theory, Journal of biomedical informatics 43 (2010) 831-843.

[8] F. S. Nawwab, T. Bench-Capon, P. E. Dunne, Emotions in rational decision making, in: International Workshop on Argumentation in Multi-Agent Systems, 2009, pp. 273-291.
<table><caption>**Table 2**

Argumentation graph for the agent i's decision</caption><thead><tr><th>ArgID</th><th>Name</th><th>Attacks</th><th>F<sub>f</sub><sup>-1</sup></th><th>F<sub>c</sub><sup>-1</sup></th></tr></thead><tbody><tr><td>1</td><td>AvoidAnyContactWhenThereIsHealthCrisis</td><td>{}</td><td>{D4, D2}</td><td>{D1}</td></tr><tr><td>5</td><td>TimeDurationAcceptability</td><td>{16, 9, 7, 6, 10, 12, 11}</td><td>{D4}</td><td>{D1, D3, D2}</td></tr><tr><td>6</td><td>CanAlwaysWalk</td><td>{}</td><td>{D3}</td><td>{}</td></tr><tr><td>7</td><td>CannotTravelLongDistance</td><td>{15, 16, 9, 13, 6, 12, 11}</td><td>{D4, D1}</td><td>{D3, D2}</td></tr><tr><td>9</td><td>BikelsAnEfficientWayForTransportation</td><td>{}</td><td>{D2}</td><td>{}</td></tr><tr><td>10</td><td>NoiseAcceptability</td><td>{}</td><td>{D1, D3, D2}</td><td>{D4}</td></tr><tr><td>11</td><td>PollutionThresholdIsNotAcceptable</td><td>{5, 1, 20, 16, 7, 10}</td><td>{D3, D2}</td><td>{D4, D1}</td></tr><tr><td>12</td><td>TooMuchExpensive</td><td>{5, 1, 20, 16, 7, 10}</td><td>{D3, D2}</td><td>{D4, D1}</td></tr><tr><td>13</td><td>IsRushHour</td><td>{}</td><td>{D3, D2}</td><td>{D4}</td></tr><tr><td>15</td><td>BikingAndWalkingIsGoodForYourHealth</td><td>{}</td><td>{D3, D2}</td><td>{}</td></tr><tr><td>16</td><td>ItIsResponsibleWayOfTransportation</td><td>{}</td><td>{D1, D3, D2}</td><td>{D4}</td></tr><tr><td>17</td><td>NotReadyToModalShift</td><td>{1, 15, 20, 16, 9, 7, 13, 6, 10, 12, 11}</td><td>{}</td><td>{}</td></tr><tr><td>20</td><td>TheWeatherIsNotGood</td><td>{}</td><td>{D4, D1}</td><td>{D3, D2}</td></tr></tbody></table>
[9] W. Ouerdane, N. Maudet, A. Tsoukias, Argumentation theory and decision aiding, Trends in multiple criteria decision analysis (2010) 177–208.

[10] T. L. van der Weide, Arguing to motivate decisions, Ph.D. thesis, Utrecht University, 2011.

[11] J. Müller, A. Hunter, An argumentation-based approach for decision making, in: 2012 IEEE 24th International Conference on Tools with Artificial Intelligence, volume 1, IEEE, 2012, pp. 564–571.

[12] E. Ferretti, L. H. Tamargo, A. J. García, M. L. Errecalde, G. R. Simari, An approach to decision making based on dynamic argumentation systems, Artificial Intelligence 242 (2017) 107–131.

[13] G. Marreiros, P. Novais, J. Machado, C. Ramos, J. Neves, An agent-based approach to group decision simulation using argumentation, in: International MultiConference on Computer Science and Information Tecnology, Workshop Agent-Based Computing III (ABC 2006), Wisla, Poland, 2006, pp. 225–232.

[14] P. Taillandier, N. Salliou, R. Thomopoulos, Coupling agent-based models and argumentation framework to simulate opinion dynamics: application to vegetarian diet diffusion, in: Advances in Social Simulation: Proceedings of the 15th Social Simulation Conference: 23–27 September 2019, Springer, 2021, pp. 341–353.

[15] R. Thomopoulos, B. Moulin, L. Bedoussac, Combined argumentation and simulation to support decision, in: International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems, 2017, pp. 275–281.

[16] K. Atkinson, T. Bench-Capon, States, goals and values: Revisiting practical reasoning, Argument & Computation 7 (2016) 135–154.

[17] L. Amgoud, H. Prade, Using arguments for making and explaining decisions, Artificial Intelligence 173 (2009) 413–436.

[18] T. J. M. Bench-Capon, Persuasion in practical argument using value-based argumentation frameworks, Journal of Logic and Computation 13(3) (2003) 429–448.

[19] L. Amgoud, J.-F. Bonnefon, H. Prade, An argumentation-based approach to multiple criteria decision, in: European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 2005, pp. 269–280.

[20] P. Besnard, A. Hunter, Argumentation based on classical logic, in: Argumentation in Artificial Intelligence, 2009, pp. 133–152.

[21] M. Caminada, Comparing two unique extension semantics for formal argumentation: ideal and eager, in: Proceedings of the 19th Belgian-Dutch conference on artificial intelligence (BNAIC 2007), Utrecht University Press, 2007, pp. 81–87.
# A Discussion of Challenges in Benchmark Generation for Abstract Argumentation

Isabelle Kuhlmann, Matthias Thimm

University of Hagen, Germany

**Abstract**

Abstract argumentation provides a formal framework for modeling and analyzing argumentative reasoning processes. As the field progresses, the need for benchmarks to evaluate and compare different algorithmic approaches becomes increasingly important. However, the process of generating suitable benchmarks for abstract argumentation is not without its challenges. This paper aims to explore the key challenges encountered in benchmark generation for abstract argumentation. In particular, we address the task of skeptical acceptability w.r.t. preferred semantics and describe a benchmark generator designed for this specific problem.

**Keywords**

Abstract argumentation, benchmarking, graph generator

## 1. Introduction

As a central aspect of human communication, the concept of argumentation has been adopted in the area of Artificial Intelligence in various forms. The principle of abstract argumentation [1], which focuses on the interplay between arguments in order to gain insights and reach conclusions, has become an established mechanism of non-monotonic reasoning. Naturally, an important issue in advancing the research in this field—in particular with regard to algorithmic solutions and applications—is the availability of benchmark data. However, generating suitable benchmarks for abstract argumentation presents several challenges that require careful consideration.

One notable initiative in advancing the evaluation of argumentation systems is the International Competition on Computational Models of Argumentation (ICCMA)¹. ICCMA serves as a platform for researchers and practitioners to showcase their systems and compare their performance on a common set of benchmarks. While ICCMA has significantly contributed to the evaluation of argumentation systems, the process of generating benchmarks for abstract argumentation remains a perpetual task. For instance, w.r.t. a set of ICCMA’17 benchmarks, it was recently pointed out that a majority of arguments that are skeptically accepted under preferred semantics (a task which is Π₂P-complete [2]) is also accepted under grounded semantics

Arg&App 2023: *International Workshop on Argumentation and Applications, September 2023, Rhodes, Greece*

<figure><img src="image_36.png" /></figure>

isabelle.kuhlmann@fernuni-hagen.de (I. Kuhlmann); matthias.thimm@fernuni-hagen.de (M. Thimm)

<figure><img src="image_37.png" /></figure>

http://mthimm.de/ (M. Thimm)

<figure><img src="image_38.png" /></figure>

0000-0001-9636-122X (I. Kuhlmann); 0000-0002-8157-1053 (M. Thimm)

<figure><img src="image_39.png" /></figure>

© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

<figure><img src="image_40.png" /></figure>

CEUR Workshop Proceedings (CEUR-WS.org)

¹http://argumentationcompetition.org/index.html
(which can be decided in polynomial time) [3]. Thus, in the majority of cases, it is sufficient to
solve a less complex problem, which may distort the interpretation of experimental results. In
this paper, we revisit this issue to highlight the impact of such properties on practical results.
Additionally, we introduce in more detail the *KWT Benchmark Generator* [3], which is designed
to circumvent the aforementioned problem. Further challenges arise in numerous respects,
including the need for diversity in benchmark scenarios, scalability concerns, or appropriate
evaluation metrics. Addressing these challenges is crucial to developing comprehensive bench-
marking methodologies that accurately reflect the performance and capabilities of different
argumentation systems.

## 2. Preliminaries

An (abstract) *argumentation framework (AF)* [1] is a pair $F = (\mathbf{Arg}, R)$, with $\mathbf{Arg}$ being a set of arguments and $R \subseteq \mathbf{Arg} \times \mathbf{Arg}$ a relation between those arguments. An argument $a \in \mathbf{Arg}$ *attacks* an argument $b \in \mathbf{Arg}$ if $(a, b) \in R$. Moreover, we define the set of arguments attacking a given argument $a$ as $a^-_F = \{b \mid (b, a) \in R\}$, and the set of arguments being attacked by $a$ as $a^+_F = \{b \mid (a, b) \in R\}$. In the same fashion we define $E^-_F$ and $E^+_F$ for a set $E \subseteq \mathbf{Arg}$. We call an argument $a \in \mathbf{Arg}$ *defended* by a set of arguments $E \subseteq \mathbf{Arg}$ if every argument $b \in \mathbf{Arg}$ that attacks $a$ is itself attacked by some argument $c \in E$, i.e., if $a^-_F \subseteq E^+_F$.

Further, a set $E \subseteq \mathbf{Arg}$ is conflict-free if $E \cap E_F^+ = \emptyset$. If a set $E \subseteq \mathbf{Arg}$ is conflict-free and each $a \in E$ is defended by $E$, we call $E$ admissible (ad). We call sets of jointly acceptable arguments *extensions*, which can be defined under various semantics. The classical semantics, following the seminal work by Dung [1], are defined as follows:

* A set $E \subseteq \mathbf{Arg}$ is *complete* (co) iff it is admissible, and if $E$ defends $a \in \mathbf{Arg}$ then $a \in E$.

* A set $E \subseteq \mathbf{Arg}$ is *grounded* (gr) iff $E$ is complete and $\subseteq$-minimal.

* A set $E \subseteq \mathbf{Arg}$ is *preferred* (pr) iff $E$ is complete and $\subseteq$-maximal.

* A set $E \subseteq \mathbf{Arg}$ is *stable* (st) iff it is complete and $E \cup E_F^+ = \mathbf{Arg}$.

In addition, we define a set $E \in \mathbf{Arg}$ to be an *ideal* (id) extension [4] if $E$ is admissible, for every preferred extension $E'$, it holds that $E \subseteq E'$, and $E$ is $\subseteq$-maximal with these two properties. Note that the grounded and the ideal extension of an AF are each a uniquely defined, and that the former is always a subset of the latter.

Typical problems in the field of abstract argumentation involve the enumeration of one extension (or all extensions), or deciding whether a given argument is included in one extension (or all extensions) w.r.t. a given semantics. Let $\Sigma = \{co, gr, pr, st, id\}$. An argument is *credulously* accepted w.r.t. $\sigma \in \Sigma$ if it is included in at least one $\sigma$ extension, and it is *skeptically* accepted if it is included in all $\sigma$ extensions. We denote the computational problem of credulous acceptability regarding a semantics $\sigma$ as $\mathrm{DC}_{\sigma}$, and the problem of skeptical acceptability regarding $\sigma$ as $\mathrm{DS}_{\sigma}$.

## 3. Challenges in Benchmark Generation

In the following, we provide a brief overview of existing benchmarks (which were used in past editions of ICCMA) and subsequently discuss challenges that arise in the development of new benchmark generation techniques.
**3.1. Existing Benchmarks**

Existing benchmarks for abstract argumentation can be roughly categorized into the following groups:

*   **Random graphs.** Some benchmark instances, e.g., those provided by AFBenchGen [5], comprise AFs generated using random graph generation algorithms. A related approach consists of connecting multiple random graphs to model communities of arguments [6].

*   **Graphs tailored for argumentation.** Some benchmarks are aimed at specific abstract argumentation problems. Examples are AdmBuster [7], which is targeted to the problems DC<sub>pr</sub> and DC<sub>gr</sub>, and SemBuster [8], which is designed for problems regarding the semi-stable semantics [9]. Further, the GroundedGenerator produces AFs with a large grounded extension, the StableGenerator produces AFs with many stable extensions, and the SccGenerator produces graphs with many strongly-connected components [10]. Although these generators are not necessarily aimed at a specific argumentation problem, they were designed with abstract argumentation as the target application in mind, and allow for investigating certain solver properties (e.g., whether a solver exploits the fact that an argument accepted under grounded semantics—which is computationally easy to obtain—is also accepted under other semantics).

*   **Translations from other domains.** AFs can be created by transforming existing problems or data sets from other domains. Examples include benchmarks from planning [11], assumption-based argumentation [12], mass transit data [13], and (inconsistent) knowledge bases expressed in the Datalog<sup>±</sup> language [14].

**3.2. Challenges in the Generation of Novel Benchmarks**

When creating a benchmark data set, the overall goal should be to obtain a *diverse* set of argumentation frameworks. Since the term “diversity” allows for multiple perspectives, we discuss some key aspects in the following.

**Graph-Theoretical Features** In order to ensure diversity in a graph-theoretical sense, benchmarks for abstract argumentation should encompass a wide range of graph properties and characteristics. This includes various properties, for example the node degree, the occurrence and number of (odd) cycles, variations in connectivity patterns, such as different levels of connectedness, etc. When creating new benchmarks, an analysis regarding such graph properties is valuable in order to check how newly generated AFs differ from existing benchmarks from a graph-theoretical perspective. New graph generators may also offer the possibility of parameterizing a number of graph features (which is already possible, to a degree, with most random graph generators). On the other hand, this may not be applicable in some scenarios (e.g., when dealing with real-world data).

**Relation to Real-World Scenarios** Creating benchmarks that reflect real-world argumentation scenarios can be challenging. Abstract argumentation frameworks might abstract from the complexity of real-world arguments and their relationships. Moreover, different domains, such as law, politics, healthcare, or ethics, have unique argumentation characteristics and
requirements. Incorporating domain-specific considerations in benchmark generation allows for more targeted evaluations and comparisons of argumentation systems within their intended domains.

**Semantic Aspects** Benchmarks should also be geared towards evaluating solution approaches to the different problems related to abstract argumentation. Some benchmarks are already designed for such purposes (such as *SemBuster*, which is aimed at problems related to the semi-stable semantics), however, there are still numerous problems that have not been specifically addressed yet. As an example, it was recently demonstrated that in most ICCMA'17 instances, a majority of skeptically accepted arguments w.r.t. pr were also included in the grounded and the ideal extension. Since the computational complexity of deciding $DS_{pr}$ is $\Pi_2^P$-complete [2], but problems related to id are “only” $\Theta_2^P$-complete, and the grounded extension can be computed in polynomial time. Hence, even though the task of deciding $DS_{pr}$ is computationally complex, it can still be computed relatively efficiently, due to the occurrence of many “easy” cases.

## 4. KWT Benchmark Generator

In the previous section, we identified a number of challenges that occur in the generation of benchmarks for abstract argumentation. Since it is not reasonable to address all concerns within one graph generator, we focus on a specific semantic aspect as an example, namely the issue that solving the $\Pi_2^P$-complete problem $DS_{pr}$ can often be bypassed by checking if the given argument is accepted w.r.t. gr or id. Note that another “easy case” regarding $DS_{pr}$ occurs when arguments are attacked by some admissible set—such arguments are never skeptically accepted w.r.t. pr—and deciding this is a problem in NP. In [3], we briefly introduced a possible solution for this problem. In the following, we provide a more thorough description of our approach.

We developed the *KWT generator*, which takes as parameters

* *num\*args*: the total number of arguments,

* *num\*pa*: the number of arguments to be skeptically accepted under preferred semantics,

* *num\*cred*: the number of arguments to be contained in at least one preferred extension,

* *num\*pref*: the number of preferred extensions,

* *num\*ideal*: the number of arguments in the ideal extension,

and further parameters that control the probability of attacks between different sets of arguments. More precisely, these parameters set the probabilities of arguments in the ideal extension to be attacked and to attack back, respectively, the probabilities of credulously accepted arguments to be attacked and to attack back, the probabilities of skeptically accepted arguments that are not contained in the ideal extension to be attacked and to attack back, and the probability of further random attacks between unaccepted arguments. Given these parameters, a random AF *F* is generated as follows:

1. The set *Arg* of *num\*args* arguments is created and arguments are associated to sets *S*<sub>pa</sub> (skeptically accepted arguments w.r.t. preferred semantics), *S*<sub>ideal</sub> (arguments in the ideal extension), *S*<sub>cred</sub> (arguments that are credulously accepted w.r.t. preferred semantics),
$S_{unacc}$ (arguments that are not credulously accepted w.r.t. preferred semantics), such that $S_{ideal} \subseteq S_{pa} \subseteq S_{cred}, S_{cred} \cup S_{unacc} = \text{Arg}$, and the corresponding cardinalities are respected. Finally, sets $E_1, \dots, E_{num_{pref}}$ (the preferred extensions) are created by adding all arguments from $S_{pa}$ and randomly drawn arguments from $S_{cred} \setminus S_{pa}$.

2. For every argument $a \in S_{ideal}$, random attackers from $S_{unacc}$ are sampled. For each of these attackers $b$, another argument from $S_{ideal}$ is sampled that attacks $b$. This ensures that the grounded extension will be empty and that the ideal extension is capable of defending itself (thus forming an admissible set).

3. For every argument $a \in S_{pa} \setminus S_{ideal}$, attacks from unaccepted arguments are sampled in a similar way (to ensure an empty grounded extension). Furthermore, every such argument $a$ must be defended by each preferred extension. Thus, for each preferred extension $E$, some arguments are sampled to defend $a$.

4. For every preferred extension $E$ and $a \in E \setminus S_{pa}$, attackers for $a$ are sampled from $\text{Arg} \setminus E$ and corresponding defenders are defined within $E$.

5. Additional random attacks are added between arguments in $S_{unacc}$.

6. In order to avoid having stable extensions (which may also ease computation of arguments that are skeptically accepted under preferred semantics, since every stable extension is also preferred), we add another self-attacking argument and some attacks between this argument and arguments from $S_{unacc}$.

Note that due to the random approach of generating an argumentation graph, it may not necessarily be the case that the number of skeptically/credulously accepted arguments (w.r.t. preferred semantics) as well as the number of arguments in the ideal extension exactly match the given parameters. However, our experiments in [3] showed that it is indeed relatively hard to decide skeptical acceptance (w.r.t. preferred semantics) for most arguments in the resulting graph.

The graph generator<fnref n="2" /> and an example demonstrating its usage<fnref n="3" /> we used can be found online.

## 5. Conclusion

Throughout this paper we discussed how the generation of new benchmarks for abstract argumentation problems can be challenging from multiple perspectives. Although existing benchmarks for abstract argumentation already provide valuable resources for evaluating and comparing different frameworks and algorithms, they may not adequately capture the challenges and requirements posed by recent developments in the field. Moreover, existing benchmarks may have limitations in terms of the problem space they cover (e.g. concerning characteristics of different graph properties).

Overall, we would like to highlight that new benchmarking techniques should yield AFs that are indeed novel in some regard, i.e., which differ from existing data—for instance, in terms of graph-theoretical properties, by addressing previously little considered semantic aspects, or by incorporating new real-world problems. Combining all of these different facets in one

<footnote n="2">²http://tweetyproject.org/r/?r=kwt_gen</footnote>

<footnote n="3">³http://tweetyproject.org/r/?r=kwt_gen_ex</footnote>
single generator is presumably rather difficult, however, considering them individually might already lead to new insights. As an example, we presented the KWT generator, which generates particularly challenging AFs for the task of deciding skeptical acceptability w.r.t. preferred semantics.

## Acknowledgments

The research reported in this work was supported by Deutsche Forschungsgemeinschaft under grant 375588274.

## References

[1] P. M. Dung, On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming and n-Person Games, Artificial Intelligence 77 (1995) 321–358.

[2] P. E. Dunne, T. J. M. Bench-Capon, Coherence in finite argument systems, Artificial Intelligence 141 (2002) 187–203.

[3] I. Kuhlmann, T. Wujek, M. Thimm, On the impact of data selection when applying machine learning in abstract argumentation, in: Computational Models of Argument, IOS Press, 2022, pp. 224–235.

[4] P. M. Dung, P. Mancarella, F. Toni, Computing ideal sceptical argumentation, Artificial Intelligence 171 (2007) 642–674.

[5] F. Cerutti, M. Giacomin, M. Vallati, Generating challenging benchmark afs., COMMA 14 (2014) 457–458.

[6] J.-M. Lagniez, E. Lonca, J.-G. Mailly, J. Rossit, Design and results of iccma 2021, arXiv preprint arXiv:2109.08884 (2021).

[7] M. Caminada, M. Podlaszewski, Admbuster: a benchmark example for (strong) admissibility, 2017. The Second International Competition on Computational Models of Argumentation (ICCMA’17).

[8] M. Caminada, B. Verheij, Sembuster: a benchmark example for semi-stable semantics, 2017.

[9] M. Caminada, W. A. Carnielli, P. E. Dunne, Semi-stable semantics, J. Log. Comput. 22 (2012) 1207–1254.

[10] M. Thimm, S. Villata, The first international competition on computational models of argumentation: Results and analysis, Artificial Intelligence 252 (2017) 267–294.

[11] F. Cerutti, M. Giacomin, M. Vallati, Exploiting planning problems for generating challenging abstract argumentation frameworks, URL: http://argumentationcompetition.org/2017/Planning2AF.pdf (2017).

[12] T. Lehtonen, J. P. Wallner, M. Järvisalo, Assumption-based argumentation translated to argumentation frameworks, URL: http://argumentationcompetition.org/2017/ABA2AF.pdf (2017).

[13] M. Diller, Traffic networks become argumentation frameworks, URL: http://argumentationcompetition.org/2017/Traffic.pdf (2017).
[14] B. Yun, M. Croitoru, Benchmark on logic-based argumentation framework with datalog±, 2019.
# Abstract Argumentation Applied to Fair Resources Allocation: A Preliminary Study

Jean-Guy Mailly¹

¹Université Paris Cité, LIPADE
F-75006 Paris, France

## Abstract

In this paper, we discuss the application of abstract argumentation mechanisms to resources allocation. We show how such problems can be modeled as abstract argumentation frameworks, such that specific sets of arguments corresponds to interesting solutions of the problem. By interesting solutions, here we mean *Local Envy-Free* (LEF) allocations. Envy-freeness is an important notion of fairness in resources allocation, assuming than no agent should prefer the resource allocated to another agent. We focus on LEF, a generalized form of envy-freeness, and we show that LEF allocations corresponds to some specific sets of arguments in our argument-based modeling of the problem. This work in progress paves the way to richer connections between the various models of argumentation and resources allocation problems.

## Keywords

Abstract argumentation, Resources allocation, Fairness

## 1. Introduction

Fairness issues are important in multi-agent scenarios, including resources allocation. Among the various fairness criteria, one of them is *envy-freeness*, i.e. the fact that no agent is envious of another agent. A generalized version of envy-freeness is *local envy-freeness* (LEF) [1], where agents are part of a social network, and the goal is to assign each agent one object such that none of them is envious of one of her neighbours in the network. In this work, we study a transformation from LEF problems to abstract argumentation [2]. We show that there is a correspondence between LEF allocations and some specific extensions of an argumentation framework built from the LEF problem at hand. The representation of LEF problems as argumentation problems offers several advantages. First of all, there are plenty of efficient tools for computing extensions of argumentation frameworks, which is not the case with LEF problems. Then, the argumentation process can offer intuitive (and visual) explanations of why an allocation is LEF, or why there is no such allocation. Finally, the vast literature on argumentation provides tools for other fairness problems, or for identifying specific allocations, e.g. weighted argumentation frameworks can provide means to obtain optimal allocations (w.r.t. agents utility functions or w.r.t. the Pareto criterion).

Section 2 provides some background notions on LEF allocations and abstract argumentation.

Arg&App 2023: International Workshop on Argumentation and Applications, September 2023, Rhodes, Greece

jean-guy.mailly@u-paris.fr (J. Mailly)

0000-0001-9102-7329 (J. Mailly)

<figure><img src="image_41.png" /></figure>

© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

<figure><img src="image_42.png" /></figure>

CEUR Workshop Proceedings (CEUR-WS.org)
Section 3 discusses our transformation from resources allocation problems to abstract argumentation, and shows the relation between LEF allocations and specific extensions. Finally Section 4 concludes the paper by discussing some interesting questions for future work.

## 2. Background

### 2.1. Local Envy-Freeness

We focus on a resource allocation scenario (previously studied in [1]) where agents may know some other agents, and have preferences over the set of resources that must be allocated. The other hypotheses in our scenario are the fact that the number of agents is equal to the number of resources, and the fact that resources are indivisible goods. Formally,

**Definition 1.** A preference-based allocation problem (PRAP) is a tuple $\mathcal{PRAP} = (\mathcal{O}, \mathcal{N}, \succ, \mathcal{G})$:

* $\mathcal{O} = \{o_1, \dots, o_n\}$ is the set of objects,

* $\mathcal{N} = \{1, \dots, n\}$ is the set of agents,

* $\succ$ is a set of binary relations $\{\succ_i | i \in \mathcal{N}\}$ where $\succ_i$ is a linear order expressing the preferences of agent $i$ over $\mathcal{O}$,

* $\mathcal{G} = (\mathcal{N}, \mathcal{E})$ is an undirected graph representing the social network of agents.

We are interested in the problem of local envy-freeness, i.e. whether we can assign each agent $i$ an object $o_k$ s.t. $i$ does not prefer the object assigned to one of her neighbors, formally $\forall j \in \mathcal{N} \text{ s.t. } \{i, j\} \in \mathcal{E}, o_l \succcurlyeq_i o_k$, where $o_k$ and $o_l$ are (respectively) the object assigned to $i$ and the object assigned to $j$.

To characterize formally this concept, we represent an allocation as a set of pairs $(i, o_k) \in \mathcal{N} \times \mathcal{O}$. Given such a pair $x = (i, o_k)$, we use $\text{Ag}(x)$ and $\text{Obj}(x)$ to denote respectively the agent $i$ and the object $o_k$ of this pair. An allocation $\gamma$ is valid if for each $x, y \in \gamma$, if $x \neq y$ then $\text{Ag}(x) \neq \text{Ag}(y)$ and $\text{Obj}(x) \neq \text{Obj}(y)$, i.e. no agent receives several objects, and no object is assigned to several agents. A valid allocation can be partial if $|\gamma| < |\mathcal{O}|$, and total if $|\gamma| = |\mathcal{O}| = |\mathcal{N}|$.

**Definition 2.** Given $\mathcal{PRAP} = (\mathcal{O}, \mathcal{N}, \succ, \mathcal{G})$, an allocation is local envy-free (LEF) iff it is a total valid allocation such that $\forall i, j \in \mathcal{N} \text{ s.t. } \{i, j\} \in \mathcal{E}, \text{ if } (i, o_k), (j, o_l) \in \gamma \text{ then } o_l \succcurlyeq_i o_k$.

**Example 1.** Figure 1a describes $\mathcal{PRAP} = (\mathcal{O}, \mathcal{N}, \succ, \mathcal{G})$ where the agents are $\mathcal{N} = \{A, B, C\}$, the objects are $\mathcal{O} = \{1, 2, 3\}$ with 1 representing some money, 2 a motorbike, and 3 a car. The social network $\mathcal{G}$ is shown at the top of the Figure, and the agents preferences $\succ$ are given underneath. We can easily find a LEF allocation by giving each agent her preferred object.

Now consider $\mathcal{PRAP}_2$ given at Figure 1b, where this time all the agents know each other, and agent C's preferences are slightly modified as well. Assume there is a LEF allocation $\gamma$. Neither A nor C can receive the object 1 (because otherwise the one receiving another object would be envious of the one receiving the object 1). Thus we must have $(B, 1) \in \gamma$. But in this case, both agents A and C are envious of agent B. So there is no LEF allocation for $\mathcal{PRAP}_2$.
<figure><img src="image_43.png" /><figcaption>**Figure 1:** Social Networks and Preferences</figcaption></figure>

## 2.2. Abstract Argumentation

Now let us recall basic notions of Dung's abstract argumentation [2].

**Definition 3.** An abstract argumentation framework (AF) is a directed graph $\mathcal{F} = \langle \mathcal{A}, \mathcal{R} \rangle$ where $\mathcal{A}$ is the set of arguments and $\mathcal{R} \subseteq \mathcal{A} \times \mathcal{A}$ is the attack relation.

Classical reasoning with AF uses the notion of *extensions*, i.e. sets of arguments that can be jointly accepted. Various semantics have been proposed to obtain the set of extensions of an AF. Formally, an extension-based semantics is a function $\sigma$ such that for any AF $\mathcal{F} = \langle \mathcal{A}, \mathcal{R} \rangle$, $\sigma(\mathcal{F}) \subseteq 2^A$. In this paper, we only need the notions of conflict-free sets and stable extensions:

**Definition 4.** Given $\mathcal{F} = \langle \mathcal{A}, \mathcal{R} \rangle$, $S \subseteq \mathcal{A}$ is conflict-free ($S \in \mathrm{cf}(\mathcal{F})$) if $\forall a, b \in S$, $(a, b) \notin \mathcal{R}$. Then, $S$ is a stable extension ($S \in \mathrm{stb}(\mathcal{F})$) if $S \in \mathrm{cf}(\mathcal{F})$ and $\forall b \in \mathcal{A} \setminus S$, $\exists a \in S$ s.t. $(a, b) \in \mathcal{R}$.

Among the various generalizations of Dung's argumentation framework, we are interested in *preference-based* AFs (PAFs) [3].

**Definition 5.** A preference-based argumentation framework is a tuple $\mathcal{P} = \langle \mathcal{A}, \mathcal{R}, \triangleright \rangle$ where $\langle \mathcal{A}, \mathcal{R} \rangle$ is an AF, and $\triangleright \subseteq \mathcal{A} \times \mathcal{A}$ is a preference relation over the set of arguments.

The preference relation is only assumed to be a pre-order, i.e. a reflexive and transitive binary relation. The main approach for reasoning with a PAF consists in reducing it into a standard AF by combining the attacks and the preferences into a *defeat relation*. Then, the extensions of the PAF for a semantics $\sigma$ are the extensions of the defeat graph under the same semantics.

**Definition 6.** Given a PAF $\mathcal{P} = \langle \mathcal{A}, \mathcal{R}, \triangleright \rangle$, we define the defeat relation $\mathcal{D} = \{(x, y) \in \mathcal{R} \mid y \not\preceq x\}$. Then, $\sigma(\mathcal{P}) = \sigma(\langle \mathcal{A}, \mathcal{D} \rangle)$.

## 3. Translation into Abstract Argumentation

In this section we show how to transform a PRAP into a PAF, such that there is a correspondence between LEF allocations and some sets of arguments, namely conflict-free sets of size $|\mathcal{N}|$, which are guaranteed to be stable extensions as well in our case.
**Definition 7.** Given $\mathcal{PRAP} = \langle \mathcal{O}, \mathcal{N}, \succ, \mathcal{G} \rangle$, we define the PAF $\mathcal{P}_{\text{LEF}} = \langle \mathcal{A}, \mathcal{R}, \triangleright \rangle$ with

• $\mathcal{A} = \{(i, o_j) \mid i \in \mathcal{N}, o_j \in \mathcal{O}\}$ (one argument $\simeq$ allocation of an object to an agent),

• $\mathcal{R} = \mathcal{R}_1 \cup \mathcal{R}_2 \cup \mathcal{R}_3$, with

– $\mathcal{R}_1 = \{( (i, o_j), (i, o_k) ) \mid i \in \mathcal{N}, o_j, o_k \in \mathcal{O} \}$ (only one object per agent),

– $\mathcal{R}_2 = \{( (i, o_k), (j, o_k) ) \mid i, j \in \mathcal{N}, o_k \in \mathcal{O} \}$ (only one agent per object),

– $\mathcal{R}_3 = \{( (i, o_k), (j, o_l) ) \mid i, j \in \mathcal{N}, o_k, o_l \in \mathcal{O}, \{i, j\} \in \mathcal{E} \text{ and } o_l \succ_i o_k \} \text{ (envy)},$

• $\triangleright = \{( (i, o_k), (i, o_j) ) \mid i \in \mathcal{N}, o_k \succ_i o_j \} \text{ (preferences)}.$

Obviously, any allocation $\gamma$ corresponds to a set of arguments in $\mathcal{A}$. Observe also that the defeat relation will only remove some of the attacks in $\mathcal{R}_1$, namely, for each pair of arguments $x = (i, o_j)$ and $y = (i, o_k)$, the defeat relation will contain the defeat $(x, y)$ if $o_j \succ_i o_k$, and the defeat $(y, x)$ if $o_k \succ_i o_j$. The other attack relations $\mathcal{R}_2$ and $\mathcal{R}_3$ are not impacted by the preferences, so they are included in the defeat relation of this PAF.

**Example 2.** Let us consider again $\mathcal{PRAP}_1$ from Example 1. Figure 2 gives the defeat relation of the corresponding PAF $\mathcal{P}_{\text{LEF}}$. More precisely, Figure 2a gives the combination of $\mathcal{R}_1$ with the preferences, Figure 2b (resp. 2c) shows $\mathcal{R}_2$ (resp. $\mathcal{R}_3$). In Figure 2c, the red arrows correspond to the situations where agent A is envious (for instance, because she has received the object 2 while B has received the object 1), blue arrows are for agent B, and green arrows correspond to agent C.

<figure><img src="image_44.png" /><figcaption>**Figure 2:** PAF Corresponding to a PRAP</figcaption></figure>

The following lemmas will help us to prove the correspondance between LEF allocations and conflict-free sets (and stable extensions) of size $|\mathcal{N}|$.

**Lemma 1.** Given an allocation $\gamma$, if $\gamma \in \text{cf}(\mathcal{P}_{\text{LEF}})$ then $\gamma$ is valid.

*Proof.* Assume $\gamma$ is not valid. If $\exists x, y \in \gamma$ s.t. $\text{Ag}(x) = \text{Ag}(y)$, then $(x, y), (y, x) \in \mathcal{R}_1$, which implies that either $(x, y)$ or $(y, x)$ is in the defeat relation of $\mathcal{P}_{\text{LEF}}$, so $\gamma \notin \text{cf}(\mathcal{F}_{\text{LEF}})$. Similarly, if $\exists x, y \in \gamma$ s.t. $\text{Obj}(x) = \text{Obj}(y)$, then $(x, y) \in \mathcal{R}_2$, which implies $\gamma \notin \text{cf}(\mathcal{P}_{\text{LEF}})$. $\square$

**Lemma 2.** Given a valid allocation $\gamma$, if $\gamma \notin \text{cf}(\mathcal{P}_{\text{LEF}})$ then $\gamma$ is not LEF.
**Proof.** Assume a valid allocation $\gamma$ which is not conflict-free in $\mathcal{P}_{\text{LEF}}$. By construction, since $\gamma$ is valid, there are no $x, y \in \gamma$ such that $(x, y) \in \mathcal{R}_1$ or $(x, y) \in \mathcal{R}_2$, so we deduce that $\exists x, y \in \gamma$ such that $(x, y) \in \mathcal{R}_3$ which implies that $\gamma$ is not LEF. $\square$

**Proposition 1.** Let $\gamma$ be an allocation. $\gamma$ is LEF iff $\gamma \in \text{cf}(\mathcal{P}_{\text{LEF}})$ and $|\gamma| = |\mathcal{N}|$.

**Proof.** First assume that $\gamma$ is a LEF allocation. From Lemma 2 we deduce that $\gamma$ is conflict-free. By definition, since $\gamma$ is LEF then $\gamma$ is total. Hence the first part of the result.

Now assume that $\gamma \in \text{cf}(\mathcal{P}_{\text{LEF}})$ and $|\gamma| = |\mathcal{N}|$. From Lemma 1, we know that $\gamma$ is valid. Then, since $\gamma \in \text{cf}(\mathcal{P}_{\text{LEF}})$, we can guarantee that there are no $x, y \in \gamma$ such that $(x, y) \in \mathcal{R}_3$. This means that, for any $i \in \mathcal{N}$ such that $(i, o_k) \in \gamma$, there is no $j \in \mathcal{N}$ such that $(j, o_l) \in \gamma$, $\{i, j\} \in \mathcal{E}$ and $o_l \succ_i o_k$. By definition, this means that $\gamma$ is LEF. $\square$

Proposition 1 implies that LEF allocations can be easily computed thanks to a minor modification of a very classical approach for solving argumentation problems. Most of the efficient approaches for reasoning with abstract argumentation frameworks use SAT solvers. For the basic notion of conflict-freeness, it is enough to consider clauses which forbid to accept together arguments which are connected by an attack. We will use a MaxSAT version of this encoding [4], where the clauses usually corresponding to conflict-freeness will be hard clauses, and additional (unit) soft clauses will be added to ensure that the solver will return a maximal solution (in terms of cardinality). Formally,

**Definition 8.** Given $\mathcal{PRAP} = \langle \mathcal{O}, \mathcal{N}, \succ, \mathcal{G} \rangle$, and $\mathcal{P}_{\text{LEF}} = \langle \mathcal{A}, \mathcal{R}, \triangleright \rangle$ the corresponding PAF. $\mathcal{D}$ denotes the defeat relation obtained from $\mathcal{R}$ and $\triangleright$. We define the following sets of hard clauses $hc$ and soft clauses $sc$:

$$hc = \{ \neg x \lor \neg y \mid (x, y) \in \mathcal{D} \} \quad sc = \{(x, 1) \mid x \in \mathcal{A}\}$$

Given the sets of clauses $hc$ and $sc$, a MaxSAT solver returns a conflict-free set of $\mathcal{P}_{\text{LEF}}$ of maximal cardinality. If this solution has a cardinality equal to $|\mathcal{N}|$, then it is a LEF allocation. Otherwise, there is no LEF allocation. Another possible approach consists in adding one cardinality constraint [5] $\sum_{x \in \mathcal{A}} x = |\mathcal{N}|$ to the set of hard clauses. In this case, if a LEF allocation exists then it will be provided by a SAT solver, otherwise the solver will answer UNSAT.

Notice that such an allocation also corresponds to a stable extension of cardinality $|\mathcal{N}|$.

**Corollary 1.** Let $\gamma$ be an allocation. $\gamma$ is LEF iff $\gamma \in \text{stb}(\mathcal{P}_{\text{LEF}})$ and $|\gamma| = |\mathcal{N}|$.

**Proof.** One side of the equivalence is obvious: if $\gamma \in \text{stb}(\mathcal{P}_{\text{LEF}})$, then $\gamma \in \text{cf}(\mathcal{P}_{\text{LEF}})$, so under the assumption that $|\gamma| = |\mathcal{N}|$, the result follows Proposition 1.

Now, assume that $\gamma$ is a LEF allocation. From Proposition 1, we know that $\gamma \in \text{cf}(\mathcal{P}_{\text{LEF}})$ and $|\gamma| = |\mathcal{N}|$. For a given object $o_k$, there is an argument $a = (i, o_k) \in \gamma$, i.e. the object $o_k$ has been assigned to agent $i$. By definition of $\mathcal{R}_2$, $a$ defeats all the arguments of the form $(j, o_k)$ for $j \neq i$. Since this is true for all the objects, any argument not in $\gamma$ is defeated by some argument in $\gamma$, so $\gamma \in \text{stb}(\mathcal{P}_{\text{LEF}})$. $\square$
## 4. Discussion

Argumentation has already shown its interest for providing explanations to other problems, like e.g. scheduling [6] or case-based reasoning [7], so drawing connections between argumentation and resources allocation is a natural question.

The preliminary study of this connection allows us to envision deeper relations between both frameworks. For instance, it seems possible to assign numerical values to assignments (e.g. the preferred object $o_k$ of agent $i$ receives the value $n$, her second preferred object receives $n-1$, etc.) in order to define a *Strength-based Argumentation Framework* (StrAF) [8] where the strength of an argument can intuitively correspond to the utility of allocating the object $o_k$ to the agent $i$. Then using the semantics of StrAFs could induce interesting allocations. We plan to investigate this connection.

We are also interested in the methods allowing the explanation of arguments status in abstract argumentation (e.g. [9, 10]). They could allow to simply explain why the allocation of a specific object to an agent is necessary (or impossible). Also, the approach proposed by [11, 12] could provide interesting means to reduce the size of the argumentation graph, hence providing a better visual explanation of the (non-)existence of desirable allocation.

Another interesting way to go further in the study of argumentation applied to resources allocation consists in using the conflict-tolerant semantics of *Weighted Argumentation Frameworks* (WAFs) [13] in order to obtain optimal (non-LEF) allocations for instances which do not admit any LEF allocation.

These few ideas are only a small part of the possible connections between resources allocation and computational argumentation, and pave the way to a rich body of work that will allow to provide explainable solutions to fairness issues in resources allocation problem.

## Acknowledgments

This work benefited from the support of the project AGGREEY ANR-22-CE23-0005 of the French National Research Agency (ANR).

## References

[1] A. Beynier, Y. Chevaleyre, L. Gourvès, A. Harutyunyan, J. Lesca, N. Maudet, A. Wilczynski, Local envy-freeness in house allocation problems, Auton. Agents Multi Agent Syst. 33 (2019) 591–627.

[2] P. M. Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artif. Intell. 77 (1995) 321–358. URL: https://doi.org/10.1016/0004-3702(94)00041-X. doi:10.1016/0004-3702(94)00041-X.

[3] L. Amgoud, C. Cayrol, A reasoning model based on the production of acceptable arguments, Ann. Math. Artif. Intell. 34 (2002) 197–215. URL: https://doi.org/10.1023/A:1014490210693. doi:10.1023/A:1014490210693.

[4] F. Bacchus, M. Järvisalo, R. Martins, Maximum satisfiability, in: A. Biere, M. Heule, H. van Maaren, T. Walsh (Eds.), Handbook of Satisfiability - Second Edition, volume 336
of *Frontiers in Artificial Intelligence and Applications*, IOS Press, 2021, pp. 929–991. URL: https://doi.org/10.3233/FAIA201008. doi:10.3233/FAIA201008.

[5] O. Roussel, V. M. Manquinho, Pseudo-boolean and cardinality constraints, in: A. Biere, M. Heule, H. van Maaren, T. Walsh (Eds.), Handbook of Satisfiability - Second Edition, volume 336 of *Frontiers in Artificial Intelligence and Applications*, IOS Press, 2021, pp. 1087–1129. URL: https://doi.org/10.3233/FAIA201012. doi:10.3233/FAIA201012.

[6] K. Cyras, D. Letsios, R. Misener, F. Toni, Argumentation for explainable scheduling, in: The Thirty-Third AAAI Conference on Artificial Intelligence, AAAI 2019, The Thirty-First Innovative Applications of Artificial Intelligence Conference, IAAI 2019, The Ninth AAAI Symposium on Educational Advances in Artificial Intelligence, EAAI 2019, Honolulu, Hawaii, USA, January 27 - February 1, 2019, AAAI Press, 2019, pp. 2752–2759. URL: https://doi.org/10.1609/aaai.v33i01.33012752. doi:10.1609/aaai.v33i01.33012752.

[7] G. Paulino-Passos, F. Toni, On monotonicity of dispute trees as explanations for case-based reasoning with abstract argumentation, in: K. Cyras, T. Kampik, O. Cocarascu, A. Rago (Eds.), 1st International Workshop on Argumentation for eXplainable AI co-located with 9th International Conference on Computational Models of Argument (COMMA 2022), Cardiff, Wales, September 12, 2022, volume 3209 of *CEUR Workshop Proceedings*, CEUR-WS.org, 2022. URL: https://ceur-ws.org/Vol-3209/8465.pdf.

[8] J. Rossit, J.-G. Mailly, Y. Dimopoulos, P. Moraitis, United we stand: Accruals in strength-based argumentation, Argument Comput. 12 (2021) 87–113. URL: https://doi.org/10.3233/AAC-200904. doi:10.3233/AAC-200904.

[9] A. Niskanen, M. Järvisalo, Smallest explanations and diagnoses of rejection in abstract argumentation, in: D. Calvanese, E. Erdem, M. Thielscher (Eds.), Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020, Rhodes, Greece, September 12-18, 2020, 2020, pp. 667–671. URL: https://doi.org/10.24963/kr.2020/67. doi:10.24963/kr.2020/67.

[10] M. Ulbricht, J. P. Wallner, Strong explanations in abstract argumentation, in: Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Thirty-Third Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021, AAAI Press, 2021, pp. 6496–6504. URL: https://ojs.aaai.org/index.php/AAAI/article/view/16805.

[11] P. Besnard, S. Doutre, T. Duchatelle, M. Lagasquie-Schiex, Explaining semantics and extension membership in abstract argumentation, Intell. Syst. Appl. 16 (2022) 200118. URL: https://doi.org/10.1016/j.iswa.2022.200118. doi:10.1016/j.iswa.2022.200118.

[12] S. Doutre, T. Duchatelle, M. Lagasquie-Schiex, Visual explanations for defence in abstract argumentation, in: N. Agmon, B. An, A. Ricci, W. Yeoh (Eds.), Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2023, London, United Kingdom, 29 May 2023 - 2 June 2023, ACM, 2023, pp. 2346–2348. URL: https://dl.acm.org/doi/10.5555/3545946.3598929. doi:10.5555/3545946.3598929.

[13] P. E. Dunne, A. Hunter, P. McBurney, S. Parsons, M. J. Wooldridge, Weighted argument systems: Basic definitions, algorithms, and complexity results, Artif. Intell. 175 (2011) 457–486. URL: https://doi.org/10.1016/j.artint.2010.09.005. doi:10.1016/j.artint.2010.09.005.
# Accessible Algorithms for Applied Argumentation

Daphne Odekerken<fnref n="1" />,<fnref n="2" />, AnneMarie Borg<fnref n="1" /> and Matti Berthold<fnref n="3" />

## Abstract

Computational argumentation is a promising research area, yet there is a gap between theoretical contributions and practical applications. Bridging this gap could potentially raise interest in this topic even more. We argue that one part of the bridge could be an open-source package of implementations of argumentation algorithms, visualised in a web interface. Therefore we present a new release of PyArg, providing various new argumentation-based functionalities – including multiple generators, a learning environment, implementations of theoretical papers and a showcase of a practical application – in a new interface with improved accessibility.

## Keywords

argumentation, implementation, visualisation, education

## 1. Introduction

Computational argumentation is a promising interdisciplinary research area, with applications in, e.g. the legal, medical and e-government domain [1]. Thanks to its natural connection with human cognition, its flexibility and its dialectic nature, argumentation seems to be particularly suitable as a logical foundation for human-centered artificial intelligence (AI) [2].

The construction of argumentation-based AI systems that are applicable to real-world use cases requires not only theoretical developments, but also effective solving of problems related to argumentation. Although there is a significant amount of work on theoretical aspects of computational argumentation, which include various argumentation formalisms, semantics and their properties, as well as a growing body of research on solvers that are sufficiently efficient to be applied in practice<fnref n="1" />, we argue that the connection between these two areas could (and should) be strengthened. This is based on our observation that real-life applications use a different formalism than those mainly studied in the community [3] or require efficient algorithms for yet unexplored problems [4].

In addition, we hypothesise that the application of argumentation-based AI is more cumbersome for non-experts than, for example, the application of machine-learning based AI, which is

Arg&App 2023: International Workshop on Argumentation and Applications, September 2023, Rhodes, Greece

d.odekerken@uu.nl (D. Odekerken); a.borg@uu.nl (A. Borg); berthold@informatik.uni-leipzig.de (M. Berthold)

https://webspace.science.uu.nl/~3827887/ (D. Odekerken); https://annemarieborg.nl/ (A. Borg); https://www.informatik.uni-leipzig.de/~berthold/ (M. Berthold)

0000-0003-0285-0706 (D. Odekerken); 0000-0002-7204-6046 (A. Borg); 0009-0006-9231-5115 (M. Berthold)

<figure><img src="image_45.png" /></figure>

© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).

<figure><img src="image_46.png" /></figure>

CEUR Workshop Proceedings (CEUR-WS.org)

<footnote n="1">¹Department of Information and Computing Sciences, Utrecht University, The Netherlands</footnote>

<footnote n="2">²National Police Lab AI, Netherlands Police, The Netherlands</footnote>

<footnote n="3">³ScaDS.AI Dresden/Leipzig, Universität Leipzig, Germany</footnote>

<footnote n="1">¹In particular by submissions to the International Competition on Computational Models of Argumentation (ICCMA): http://argumentationcompetition.org/</footnote>
more convenient thanks to the availability of numerous software packages (such as Scikit-learn<fnref n="2" /> and Tensorflow<fnref n="3" />) as well as user-friendly interfaces to try this AI.<fnref n="4" /> This makes argumentation less accessible to students, software developers and companies searching for AI-based solutions to domain-specific problems.

In order to improve both the connection within theoretical and practical work within the computational argumentation community and the connection with stakeholders outside the community, it would be helpful to have open-source software, paired with an accessible web interface. In this paper, we therefore present a new release of PyArg.

PyArg is an open-source software implementation in Python that not only provides practical algorithms for theoretical problems in various argumentation formalisms, but also makes (potential) applications of these algorithms visible in a user interface that is accessible from the internet without installation. PyArg is intended to be a software solution for researchers within the argumentation community, students who may become part of it, as well as stakeholders outside the community, thanks to the following features:

1. Open-source implementations of argumentation algorithms on GitHub can be validated and extended by community members (https://github.com/DaphneOdekerken/PyArg);

2. The Python package can be installed using `pip install python-argumentation` and is therefore directly usable for software developers;

3. The web interface on https://pyarg.npai.science.uu.nl/ makes argumentation more accessible to those who wish to learn more about argumentation and serves as a platform for showcasing applications of argumentation to stakeholders outside the community.

The release presented here is a major update compared to the preliminary version earlier presented in [5]. In the following sections, we describe PyArg's new functionalities.

## 2. Support for more formalisms

Research on computational argumentation ranges over an ever-growing number of formalisms and extensions of formalisms. Whereas the initial version of PyArg [5] only supported abstract argumentation frameworks and ASPIC⁺, in this iteration we added support for assumption-based argumentation (ABA) [6, 7]. In particular, PyArg can now (1) compute the extensions of a given ABA framework under the prominent semantics and visualise them in the instantiated abstract argumentation framework; and (2) verify if a specific set of extensions can be realised under a given semantics (see Section 3.2).

## 3. Algorithms for argumentation problems

The new PyArg version still contains all algorithms presented in [5], including various implementations of formalisms and algorithms in both abstract argumentation [8] and ASPIC⁺ [9]. It provides algorithms for evaluating argumentation settings in different semantics [10], as well

<footnote n="2">²https://scikit-learn.org/</footnote>

<footnote n="3">³https://www.tensorflow.org/</footnote>

<footnote n="4">⁴e.g. https://freegpt.cc/</footnote>
as explaining the (non-)acceptance of arguments and formulas in various ways [11, 12]. In the
new version, we also provide algorithms for dynamic argumentation problems as well as for
the construction of canonical representations.

**3.1. Dynamic argumentation problems**

Many problems in argumentation assume that all information required to decide upon, for
example, the acceptance of an argument is present. This is however not always a realistic as-
sumption in applied settings. Therefore, recently the problems of stability [4] and relevance [13]
have been introduced for various formalisms, including ASPIC$^+$. Informally, the stability status
of a “topic” argument or formula represents the impossibility that its acceptability status may
change in view of additional, yet uncertain information. For topics that are not stable, it is
interesting to study relevance, where only information that can change the stability status of
the topic is relevant. PyArg provides an implementation of the approximation algorithm for
stability from [4], as well as an inexact but efficient algorithm for estimating relevance based
on the labels from the aforementioned stability algorithm.

**3.2. Canonical argumentation frameworks**

The work by Dunne et al. [14] studies the realisability in abstract argumentation: given a semantics $\sigma$ and a set of extensions $\mathcal{S}$, is there an argumentation framework $F$ realising $\mathcal{S}$ under $\sigma$, i.e., such that $\sigma(F) = \mathcal{S}$ – and which characteristics determine whether such an argumentation framework exists? Similarly, realisability can be characterised for ABAFs [15]. PyArg now provides the algorithms to determine whether a given set extensions satisfies these characteristic properties and generates “canonical” argumentation frameworks or ABA frameworks, when they exist; see Figure 1.

# 4. Practical features

**4.1. Generators**

There are various situations in which it is useful to randomly generate an argumentation
setting. One example would be for testing new algorithms: a large part of the data sets used
in the ICCMA competition to assess runtime of algorithms is based on randomly generated
argumentation frameworks. A second example is related to education: in order to assess a
student’s understanding of, e.g., specific argumentation semantics, it is convenient to have a
generator for automatically creating new exercises.

In order to address this demand, PyArg provides several generators. For generating ASPIC$^+$ argumentation systems, PyArg uses the “layered” generator from [4, Section 4.2.5]. In addition, PyArg provides a basic random generator for abstract argumentation frameworks.

The generators can be found in the source code; in addition, the web interface provides
functionality for generating a single argumentation framework or system, parameterised by the
values given in input fields. The resulting argumentation setting can then be downloaded for
further use within or outside PyArg.
<figure><img src="image_47.png" /></figure>

## Create canonical AFs based on sets of extensions

**Enter your set of extensions here**

[]
(a)
(a,b)

**Properties and semantics**

<figure><img src="image_48.png" /></figure>

**Canonical argumentation framework**

AF = (A, D) where A = (b, a, b_(a)) and D = ((b_(a), b_(a)): (b_(a), b): (a, b_(a)))

<figure><img src="image_49.png" /><figcaption>**Figure 1:** Given an extension set provided by the user, PyArg computes certain properties and generates a canonical argumentation framework when possible.</figcaption></figure>

<figure><img src="image_50.png" /></figure>

## Visualisation of abstract argumentation frameworks

<figure><img src="image_51.png" /></figure>

<figure><img src="image_52.png" /><figcaption>**Figure 2:** Improved visualisation of the abstract argumentation environment.</figcaption></figure>

## 4.2. Improved visualisation

Compared to the previous version, PyArg's user interface has been made more user-friendly and accessible. A screenshot of the new visualisation for abstract argumentation frameworks is shown in Figure 2. PyArg now features both a *regular* mode (in which accepted arguments are coloured green, while other arguments are yellow or red) and a *colourblind-friendly* mode that uses an adapted colour palette.
### 4.3. Importers and exporters

PyArg provides various importers and exporters to convert argumentation settings to various formats. For abstract argumentation frameworks, it is possible to read from and write to all formats used in recent ICCMA competitions, that is: the ASPARTIX format (.APX), the Trivial Graph Format (.TGF) and the input format used for ICCMA 2023 (.ICCMA23). In addition, for both abstract argumentation frameworks and ASPIC⁺ argumentation systems, there are importers and exporters to and from JSON.

## 5. Applications of algorithms in the web interface

In order to demonstrate how PyArg’s algorithms can be applied in various settings, we provide two use cases in the web interface: a learning environment and a chat interface.

### 5.1. Learning environment

The learning environment is intended for anyone interested in learning computational argumentation. In this functionality in the web interface, a learner can choose between various exercises. The current PyArg version features three exercises: identifying grounded, complete and preferred extensions in abstract argumentation. As the learner starts an exercise, PyArg generates a random abstract argumentation framework using its generators. The learner then gives the extensions, and PyArg uses its semantics algorithms for validating the learner’s solutions.

### 5.2. Chat interface

The chat interface showcases an application for the algorithms for stability and relevance in inquiy dialogue. First, the user chooses an ASPIC⁺ argumentation system (which can be randomly generated, hand-made or the predefined fraud example), a set of queryables (e.g. formulas that can be asked in a dialogue), a topic formula for the chat and an initial knowledge base. PyArg then uses the stability algorithm to find out if it makes sense to ask for more information - if so, it uses the relevance algorithm for identifying relevant questions.

## 6. Related work

For an extended overview of software related to computational argumentation, we refer to [16]. In this section, we relate to implementations that are most similar to PyArg. Tweety [17] is a comprehensive collection of Java libraries that includes algorithms for both abstract and structured approaches to argumentation. It is in fact more comprehensive than PyArg, but does not have a visualisation option. The Online Argument Structures Tool (TOAST) [18] does provide a visualisation for ASPIC⁺, but the source code is not openly available. Gorgias Cloud [19] is a recent system that is similar to PyArg, but is based on the Gorgias argumentation system. NEXAS [20] is an alternative approach to visualising extensions of abstract argumentation frameworks, which, compared to PyArg, is more aimed towards (large) frameworks with many extensions. Finally, many algorithms for argumentation-related problems have been submitted
to the ICCMA competition. However, these are mostly focused on fast implementation of limited problems, mainly in the context of abstract argumentation.

## 7. Conclusion and future work

PyArg combines algorithms for argumentation problems with a web interface, aiming to improve the connections between theoretical and practical work on argumentation on the one hand, and inside and outside the community on the other hand.

The contributions of this version of PyArg are mainly focused on the front-end. In the back-end, the algorithms for computing the semantics are not state-of-the-art. This becomes noticeable if the visualisation is tested on hard (large) instances, as no output will appear on the screen within a reasonable amount of time. In a next version of PyArg, we plan to improve this performance aspect by calling more efficient solvers in the back-end. In addition, we aim to add support more formalisms, such as abstract dialectical frameworks [21], abstract frameworks with collective attacks [22] and abstract frameworks with support for claims [23], and to implement their intertranslations [24].

On a final note, we hope that the functionalities presented in this paper are just the beginning, as are the plans for future work mentioned above. We are open to any suggestions for additional functionalities, algorithms or other feedback, which we hope to incorporate in future releases of PyArg. Hopefully, this leads to an increase of interest and understanding of computational argumentation, both within and outside the community, eventually resulting in more responsible applications of artificial intelligence.

## Acknowledgments

The authors have not been sorted alphabetically. They acknowledge the financial support by the Federal Ministry of Education and Research of Germany and by the Sächsische Staatsministerium für Wissenschaft Kultur und Tourismus in the program Center of Excellence for AI-research "Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig", project identification number: ScaDS.AI.

## References

[1] K. Atkinson, P. Baroni, M. Giacomin, A. Hunter, H. Prakken, C. Reed, G. Simari, M. Thimm, S. Villata, Towards artificial argumentation, AI magazine 38 (2017) 25–36.

[2] E. Dietz, A. Kakas, L. Michael, Argumentation: A calculus for human-centric AI, Frontiers in Artificial Intelligence 5 (2022).

[3] A. C. Kakas, P. Moraitis, N. I. Spanoudakis, Gorgias: Applying argumentation, Argument & Computation 10 (2019) 55–81.

[4] D. Odekerken, F. Bex, A. Borg, B. Testerink, Approximating stability for applied argument-based inquiry, Intelligent Systems with Applications 16 (2022) 200110.

[5] A. Borg, D. Odekerken, PyArg for solving and explaining argumentation in Python: Demonstration, in: Proceedings of (COMMA-22), 2022, pp. 349–350.
[6] A. Bondarenko, F. Toni, R. A. Kowalski, An assumption-based framework for non-monotonic reasoning, in: Proceedings of (LPNMR-93), 1993, pp. 171–189.

[7] K. Čyras, X. Fan, C. Schulz, F. Toni, Assumption-based argumentation: Disputes, explanations, preferences, in: Handbook of Formal Argumentation, volume 1, 2018, pp. 365–408.

[8] P. M. Dung, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artificial Intelligence 77 (1995) 321–357.

[9] H. Prakken, An abstract framework for argumentation with structured arguments, Argument & Computation 1 (2010) 93–124.

[10] P. Baroni, M. Caminada, M. Giacomin, An introduction to argumentation semantics, The Knowledge Engineering Review 26 (2011) 365–410.

[11] A. Borg, F. Bex, A basic framework for explanations in argumentation, IEEE Intelligent Systems 36 (2021) 25–35.

[12] A. Borg, F. Bex, Necessary and sufficient explanations for argumentation-based conclusions, in: Proceedings of (ECSQARU-21), Springer, 2021, pp. 45–58.

[13] D. Odekerken, T. Lehtonen, A. Borg, J. P. Wallner, M. Järvisalo, Argumentative reasoning in ASPIC+ under incomplete information, in: Proceedings of (KR-23), 2023, pp. 531–541.

[14] P. E. Dunne, W. Dvořák, T. Linsbichler, S. Woltran, Characteristics of multiple viewpoints in abstract argumentation, Artificial Intelligence 228 (2015) 153–178.

[15] M. Berthold, A. Rapberger, M. Ulbricht, On the expressive power of assumption-based argumentation, in: Proceedings of (JELIA-23), 2023.

[16] F. Cerutti, S. A. Gaggl, M. Thimm, J. Wallner, Foundations of implementations for formal argumentation, IfCoLog Journal of Logics and their Applications 4 (2017) 2623–2705.

[17] M. Thimm, The formal argumentation libraries of Tweety, in: Proceedings of (TAFA-17), Springer, 2018, pp. 137–142.

[18] M. Snaith, C. Reed, TOAST: Online ASPIC+ implementation, in: Proceedings of (COMMA-12), IOS Press, 2012, pp. 509–510.

[19] N. I. Spanoudakis, G. Gligoris, A. Koumi, A. C. Kakas, Explainable argumentation as a service, Journal of Web Semantics (2023) 100772.

[20] R. Dachselt, S. Gaggl, M. Krötzsch, J. Méndez, D. Rusovac, M. Yang, Nexas: A visual tool for navigating and exploring argumentation solution spaces, in: Proceedings of (COMMA-22), volume 353, IOS Press, 2022, pp. 116–127.

[21] G. Brewka, H. Strass, S. Ellmauthaler, J. P. Wallner, S. Woltran, Abstract dialectical frameworks revisited, in: Proceedings of (IJCAI-13), 2013, pp. 803–809.

[22] S. H. Nielsen, S. Parsons, A generalization of dung's abstract framework for argumentation: Arguing with sets of attacking arguments, in: Proceedings of (ArgMAS-2006), Springer, 2006, pp. 54–73. doi:10.1007/978-3-540-75526-5_4.

[23] W. Dvorák, A. Rapberger, S. Woltran, Argumentation semantics under a claim-centric view: Properties, expressiveness and relation to setafs, in: Proceedings of (KR-20), 2020, pp. 341–350. doi:10.24963/kr.2020/35.

[24] M. König, A. Rapberger, M. Ulbricht, Just a matter of perspective, in: Proceedings of (COMMA-22), 2022, pp. 212–223. doi:10.3233/FAIA220154.