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-grounded and w-preferred extensions starting from a w-admissible extension.
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).
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.
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…
Weighted Assumption Based Argumentation to reason about ethical principles and actions
Dept. of Human Studies, University of Salento, Lecce, Italy（人类研究系，萨莱诺大学）；Dept. of Informatics, University of Bari ``Aldo Moro'', Via E. Orabona 4, Bari, 70125, Italy（信息系，巴里“阿尔多·莫罗”大学）；Centro Interdipartimentale di Logica e Applicazioni (CILA), University of Bari ``Aldo Moro'', Via E. Orabona 4, Bari, 70125, Italy（逻辑与应用跨院系中心（CILA），巴里“阿尔多·莫罗”大学）
Institute of Cognitive Science, University of Osnabrück（奥斯纳布吕克大学认知科学研究所）
Weighted bipolar argumentation frameworks allow modeling decision problems and online discussions by defining arguments and their relationships. The strength of arguments can be computed based on an initial weight and the strength of attacking and supporting arguments. While previous approaches assumed an acyclic argumentation graph and successively set arguments' strength based on the strength of their parents, recently continuous dynamical systems have been proposed as an alternative. Continuous models update arguments' strength simultaneously and continuously. While there are currently no a…
ConArg is a Constraint Programming-based tool that can be used to model and solve different problems related to Abstract Argumentation Frameworks (AFs). To implement this tool we have used JaCoP, a Java library that provides the user with a Finite Domain Constraint Programming paradigm. ConArg is able to randomly generate networks with small-world properties in order to find conflict-free, admissible, complete, stable grounded, preferred, semi-stable, stage and ideal extensions on such interaction graphs. We present the main features of ConArg and we report the performance in time, showing als…
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…
After Dung's founding work in Abstract Argumentation Frameworks there has been a growing interest in extending the Dung's semantics in order to describe more complex or real life situations. Several of these approaches take the direction of weighted or probabilistic extensions. One of the most prominent probabilistic approaches is that of constellation Probabilistic Abstract Argumentation Frameworks from Li~et~al. In this paper, we present a normal form for constellation probabilistic abstract argumentation frameworks. Furthermore, we present a transformation from general constellation probabi…
The notion of stability in a structured argumentation setup characterizes situations where the acceptance status associated with a given literal will not be impacted by any future evolution of this setup. In this paper, we abstract away from the logical structure of arguments, and we transpose this notion of stability to the context of Dungean argumentation frameworks. In particular, we show how this problem can be translated into reasoning with Argument-Incomplete AFs. Then we provide preliminary complexity results for stability under four prominent semantics, in the case of both credulous an…
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…
Among the most general structures extending the framework by Dung are the abstract dialectical frameworks (ADFs). They come equipped with various types of semantics, with the most prominent - the labeling-based one - analyzed in the context of computational complexity, signatures, instantiations and software support. This makes the abstract dialectical frameworks valuable tools for argumentation. However, there are fewer results available concerning the relation between the ADFs and other argumentation frameworks. In this paper we would like to address this issue by introducing a number of tra…
In this paper, we present a preliminary work on an approach to fill the gap between logic-based argumentation and the numerous approaches to tackle the dynamics of abstract argumentation frameworks. Our idea is that, even when arguments and attacks are defined by means of a logical belief base, there may be some uncertainty about how accurate is the content of an argument, and so the presence (or absence) of attacks concerning it. We use enthymemes to illustrate this notion of uncertainty of arguments and attacks. Indeed, as argued in the literature, real arguments are often enthymemes instead…
Eliciting Rational Initial Weights in Gradual Argumentation
University of Aberdeen（阿伯丁大学）；Universite Claude Bernard Lyon 1（里昂第一大学）；CNRS（法国国家科学研究中心）；Ecole Centrale de Lyon（里昂中央理工学院）；INSA Lyon（里昂国立应用科学学院）；Université Lumière Lyon 2（里昂第二大学）；LIRIS（里昂信息与图像系统实验室）；UMR5205（联合研究单位5205）
Department of Computing, Imperial College London, UK（帝国理工学院计算系）；School of Computer Science and Informatics, Cardiff University, UK（卡迪夫大学计算机科学与信息学学院）；Department of Computing Science, Umeå University, Sweden（乌梅大学计算科学系）
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…
Otto-von-Guericke Universität Magdeburg（马格德堡奥托·冯·格里克大学）
This paper discusses the semantics of weighted argumentation graphs that are biplor, i.e. contain both attacks and support graphs. The work builds on previous work by Amgoud, Ben-Naim et. al., which presents and compares several semantics for argumentation graphs that contain only supports or only attacks relationships, respectively.
Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit …
Otto-von-Guericke Universität Magdeburg（马格德堡奥托·冯·格里克大学）
This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. It builds on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of acceptability semantics that have been introduced in these works, and introduce the notion of a modular acceptability semantics. A semantics is modular if it cleanly separates aggregation of attacking and supporting arguments (for a given argument $a$) from the computation of their influence on $a$'s initial weight. We show that the various semantics for bipolar …
