Argumentation is a formalism allowing to reason with contradictory information by modeling arguments and their interactions. There are now an increasing number of gradual semantics and impact measures that have emerged to facilitate the interpretation of their outcomes. An impact measure assesses, for each argument, the impact of other arguments on its score. In this paper, we refine an existing impact measure from Delobelle and Villata and introduce a new impact measure rooted in Shapley values. We introduce several principles to evaluate those two impact measures w.r.t. some well-known gradual semantics. This comprehensive analysis provides deeper insights into their functionality and desirability.

Weighted gradual semantics provide an acceptability degree to each argument representing the strength of the argument, computed based on factors including background evidence for the argument, and taking into account interactions between this argument and others. We introduce four important problems linking gradual semantics and acceptability degrees. First, we reexamine the inverse problem, seeking to identify the argument weights of the argumentation framework which lead to a specific final acceptability degree. Second, we ask whether the function mapping between argument weights and acceptability degrees is injective or a homeomorphism onto its image. Third, we ask whether argument weights can be found when preferences, rather than acceptability degrees for arguments are considered. Fourth, we consider the topology of the space of valid acceptability degrees, asking whether gaps exist in this space. While different gradual semantics have been proposed in the literature, in this paper, we identify a large family of weighted gradual semantics, called abstract weighted based gradual semantics. These generalise many of the existing semantics while maintaining desirable properties such as convergence to a unique fixed point. We also show that a sub-family of the weighted gradual semantics, called abstract weighted (Lp,lambda,mu,A)-based gradual semantics and which include well-known semantics, solve all four of the aforementioned problems.

Evaluating argument strength in quantitative argumentation systems has received increasing attention in the field of abstract argumentation. The concept of acceptability degree is widely adopted in gradual semantics, however, it may not be sufficient in many practical applications. In this paper, we provide a novel quantitative method called fuzzy labeling for fuzzy argumentation systems, in which a triple of acceptability, rejectability, and undecidability degrees is used to evaluate argument strength. Such a setting sheds new light on defining argument strength and provides a deeper understanding of the status of arguments. More specifically, we investigate the postulates of fuzzy labeling, which present the rationality requirements for semantics concerning the acceptability, rejectability, and undecidability degrees. We then propose a class of fuzzy labeling semantics conforming to the above postulates and investigate the relations between fuzzy labeling semantics and existing work in the literature.

A gradual semantics takes a weighted argumentation framework as input and outputs a final acceptability degree for each argument, with different semantics performing the computation in different manners. In this work, we consider the problem of attack inference. That is, given a gradual semantics, a set of arguments with associated initial weights, and the final desirable acceptability degrees associated with each argument, we seek to determine whether there is a set of attacks on those arguments such that we can obtain these acceptability degrees. The main contribution of our work is to demonstrate that the associated decision problem, i.e., whether a set of attacks can exist which allows the final acceptability degrees to occur for given initial weights, is NP-complete for the weighted h-categoriser and cardinality-based semantics, and is polynomial for the weighted max-based semantics, even for the complete version of the problem (where all initial weights and final acceptability degrees are known). We then briefly discuss how this decision problem can be modified to find the attacks themselves and conclude by examining the partial problem where not all initial weights or final acceptability degrees may be known.

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 semantics. That is, given an argumentation framework and a desired argument ranking, we ask whether there exist initial weights such that a particular semantics produces the given ranking. The contribution of this paper are: (1) an algorithm to answer this problem, (2) a characterisation of the properties that a gradual semantics must satisfy for the algorithm to operate, and (3) an empirical evaluation of the proposed algorithm.

This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. We build on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of acceptability semantics that have been introduced in these works. We provide a simplified and mathematically elegant formulation of these characteristics. The formulation is modular because 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 discuss various semantics for bipolar argumentation graphs in the light of these characteristics. Based on the modular framework, we prove general convergence and divergence theorems. We show that all semantics converge for all acyclic graphs and that no sum-based semantics can converge for all graphs. In particular, we show divergence of Euler-based semantics for certain cyclic graphs. We also provide the first semantics for bipolar weighted graphs that converges for all graphs.

In [3] we presented a prototype of a system that enables users to explore arguments for a given topic. This involves these steps: 1. Argument identification. In the first step, arguments concerning a given topic are identified in a given text and attacking and supporting relationships between the propositions are established. The result is an argumentation graph. In the future we hope to use argumentation mining techniques to automate this step. At this time, this is done manually by marking up some text.

An argument is a reason or justification of a claim. It has an intrinsic strength and may be attacked by other arguments. Hence, the evaluation of its overall strength becomes mandatory, especially for judging the reliability of its claim. Such an evaluation is done by acceptability semantics. The aim of this paper is to set up the foundations of acceptability semantics. 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 identifying families of semantics that have not been explored yet. The paper defines the building blocks of a semantics. It introduces key concepts and principles on which an evaluation is based. Each concept (principle) is described by an axiom. We investigate properties of semantics that satisfy the axioms, show the foundations of the two crucial notions of reinstatement and defence, and analyse some existing semantics against the axioms.