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We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Abstract argumentation framework (\AFname) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and…
We introduce matrix and its block to the Dung's theory of argumentation framework. It is showed that each argumentation framework has a matrix representation, and the indirect attack relation and indirect defence relation can be…
Dung's Abstract Argumentation Framework (AF) has emerged as a key formalism for argumentation in Artificial Intelligence. It has been extended in several directions, including the possibility to express supports, leading to the development…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
This paper presents a novel framework for structured argumentation, named extend argumentative decision graph ($xADG$). It is an extension of argumentative decision graphs built upon Dung's abstract argumentation graphs. The $xADG$…
In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the…
Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that…
The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Argumentation frameworks ($AF$s) have been a useful tool for approximate reasoning. The encoding method is an important approach to formally model $AF$s under related semantics. The aim of this paper is to develop the encoding method from…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
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…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
The act of persuasion, a key component in rhetoric argumentation, may be viewed as a dynamics modifier. We extend Dung's frameworks with acts of persuasion among agents, and consider interactions among attack, persuasion and defence that…
Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour - repetitive boilerplate and the overly complicated…
In recent years, large language models (LLMs) have made significant advancements in developing human-like and engaging dialogue systems. However, in tasks such as consensus-building and persuasion, LLMs often struggle to resolve conflicts…
We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…
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…
Within the area of computational models of argumentation, the instantiation-based approach is gaining more and more attention, not at least because meaningful input for Dung's abstract frameworks is provided in that way. In a nutshell, the…