After a few decades of development, computational argumentation has become one of the active realms in AI. This paper considers extension-based concrete and abstract semantics of argumentation. For concrete ones, based on Grossi and Modgil's recent work, this paper considers some issues on graded extension-based semantics of abstract argumentation framework (AAF, for short). First, an alternative fundamental lemma is given, which generalizes the corresponding result due to Grossi and Modgil by relaxing the constraint on parameters. This lemma provides a new sufficient condition for preserving conflict-freeness and brings a Galois adjunction between admissible sets and complete extensions, which is of vital importance in constructing some special extensions in terms of iterations of the defense function. Applying such a lemma, some flaws in Grossi and Modgil's work are corrected, and the structural property and universal definability of various extension-based semantics are given. Second, an operator so-called reduced meet modulo an ultrafilter is presented, which is a simple but powerful tool in exploring infinite AAFs. The neutrality function and the defense function, which play central roles in Dung's abstract argumentation theory, are shown to be distributive over reduced meets modulo any ultrafilter. A variety of fundamental semantics of AAFs, including conflict-free, admissible, complete and stable semantics, etc, are shown to be closed under this operator. Based on this fact, a number of applications of such operators are considered. In particular, we provide a simple and uniform method to prove the universal definability of a family of range related semantics. Since all graded concrete semantics considered in this paper are generalizations of corresponding non-graded ones, all results about them obtained in this paper also hold in the traditional situation.
Institute for Web Science and Technologies（网络科学与技术研究所）；University of Koblenz-Landau（科布伦茨-兰道大学）
We propose a novel ranking-based semantics for Dung-style argumentation frameworks with the help of conditional logics. Using an intuitive translation for an argumentation framework to generate conditionals, we can apply nonmonotonic inference systems to generate a ranking on possible worlds. With this ranking we construct a ranking for our arguments. With a small extension to this ranking-based semantics we already satisfy some desirable properties for a ranking over arguments.
We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default reasoning. In this context, we consider the path from structured to logical to shallow semantic instantiations. The resulting well-justified JZ-extension semantics diverges from more traditional approaches.
Argumentation is one of the most popular approaches of defining a~non-monotonic formalism and several argumentation based semantics were proposed for defeasible logic programs. Recently, a new approach based on notions of conflict resolutions was proposed, however with declarative semantics only. This paper gives a more procedural counterpart by developing skeptical and credulous argument games for complete semantics and soundness and completeness theorems for both games are provided. After that, distribution of defeasible logic program into several contexts is investigated and both argument g…
Dung's abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations. Hereby, the knowledge is represented by so-called argumentation frameworks (AFs) and the reasoning is done via semantics extracting acceptable sets. All reasonable semantics are based on the notion of conflict-freeness which means that arguments are only jointly acceptable when they are not linked within the AF. In this paper, we study the question which information on top of conflict-free sets is needed to compute extensions of a semantics at hand. We in…
TU Dresden（德累斯顿工业大学）；Université Libre de Bruxelles（布鲁塞尔自由大学）
In abstract argumentation, multiple argumentation semantics have been proposed that allow to select sets of jointly acceptable arguments from a given argumentation framework, i.e. based only on the attack relation between arguments. The existence of multiple argumentation semantics raises the question which of these semantics predicts best how humans evaluate arguments. Previous empirical cognitive studies that have tested how humans evaluate sets of arguments depending on the attack relation between them have been limited to a small set of very simple argumentation frameworks, so that some se…
A fuzzy multipreference semantics has been recently proposed for weighted conditional knowledge bases, and used to develop a logical semantics for Multilayer Perceptrons, by regarding a deep neural network (after training) as a weighted conditional knowledge base. This semantics, in its different variants, suggests some gradual argumentation semantics, which are related to the family of the gradual semantics studied by Amgoud and Doder. The relationships between weighted conditional knowledge bases and MLPs extend to the proposed gradual semantics to capture the stationary states of MPs, in ag…
Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms of different semantics proposed for abstract argumentation frameworks, a nonmonotonic yet simple formalism which received increasing interest within the last decade. Although the properties of these different semantics are nowadays well understood, there are no explicit results about intertranslatability. We provide such translations wrt. different properti…
Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability, i.e. how "much" it is attacked by other arguments. Many different gradual semantics have been proposed in the literature, each following different principles and producing different argument rankings. A sub-class of such semantics, the so-called weighted semantics, takes, in addition to the graph structure, an initial set of weights over the arguments as input, with these weights affecting the resultant argument ranking. In this work, we consider the inverse problem over such weighted…
Nanjing University（南京大学）；State Key Laboratory for Novel Software Technology at Nanjing University（南京大学计算机软件新技术国家重点实验室）
Abstract argumentation frameworks are formal systems that facilitate obtaining conclusions from non-monotonic knowledge systems. Within such a system, an argumentation semantics is defined as a set of arguments with some desired qualities, for example, that the elements are not in conflict with each other. Splitting an argumentation framework can efficiently speed up the computation of argumentation semantics. With respect to stable semantics, two methods have been proposed to split an argumentation framework either in a unidirectional or bidirectional fashion. The advantage of bidirectional s…
An extension of an abstract argumentation framework, called collective argumentation, is introduced in which the attack relation is defined directly among sets of arguments. The extension turns out to be suitable, in particular, for representing semantics of disjunctive logic programs. Two special kinds of collective argumentation are considered in which the opponents can share their arguments.
The matrices and their sub-blocks are introduced into the study of determining various extensions in the sense of Dung's theory of argumentation frameworks. It is showed that each argumentation framework has its matrix representations, and the core semantics defined by Dung can be characterized by specific sub-blocks of the matrix. Furthermore, the elementary permutations of a matrix are employed by which an efficient matrix approach for finding out all extensions under a given semantics is obtained. Different from several established approaches, such as the graph labelling algorithm, Constrai…
In the present paper, the existence and multiplicity problems of extensions are addressed. The focus is on extension of the stable type. The main result of the paper is an elegant characterization of the existence and multiplicity of extensions in terms of the notion of dialectical justification, a close cousin of the notion of admissibility. The characterization is given in the context of the particular logic for dialectical argumentation DEFLOG. The results are of direct relevance for several well-established models of defeasible reasoning (like default logic, logic programming and argumenta…
Università degli Studi di Perugia（佩鲁贾大学）；Gran Sasso Science Institute（格兰萨索科学研究所）
We study invariant local expansion operators for conflict-free and admissible sets in Abstract Argumentation Frameworks (AFs). Such operators are directly applied on AFs, and are invariant with respect to a chosen "semantics" (that is w.r.t. each of the conflict free/admissible set of arguments). Accordingly, we derive a definition of robustness for AFs in terms of the number of times such operators can be applied without producing any change in the chosen semantics.
Sun Yat-sen University（中山大学）；University of Amsterdam（阿姆斯特丹大学）
An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the second. When modelling a group of agents engaged in a debate, we may wish to aggregate their individual argumentation frameworks to obtain a single such framework that reflects the consensus of the group. Even when agents disagree on many details, there may well be high-level agreement on important semantic properties, such as the acceptability of a given argumen…
This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to other argumentation semantics, including those of Dung, and Prakken and Sartor. We present a general dialectical proof theory for these argumentation semantics.
We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is given by the success probability of a query, which corresponds to the probability that the query succeeds in a randomly sampled program. It is well-defined when each random sample uniquely determines the truth values of all logical atoms. Argumentation problems, however…
Dung's abstract argumentation framework consists of a set of interacting arguments and a series of semantics for evaluating them. Those semantics partition the powerset of the set of arguments into two classes: extensions and non-extensions. In order to reason with a specific semantics, one needs to take a credulous or skeptical approach, i.e. an argument is eventually accepted, if it is accepted in one or all extensions, respectively. In our previous work \cite{ref-pu2015counting}, we have proposed a novel semantics, called \emph{counting semantics}, which allows for a more fine-grained asses…
Dung's abstract framework for argumentation enables a study of the interactions between arguments based solely on an ``attack'' binary relation on the set of arguments. Various ways to solve conflicts between contradictory pieces of information have been proposed in the context of argumentation, nonmonotonic reasoning or logic programming, and can be captured by appropriate semantics within Dung's framework. A common feature of these semantics is that one can always maximize in some sense the set of acceptable arguments. We propose in this paper to extend Dung's framework in order to allow for…
University of Osnabrück, Institute of Cognitive Science（奥斯纳布吕克大学认知科学研究所）
Weighted bipolar argumentation frameworks offer a tool for decision support and social media analysis. Arguments are evaluated by an iterative procedure that takes initial weights and attack and support relations into account. Until recently, convergence of these iterative procedures was not very well understood in cyclic graphs. Mossakowski and Neuhaus recently introduced a unification of different approaches and proved first convergence and divergence results. We build up on this work, simplify and generalize convergence results and complement them with runtime guarantees. As it turns out, t…
University of Groningen（格罗宁根大学）；King's College London（伦敦国王学院）
The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they…
Università degli Studi di Perugia（佩鲁贾大学）；Gran Sasso Science Institute（格兰萨索科学研究所）
The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary matrix, and we characterize the basic extensions (such as w-admissible, w- stable, w-complete) by analysing sub-blocks of this matrix. Also, we show how to reduce the matrix into another one of smaller size, that is equivalent to the original one for the determination of extensions. Furthermore, we provide two algorithms that allow to build incrementally w-grounde…
Cycles of attacking arguments pose non-trivial issues in Dung style argumentation theory, apparent behavioural difference between odd and even length cycles being a notable one. While a few methods were proposed for treating them, to - in particular - enable selection of acceptable arguments in an odd-length cycle when Dung semantics could select none, so far the issues have been observed from a purely argument-graph-theoretic perspective. Per contra, we consider argument graphs together with a certain lattice like semantic structure over arguments e.g. ontology. As we show, the semantic-argum…
This paper introduces the notion of value-based argumentation frameworks, an extension of the standard argumentation frameworks proposed by Dung, which are able toshow how rational decision is possible in cases where arguments derive their force from the social values their acceptance would promote.
This research advocates the idea of combining argumentation theory with the social web technology, aiming to enact large scale or mass argumentation. The proposed framework allows mass-collaborative editing of structured arguments in the style of semantic wikipedia. The long term goal is to apply the abstract machinery of argumentation theory to more practical applications based on human generated arguments, such as deliberative democracy, business negotiation, or self-care. The ARGNET system was developed based on ther Semantic MediaWiki framework and on the Argument Interchange Format (AIF) …
Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise) and rebuts (attack to an argument's conclusion). In this paper, we formulate a variety of notions of attack for extended logic programs from combinations of undercuts and rebuts and define a general hierarchy of argumentation semantics parameterised by the notions of attack chosen by proponent and opponent. We prove the equivalence and subset relationships …
International Center for Computational Logic, TU Dresden（德累斯顿工业大学国际计算逻辑中心）；University of Luxembourg（卢森堡大学）
In abstract argumentation theory, many argumentation semantics have been proposed for evaluating argumentation frameworks. This paper is based on the following research question: Which semantics corresponds well to what humans consider a rational judgment on the acceptability of arguments? There are two systematic ways to approach this research question: A normative perspective is provided by the principle-based approach, in which semantics are evaluated based on their satisfaction of various normatively desirable principles. A descriptive perspective is provided by the empirical approach, in …
Universidad de las Américas - Puebla（普埃布拉美洲大学）；Umeå University（于默奥大学）
Characterizations of semi-stable and stage extensions in terms of 2-valued logical models are presented. To this end, the so-called GL-supported and GL-stage models are defined. These two classes of logical models are logic programming counterparts of the notion of range which is an established concept in argumentation semantics.
Argumentation Frameworks (AFs) are a key formalism in AI research. Their semantics have been investigated in terms of principles, which define characteristic properties in order to deliver guidance for analysing established and developing new semantics. Because of the simple structure of AFs, many desired properties hold almost trivially, at the same time hiding interesting concepts behind syntactic notions. We extend the principle-based approach to Argumentation Frameworks with Collective Attacks (SETAFs) and provide a comprehensive overview of common principles for their semantics. Our analy…
Institute of Information Systems（信息系统研究所）；Vienna University of Technology（维也纳工业大学）
Dung's famous abstract argumentation frameworks represent the core formalism for many problems and applications in the field of argumentation which significantly evolved within the last decade. Recent work in the field has thus focused on implementations for these frameworks, whereby one of the main approaches is to use Answer-Set Programming (ASP). While some of the argumentation semantics can be nicely expressed within the ASP language, others required rather cumbersome encoding techniques. Recent advances in ASP systems, in particular, the metasp optimization frontend for the ASP-package gr…
Federal University of Technology - Paraná (UTFPR)（巴拉那联邦理工大学）；Umeå University（于默奥大学）
Some abstract argumentation approaches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a abstract argumentation framework (AAF) under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real life situations the exact probabilities values are unknown and sometimes there is a need for aggregating the probability values of different sources. In this paper, we tackle the problem of calculating the degree of u…
Recently, Strength-based Argumentation Frameworks (StrAFs) have been proposed to model situations where some quantitative strength is associated with arguments. In this setting, the notion of accrual corresponds to sets of arguments that collectively attack an argument. Some semantics have already been defined, which are sensitive to the existence of accruals that collectively defeat their target, while their individual elements cannot. However, until now, only the surface of this framework and semantics have been studied. Indeed, the existing literature focuses on the adaptation of the stable…
In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level rather than on the argument-level, while under certain natural restrictions (arguments with the same claims have the same outgoing attacks) these properties are conserved. We now investigate these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments. As we shall see, th…
Intelligent Systems Department（智能系统部）；Computer Science Institute（计算机科学研究所）；Leipzig University（莱比锡大学）
MatrixX is a solver for Abstract Argumentation Frameworks. Offensive and defensive properties of an Argumentation Framework are notated in a matrix style. Rows and columns of this matrix are systematically reduced by the solver. This procedure is implemented through the use of hash maps in order to accelerate calculation time. MatrixX works for stable and complete semantics and was designed for the ICCMA 2021 competition.
University of Koblenz（科布伦茨大学）；TU Dortmund（多特蒙德工业大学）
We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using ranks instead of the usual labels in, out, and undecided. We relate the framework of stratified labelings to conditional logic and, in particular, to the System Z ranking functions.
Leipzig University（莱比锡大学）；University of Vienna（维也纳大学）；Vienna University of Technology（维也纳工业大学）
Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different se…
TU Dresden（德累斯顿工业大学）；TU Wien（维也纳工业大学）；University of Potsdam（波茨坦大学）
In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extension…
Facets in Argumentation: A Formal Approach to Argument Significance
Department of Computer and Information Science, Linköping University, Sweden（林雪平大学计算机与信息科学系）；Leibniz Universität Hannover, Germany（汉诺威莱布尼茨大学）；Univ. Artois, CNRS, France（阿诺伊大学）；CSAIL, Massachusetts Institute of Technology, USA（麻省理工学院计算机科学与人工智能实验室）；DICE group, Paderborn University, Germany（波德生大学DICE小组）
Department of Computer and Information Science (IDA), Linköping University, Sweden（链接öping大学计算机与信息科学系（IDA））；University of Potsdam, Germany & University of Artois, CNRS, UMR8188 (CRIL), France（波茨坦大学 & 阿尔托伊斯大学、法国CNRS UMR8188（CRIL））；Data Science Group, Heinz Nixdorf Institute, Paderborn University, Germany（帕德博恩大学数据科学小组、海因茨·尼克斯多夫研究所）
University of Aberdeen（阿伯丁大学）；Univ. Artois（阿图瓦大学）；CRIL（朗斯计算机科学研究所）
Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived. While some semantics operate over standard argumentation frameworks, many utilise a weighted framework, where a numeric initial weight is associated with each argument. Recent work has examined the inverse problem within gradual semantics. Rather than determining a preference ordering given an argumentation framework and a semantics, the inverse problem takes a…
Assumption-Based Argumentation (ABA) is an argumentation framework that has been proposed in the late 20th century. Since then, there was still no solver implemented in a programming language which is easy to setup and no solver have been interfaced to the web, which impedes the interests of the public. This project aims to implement an ABA solver in a modern programming language that performs reasonably well and interface it to the web for easier access by the public. This project has demonstrated the novelty of development of an ABA solver, that computes conflict-free, stable, admissible, gr…
Abstract dialectical frameworks (ADFs) are a powerful generalisation of Dung's abstract argumentation frameworks. In this paper we present an answer set programming based software system, called DIAMOND (DIAlectical MOdels eNcoDing). It translates ADFs into answer set programs whose stable models correspond to models of the ADF with respect to several semantics (i.e. admissible, complete, stable, grounded).
The recent Control Argumentation Framework (CAF) is a generalization of Dung's Argumentation Framework which handles argumentation dynamics under uncertainty; especially it can be used to model the behavior of an agent which can anticipate future changes in the environment. Here we provide new insights on this model by defining the notion of possible controllability of a CAF. We study the complexity of this new form of reasoning for the four classical semantics, and we provide a logical encoding for reasoning with this framework.
LAMSADE, CNRS, Paris, France（法国国家科学研究中心LAMSADE实验室）；Department of Theoretical Computer Science, Masaryk University, Brno, Czech Republic（马萨里克大学理论计算机科学系）；Institute of Information Systems, Vienna University of Technology, Vienna, Austria（维也纳工业大学信息系统研究所）
We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given. - The Repair problem asks whether a given set of arguments can be modified into an extension by at most k elementary changes (i.e., the extension is of distance k from the given set). - The Adjust problem asks whether a given extension can be modified by at most k elementary changes into an extension tha…
