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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 $xADG$…
Strong equivalence between knowledge bases ensures the possibility of replacing one with the other without affecting reasoning outcomes, in any given context. This makes it a crucial property in nonmonotonic formalisms. In particular, the…
In Dung's abstract argumentation, arguments are either acceptable or unacceptable, given a chosen notion of acceptability. This gives a coarse way to compare arguments. In this paper, we propose a counting approach for a more fine-gained…
We add strong negation $N$ to classical logic and interpret the attack relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a corresponding object level (using $N$ only) classical theory for each argumentation network and…
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…
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…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
In argumentative discourse, persuasion is often achieved by refuting or attacking others arguments. Attacking is not always straightforward and often comprise complex rhetorical moves such that arguers might agree with a logic of an…
We show that preferred, stable, complete, and grounded semantics satisfy attack removal monotonicity. This means that if an attack from b to a is removed, the status of a cannot worsen, e.g. if a was skeptically accepted, it cannot become…
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…
The problem of explaining inconsistency-tolerant reasoning in knowledge bases (KBs) is a prominent topic in Artificial Intelligence (AI). While there is some work on this problem, the explanations provided by existing approaches often lack…
Abstraction logic is a new logic, serving as a foundation of mathematics. It combines features of both predicate logic and higher-order logic: abstraction logic can be viewed both as higher-order logic minus static types as well as…
This paper builds on the recent ASPIC+ formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC+ to accommodate a broader range of…
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…
In this paper we introduce a novel family of semantics called weakly complete semantics. Differently from Dung's complete semantics, weakly complete semantics employs a mechanism called undecidedness blocking by which the label undecided of…
In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [9] with the aim of characterising the nature of argument based reasoning. In doing so, we consider…
Abstract argumentation has emerged as a method for non-monotonic reasoning that has gained popularity in the symbolic artificial intelligence community. In the literature, the different approaches to abstract argumentation that were refined…
One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their…
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…
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…