Assessing the strength of arguments is essential for determining the outcomes of any argument-based system. A wide range of semantics has been proposed in the literature. These take as input a set of arguments—each assigned a basic weight and potentially subject to attacks from others—and compute a single strength value for each argument. Despite the diversity of argument types (or schemes), existing semantics apply uniform evaluation criteria across all arguments. In this paper, we advocate for type-dependent evaluations, acknowledging that the impact of attacks can vary across types. Given that many argument-based systems involve heterogeneous types of arguments, we propose a broad family of hybrid semantics that combine distinct base semantics, each tailored to specific argument types. We investigate their theoretical properties, present concrete instances within this family, and examine their computational complexity.

This paper investigates complex argumentation settings, called weighted higher-order argumentation frameworks (wHO-AFs), where both arguments and attacks carry initial weights and may be subject to attacks from arguments. It focuses on developing gradual semantics capable of rationally evaluating these elements by assigning each argument and attack a numerical value, representing their respective degrees of acceptance and seriousness. The contributions of the paper are five-fold: i) It identifies key technical challenges for semantics in wHO-AFs, such as handling the distinction between arguments and attacks, and determining how their values should be combined. To address these challenges, the paper introduces a set of guiding principles that capture various semantic strategies. ii) It introduces a broad family of semantics that treat arguments and attacks uniformly, evaluating them in the same way. This family encompasses both semantics inspired by extension-based approaches and those that are purely gradual. iii) It defines a second extensive family of semantics that differentiate between arguments and attacks. This includes instances where a single function evaluates both types of elements, as well as hybrid variants that apply distinct evaluation functions to arguments and attacks. iv) It offers a formal analysis and comprehensive comparison of the resulting diverse semantics. v) It presents an empirical evaluation of these semantics. The results are promising as they show that the values of all elements can be computed in fewer than 20 iterations, even for large frameworks, while maintaining very low runtime. The paper ultimately delivers a catalogue of semantics, each offering distinct formal properties and behaviors, contributing a flexible toolkit for reasoning in rich argumentative contexts.

The evaluation of argument strength lies at the core of any argumentation system. Numerous semantics have been proposed for this purpose, along with a variety of principles (or axioms) that such semantics are expected to satisfy. Most existing semantics in the literature have been analyzed and compared in light of these principles. While this body of work marks a significant step toward establishing the theoretical foundations of argumentation semantics, it remains incomplete. In particular, characterizations of entire classes of semantics that uniquely satisfy specific subsets of axioms are still lacking, leaving open questions on the kind of semantics that can still be defined and their added values. This paper addresses this gap by establishing representation theorems that explicitly relate subsets of principles to corresponding classes of semantics. These semantics are defined through two mathematical functions: an impact function and an aggregation operator, each satisfying specific structural properties. We demonstrate how these principles offer a uniform and concise explanatory framework for the identified semantics. Finally, we show that classical extension-based semantics do not belong to these classes.

Extension semantics are formal methods that evaluate acceptability status of arguments in argumentation graphs where arguments may attack each other. Understanding and explaining their outcomes is of utmost importance in applications like decision making. Consequently, a plethora of works has been devoted to answer questions of the form “why an argument A is (not) accepted under semantics δ”. Existing approaches explain the inner working and decision logic of δ. Their explanations refer thus to the semantics’s building blocks like attack, defence and admissibility. This paper complements the existing landscape with a post-hoc approach that discloses relationships between argumentation graphs and outputs of a semantics, regardless of its internals. The new approach offers several advantages, namely it explains more acceptability statuses than just the two (accepted, not accepted) considered in the literature, treats all statuses in a similar way, applies to any extension semantics that satisfies two key properties (monotonicity and maximality), and provides subsets of attackers, thus the size of its explanations is bounded by the number of attackers of an argument. We characterize the types of attacks that may target an argument. We show that some have no impact on their target’s status while others are influential. Then, we introduce three explanation functions that harness influential attacks. One of them provides sufficient reasons that guarantee an argument’s status while the others identify changes in the graph that guarantee a change of status to any value (counterfactuals) or to a specified one (contrastive). We show that sufficient reasons are minimal hitting sets of the counterfactuals and vice-versa.

Explaining decisions of black-box classifiers is both important and computationally challenging. In this paper, we scrutinize explainers that generate feature-based explanations from samples or datasets. We start by presenting a set of desirable properties that explainers would ideally satisfy, delve into their relationships, and highlight incompatibilities of some of them. We identify the entire family of explainers that satisfy two key properties which are compatible with all the others. Its instances provide sufficient reasons, called weak abductive explanations. We then unravel its various sub-families that satisfy subsets of compatible properties. Indeed, we fully characterize all the explainers that satisfy any subset of compatible properties. In particular, we introduce the first (broad family of) explainers that guarantee the existence of explanations and their global consistency. We discuss some of its instances including the irrefutable explainer and the surrogate explainer whose explanations can be found in polynomial time.

Abductive explanations (AXp’s) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead to an explosion in the number of redundant or superfluous AXp’s. We propose three new types of explanations that take into account constraints and that can be generated from the whole feature space or from a sample (such as a dataset). They are based on a key notion of coverage of an explanation, the set of instances it explains. We show that coverage is powerful enough to discard redundant and superfluous AXp’s. For each type, we analyse the complexity of finding an explanation and investigate its formal properties. The final result is a catalogue of different forms of AXp’s with different complexities and different formal guarantees.

Explaining predictions made by inductive classifiers has become crucial with the rise of complex models acting more and more as black-boxes. Abductive explanations are one of the most popular types of explanations that are provided for the purpose. They highlight feature-values that are sufficient for making predictions. In the literature, they are generated by exploring the whole feature space, which is unreasonable in practice. This paper solves the problem by introducing explanation functions that generate abductive explanations from a sample of instances. It shows that such functions should be defined with great care since they cannot satisfy two desirable properties at the same time, namely existence of explanations for every individual decision (success) and correctness of explanations (coherence). The paper provides a parameterized family of argumentation-based explanation functions, each of which satisfies one of the two properties. It studies their formal properties and their experimental behaviour on different datasets.

Compensation is a strategy that a semantics may follow when it faces dilemmas between quality and quantity of attackers. It allows several weak attacks to compensate one strong attack. It is based on compensation degree, which is a tuple that indicates (i) to what extent an attack is weak and (ii) the number of weak attacks needed to compensate a strong one. Existing principles on compensation do not specify the parameters, thus it is unclear whether semantics satisfying them compensate at only one degree or several degrees, and which ones. This paper proposes a parameterised family of gradual semantics, which unifies multiple semantics that share some principles but differ in their strategy regarding solving dilemmas. Indeed, we show that the two semantics taking the extreme values of the parameter favour respectively quantity and quality, while all the remaining ones compensate at some degree. We define three classes of compensation degrees and show that the novel family is able to compensate at all of them while none of the existing gradual semantics does.

Improving trust in decisions made by classification models is becoming crucial for the acceptance of automated systems, and an important way of doing that is by providing explanations for the behaviour of the models. Different explainers have been proposed in the recent literature for that purpose, however their formal properties are under-studied. This paper investigates theoretically explainers that provide reasons behind decisions independently of instances. Its contributions are fourfold. The first is to lay the foundations of such explainers by proposing key axioms, i.e., desirable properties they would satisfy. Two axioms are incompatible leading to two subsets. The second contribution consists of demonstrating that the first subset of axioms characterizes a family of explainers that return sufficient reasons while the second characterizes a family that provides necessary reasons. This sheds light on the axioms which distinguish the two types of reasons. As a third contribution, the paper introduces various explainers of both families, and fully characterizes some of them. Those explainers make use of the whole feature space. The fourth contribution is a family of explainers that generate explanations from finite datasets (subsets of the feature space). This family, seen as an abstraction of Anchors and LIME, violates some axioms including one which prevents incorrect explanations.

An argumentation framework is a pair made of a graph and a semantics. The nodes and the edges of the graph represent respectively arguments and relations (e.g., attacks, supports) between arguments while the semantics evaluates the strength of each argument of the graph. This paper investigates gradual semantics dealing with weighted graphs, a family of graphs where each argument has an initial weight and may be attacked by other arguments. It contains four contributions. The first consists of laying the foundations of gradual semantics by proposing key principles on which evaluation of argument strength may be based. Foundations are important not only for a better understanding of the evaluation process in general, but also for clarifying the basic assumptions underlying semantics, for comparing different (families of) semantics, and for identifying families of semantics that have not been explored yet. The second contribution consists of providing a formal analysis and a comprehensive comparison of the semantics that have been defined in the literature for evaluating arguments in weighted graphs. As a third contribution, the paper proposes three novel semantics and shows which principles they satisfy. The last contribution is the implementation and empirical evaluation of the three novel semantics. We show that the three semantics are very efficient in that they compute the strengths of arguments in less than 20 iterations and in a very short time. This holds even for very large graphs, meaning that the three semantics scale very well.

The paper discusses theoretical foundations that describe principles and processes involved in defining semantics that deal with similarity between arguments. Such semantics compute the strength of an argument on the basis of the strengths of its attackers, similarities between those attackers, and an initial weight ascribed to the argument. We define a semantics by three functions: an adjustment function that updates the strengths of attackers on the basis of their similarities, an aggregation function that computes the strength of the group of attackers, and an influence function that evaluates the impact of the group on the argument's initial weight. We propose intuitive constraints for the three functions and key rationality principles for semantics, and show how the former lead to the satisfaction of the latter. Then, we propose a broad family of semantics whose instances satisfy the principles. Finally, we analyse the existing adjustment functions and show that they violate some properties, then we propose novel ones and use them for generalizing h-Categorizer.

Two approaches for explaining black-box classification models have been studied: a global approach which aims at stressing when classes are predicted independently of instances, and a local approach which looks for justifying individual predictions. Besides, different types of local explanations have been studied in the recent literature, however their links to global explanations remain unclear.The present paper proposes a unified setting for global explanations and local ones. It is based on dual concepts that provide global explanations: arguments in favour of predictions and arguments against predictions. The former justify why a class is suggested by a black-box classifier and the latter state why a class is not. We investigate the properties of both types of arguments, and provide ways for generating arguments pro a class from arguments con the class and vice versa. Finally, we define various notions of local explanations from the literature by arguments pros/con, characterizing formally their relationships and differences, and also their relations with global explanations.

A large number of evaluation methods, called semantics, have been proposed in the literature for assessing strength of arguments. This paper investigates their equivalence. It argues that for being equivalent, two semantics should have compatible evaluations of both individual arguments and pairs of arguments. The first requirement ensures that the two semantics judge an argument in the same way, while the second states that they provide the same ranking of arguments. We show that the two requirements are completely independent. The paper introduces three novel relations between semantics based on their rankings of arguments: weak equivalence, strong equivalence and refinement. They state respectively that two semantics do not disagree on their strict rankings; the rankings of the semantics coincide; one semantics agrees with the strict comparisons of the second and it may break some of its ties. We investigate the properties of the three relations and their links with existing principles of semantics, and study the nature of relations between most of the existing semantics. The results show that the main extensions semantics are pairwise weakly equivalent. The gradual semantics we considered are pairwise incompatible, however some pairs are strongly equivalent in case of flat graphs including Max-based (Mbs) and Euler-based (Ebs), for which we provide full characterizations in terms respectively of Fibonacci numbers and the numbers of an exponential series. Furthermore, we show that both semantics (Mbs, EMbs) refine the grounded semantics, and are weakly equivalent with the other extension semantics. We show also that in case of flat graphs, the two gradual semantics Trust-based and Iterative Schema characterize the grounded semantics, making thus bridges between gradual semantics and extension semantics. Finally, the other gradual semantics are incompatible with extension semantics.

Analogical arguments are a special type of inductive arguments, whereby perceived similarities are used as a basis to infersome further similarity that has yet to be observed. Although they arenot deductively valid, they may yield conclusions that are very prob-ably true, and may be more cogent than others in persuasive contexts.This paper tackles the question of their evaluation. It starts by dis-cussing their features, how they can be attacked/supported, and keyconsiderations for their evaluation. It argues in particular for the needof semantics that are able to take into account possible interactions(synergies, redundancies) between attackers (respectively support-ers) of any analogical argument. It presents principles that serve asguidelines for choosing candidate semantics. Then, it shows that ex-isting (extension, gradual, ranking) semantics are not suitable as theymay lead to inaccurate assessments. Finally, it redefines three exist-ing semantics using the well-known Choquet Integral for aggregatingattackers/supporter, and discusses their properties.

Argumentation aims at increasing acceptability of claims by supporting them with arguments. Roughly speaking, an argument is a set of premises intended to establish a definite claim. Its strength depends on the plausibility of the premises, the nature of the link between the premises and claim, and the prior acceptability of the claim. It may generally be weakened by other arguments that undermine one or more of its three components. Evaluation of arguments is a crucial task, and a sizable amount of methods, called semantics, has been proposed in the literature. This paper discusses two classifications of the existing semantics: the first one is based on the type of semantics' outcomes (sets of arguments, weighting, and preorder), the second is based on the goals pursued by the semantics (acceptability, strength, coalitions).

Several argument-based logics have been defined for handling inconsistency in propositional knowledge bases. We show that they may miss intuitive consequences, and discuss two sources of this drawback: the definition of logical argument i) may prevent formulas from being justified, and ii) may allow irrelevant information in argument's support. We circumvent these two issues by considering a general definition of argument and compiling each argument. A compilation amounts to forgetting in an argument's support any irrelevant variable. This operation returns zero, one or several concise arguments, which we then use in an instance of Dung's abstract framework. We show that the resulting logic satisfies existing rationality postulates, namely consistency and closure under deduction. Furthermore, it is more productive than the existing argument-based and coherence-based logics.

The paper studies how arguments can be evaluated in weighted bipolar argumentation graphs (i.e., graphs whose arguments have basic weights and may be supported and attacked). It introduces principles that an evaluation method (or semantics) would satisfy, analyzes existing semantics with respect to them, and finally proposes a new semantics for the class of non-maximal acyclic graphs.

The paper studies semantics that evaluate arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.

In an argumentation setting, a semantics evaluates the overall acceptability of arguments. Consequently, it reveals the global loss incurred by each argument due to attacks. However, it does not say anything on the contribution of each attack to that loss. This paper introduces the novel concept of contribution measure which evaluates those contributions. It starts by defining a set of axioms that a reasonable measure would satisfy, then shows that the Shapley value is the unique measure that satisfies them. Finally, it investigates the properties of the latter under existing semantics.

An argument is seen as reason in favour of a claim. It is made of three parts: a set of premises representing the reason, a conclusion representing the supported claim, and a connection showing how the premises lead to the conclusion. Arguments are frequently exchanged by human agents in natural language (spoken or written) in discussion, debate, negotiation, persuasion, etc. They may be very different in that their three components may have various forms. In this paper, we propose a language for representing such arguments. We show that it is general enough to capture the various forms of arguments encountered in natural language, and that it is possible to represent attack and support relations between arguments as formulas of the same language.

Several systems were developed for supporting public persuasion dialogs where two agents with conflicting opinions try to convince an audience. For computing the outcomes of dialogs, these systems use (abstract or structured) argumentation systems that were initially developed for nonmonotonic reasoning. Despite the increasing number of such systems, there are almost no work on high level properties they should satisfy. This paper is a first attempt for defining postulates that guide the well-definition of dialog systems and that allow their comparison. We propose six basic postulates (including e.g. the finiteness of generated dialogs). We then show that this set of postulates is incompatible with those proposed for argumentation systems devoted for nonmonotonic reasoning. This incompatibility confirms the differences between persuading and reasoning. It also suggests that reasoning systems are not suitable for computing the outcomes of dialogs.

This paper proposes the notion of experience to help situate agents in their environment, providing a link on how the continually evolving environment impacts the evolution of an agent's BDI model and vice versa. Then, using the notion of shared experience as a primitive construct, we develop a novel formal model of shared intention which we believe more adequately describes social behaviour than traditional BDI logics that focus on individual agents. Whilst many philosophers have argued that collective intentionality cannot always be equated to the collection of the individual agents' intentions, there has been no AI model that addresses this issue. We believe this is the first attempt to develop an explicit notion of shared experience from an AI perspective.

This article proposes an abstract framework for argumentation-based negotiation in which the impact of exchanging arguments on agents' theories is formally described, the different types of solutions in negotiation are investigated, and the added value of argumentation in negotiation dialogues is analysed. We study when, how and to which extent an exchange of arguments can be beneficial in negotiation. The results show that argumentation can improve the quality of an outcome but never decrease it.

Decision making is usually based on the comparative evaluation of different options by means of a decision criterion. Recently, the qualitative pessimistic criterion was articulated in terms of a four-step argumentation process: (i) to build arguments in favour/against each option, (ii) to compare and evaluate those arguments, (iii) to assign a status for each option, and (iv) to rank order the options on the basis of their status. Thus, the argumentative counter-part of the pessimistic criterion provides not only the ‘best’ option to the user but also the reasons justifying this recommendation. The aim of this article is to study the dynamics of this argumentation model. The idea is to study how the ordering on options changes in light of a new argument. For this purpose, we study under which conditions an option may change its status, and under which conditions the new argument has no impact on the status of options, and consequently, on the ordering. This amounts to study how the acceptability of arguments evolves when the decision system is extended by new arguments. In the article, we focus on two acceptability semantics the skeptical grounded semantics and the credulous preferred semantics.

We are interested by argumentation systems which build their arguments from a propositional knowledge base (KB), and evaluate them using Dung's acceptability semantics. We start by showing that such systems are infinite, i.e. from a finite KB, an infinite set of arguments and an infinite set of attacks among them are generated. While the construction of arguments under propositional logic is costly even in the finite case, the fact that those systems are infinite makes them completely useless. Then, we provide a procedure which, given an argumentation system, computes its finite sub-system, called core. A core considers a finite subset of arguments and a finite subset of attacks, and returns all the results of the original system. This means that a finite subset of arguments is sufficient to draw all the expected conclusions from a KB.

An argumentation system consists mainly of a set of interacting arguments and a semantics for evaluating them. In this paper, we study when two argumentation systems are equivalent. We focus on argumentation systems defined around a Tarskian logic. We propose different equivalence criteria, study their links and finally show under which conditions two systems are equivalent wrt each of the proposed criteria.

Different proposals have been made in the literature for refining Dung's argumentation framework by preferences between arguments. The idea is to ignore an attack if the attacked argument is stronger than its attacker. Acceptability semantics are then applied on the remaining attacks. Unfortunately, these proposals may return some unintended results, in particular, when the attack relation is asymmetric.

Many works have identified the potential benefits of using argumentation to address a large variety of multiagent problems. In this paper we take this idea one step further and develop the concept of a fully integrated argumentation-based agent architecture that allows us to develop agents that are coherently designed on an underlying argumentation based foundation. Under this architecture, an agent is composed of a collection of modules each of which is equipped with a local argumentation theory. Similarly, the intra-agent control of the agent is governed by local argumentation theories that are sensitive to the current situation of the agent through dynamically enabled feasibility arguments.

The aim of this paper is to study how preferences, which are used to model intrinsic strengths of arguments, can be used in argumentation. We show that they play two roles: i) to repair the attack relation between arguments, and ii) to refine the evaluation of arguments. Then, we point out that the existing approaches for preference-based argumentation model only the first role. They may also return non conflict-free extensions. We propose a general framework that overcomes those limitations.

During the last years, argumentation has been gaining increasing interest in modeling different reasoning tasks of an agent. Many recent works have acknowledged the importance of incorporating preferences or priorities in argumentation. However, relatively little is known about the theoretical and computational implications of preferences in argumentation.

In this article, we propose a survey of the use of bipolarity in argumentation frameworks. On the one hand, the notion of bipolarity relies on the presence of two kinds of entities that have a diametrically opposed nature and that represent repellent forces (a positive entity and a negative entity). The notion exists in various domains (for example with the representation of preferences in artificial intelligence, or in cognitive psychology). On the other hand, argumentation process is a promising approach for reasoning, based on the construction and the comparison of arguments. It follows five steps: building the arguments, defining the interactions between these arguments, valuating the arguments, selecting the most acceptable arguments and, finally, drawing a conclusion. Using the nomenclature proposed by Dubois and Prade, this article shows on various applications, and with some formal definitions, that bipolarity appears in argumentation (in some cases if not always) and can be used in each step of this process under different forms. © 2008 Wiley Periodicals, Inc.

In complex multiagent systems, the agents may be heterogeneous and possibly designed by different programmers. Thus, the importance of defining a standard framework for agent communication languages (ACL) with a clear semantics has been widely recognized. The semantics should be verifiable, clear, and practical. Most classical proposals (for instance, mentalistic semantics) fail to meet these objectives. This paper proposes a logic-based semantics, which is social in nature. The basic idea is to associate with each speech act a clear meaning in terms of a commitment induced by that speech act, and a penalty to be paid in case that commitment is violated. A violation criterion based on the existence of arguments is then defined per speech act. We show that the proposed semantics satisfies some key properties that ensure that the approach is well founded. The logical setting makes the semantics verifiable. Moreover, it is shown that the new semantics is practical because it captures the dynamic of dialogues and shows clearly how isolated speech acts can be connected for building dialogues. © 2008 Wiley Periodicals, Inc.

The paper presents a preliminary work that investigates the interest and the questions raised by the introduction of argumentation capabilities in a flexible querying system to a database. Indeed, emphasizing the positive and the negative aspects of retrieved items, or explaining why no answers are found may be of a value for the user

Current logic-based handling of arguments has mainly focused on explanation or justification-oriented purposes in presence of inconsistency. So only one type of argument has been considered, and several argumentation frameworks have then been proposed for generating and evaluating such arguments. However, recent works on argumentation-based negotiation have emphasized different other types of arguments such as threats, rewards, and appeals. The purpose of this article is to provide a logical setting that encompasses the classical argumentation-based framework and handles the new types of arguments. More precisely, we give the logical definitions of these arguments and their weighting systems. These definitions take into account that negotiation dialogues involve not only agents' beliefs (of various strengths), but also their goals (having maybe different priorities), as well as the beliefs on the goals of other agents. In other words, from the different beliefs and goals bases maintained by agents, all the possible threats, rewards, explanations, and appeals that are associated with them can be generated. It may also happen that an intended threat, or reward, is not perceived as such by the addressee and thus misses its target because the addresser misrepresents the addressee's goals. The proposed approach accounts for that phenomenon. Finally, we show how to evaluate conflicting arguments of different types. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 1195–1218, 2005.

Argumentation-based decision provides a way for explaining choices which are already made, and for evaluating potential choices in terms of arguments. Each potential choice has pros and cons of various strengths, which are computed in the framework of possibilistic logic. Depending on the pessimistic, or optimistic nature of the decision-maker's attitude, arguments in favour of or against a possible choice have slightly different structures. When the available, maybe uncertain, knowledge is consistent, as well as the set of prioritized goals (which have to be fulfilled as far as possible), the method for evaluating decisions on the basis of arguments agrees with the possibility theory-based approach to decision-making under uncertainty. The proposed framework can be generalized in case of partially inconsistent knowledge or goals.

This paper studies argumentation-based dialogues between agents. It defines a set of locutions by which agents can trade arguments, a set of agent attitudes which relate what arguments an agent can build and what locutions it can make, and a set of protocols by which dialogues can be carried out. The paper then considers some properties of dialogues under the protocols, in particular termination, dialogue outcomes, and complexity, and shows how these relate to the agent attitudes.

Argument-based reasoning is a promising approach to handle inconsistent belief bases. The basic idea is to justify each plausible conclusion by acceptable arguments. The purpose of the paper is to enforce the concept of acceptability by the integration of preference orderings. Pursuing previous work on preference-based argumentation, the authors focus on the definition of preference relations for comparing conflicting arguments. They present a comparative study of several proposals. They then propose techniques for computing and comparing arguments, taking advantage of an assumption-based truth maintenance system (ATMS).