In this paper, we present a general framework for ranking sets of arguments in abstract argumentation frameworks based on their plausibility of acceptance. We present a generalisation of Dung’s extension semantics as extension-ranking semantics, which induce a preorder over the power set of all arguments, allowing us to state that one set is “closer” to being acceptable than another. To evaluate the extension-ranking semantics, we introduce a number of principles that a well-behaved extensionranking semantics should satisfy. We consider several simple base relations, each of which models a single central aspect of argumentative reasoning. The combination of these base relations provides us with a family of extension-ranking semantics.

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals, and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that relationships between belief revision, defeasible conditionals, and nonmonotonic inference similar to those in propositional logic hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialectical frameworks (in short, cADFs). We define the semantics of cADFs in terms of a non-truth-functional four-valued logic, and study the semantics in-depth, by showing existence results and proving that all semantics are generalizations of the corresponding semantics for ADFs.

In this paper, we give an overview of several recent proposals for non-admissible non-naive semantics for abstract argumentation frameworks. We highlight the similarities and differences between weak admissibility-based approaches and undecidedness-blocking approaches using examples and principles as well as a study of their computational complexity. We introduce a kind of strengthened undecidedness-blocking semantics combining some of the distinctive behaviours of weak admissibility-based semantics with the lower complexity of undecidedness-blocking approaches. We call it loop semantics, because in our new semantics, an argument can only be undecided if it is part of a loop of undecided arguments. Our paper shows how a principle-based approach and a complexity-based approach can be used in tandem to further develop the foundations of formal argumentation.

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We show that possibilistic logic is the unique logic that can faithfully encode all other semantical concepts for ADFs. Based on this result, we also characterise strong equivalence and introduce possibilistic ADFs.

Extension-based semantics in abstract argumentation provide a criterion to determine whether a set of arguments is acceptable or not. In this paper, we present the notion of extension-ranking semantics, which determines a preordering over sets of arguments, where one set is deemed more plausible than another if it is somehow more acceptable. We obtain extension-based semantics as a special case of this new approach, but it also allows us to make more fine-grained distinctions, such as one set being "more complete'' or "more admissible'' than another. We define a number of general principles to classify extension-ranking semantics and develop concrete approaches. We also study the relation between extension-ranking semantics and argument-ranking based semantics, which rank individual arguments instead of sets of arguments.

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

In abstract argumentation, the admissible semantics can be said to distinguish the preferred semantics in the sense that argumentation frameworks with the same admissible extensions also have the same preferred extensions. In this paper we present an exhaustive study of such distinguishability relationships, including those between sets of semantics. We further examine restricted classes of argumentation frameworks, such as self-attack-free and acyclic frameworks. We discuss the relevance of our results in the context of the argumentation framework elicitation problem.

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In this paper we study the problem of concept contraction for the description logic EL. Concept contraction is concerned with the following question: Given two concepts C and D (with the interesting case being that D subsumes C) how can we find a generalisation of C that is not subsumed by D but is otherwise as similar as possible to C? We take an AGM-style approach and model this problem using the notion of a concept contraction operator. We consider constructive definitions as well as sets of postulates for concept contraction,and link the two by means of representation theorems.

We investigate the notion of independence in abstract argumentation, i.e., the question of whether the evaluation of one set of arguments is independent of the evaluation of another set of arguments, given that we already know the status of a third set of arguments. We provide a semantic definition of this notion and develop a method to discover independencies based on transforming an argumentation framework into a DAG on which we then apply the well-known d-separation criterion. We also introduce the SCC Markov property for argumentation semantics, which generalises the Markov property from the classical acyclic case and guarantees the soundness of our approach.

We study rankings over labelings as a generalization of traditional labeling-based semantics in abstract argumentation. Our approach is an alternative to recent developments on rankings over arguments. The formal basis is a qualitative abstraction of probability theory called ranking theory. We propose a fundamental property, called SCC stratification, that a ranking-theoretic semantics can be expected to satisfy, present a general scheme to define a ranking-theoretic semantics, and determine conditions under which this scheme satisfies SCC stratification.

We propose a new graded semantics for abstract argumentation frameworks that is based on the constellations approach to probabilistic argumentation. Given an abstract argumentation framework, our approach assigns uniform probability to all arguments and then ranks arguments according to the probability of acceptance wrt. some classical semantics. Albeit relying on a simple idea this approach (1) is based on the solid theoretical foundations of probability theory, and (2) complies with many rationality postulates proposed for graded semantics. We also investigate an application of our approach for inconsistency measurement in argumentation frameworks and show that the measure induced by the probabilistic graded semantics also complies with the basic rationality postulates from that area.

This paper studies representation of argumentation frameworks (AFs) in answer set programming (ASP). Four different transformations from AFs to logic programs are provided under the complete semantics, stable semantics, grounded semantics and preferred semantics. The proposed transformations encode labelling-based argumentation semantics in a simple manner, and different semantics of AFs are uniformly characterized by stable models of transformed programs. We apply transformed programs to solving AF problems such as query-answering, enforcement of arguments, agreement or equivalence of different AFs. Logic programming encodings of AFs are also used for representing assumption-based argumentation (ABA) in ASP. The results of this paper exploit new connections between argumentation theory and logic programming, and enable one to perform various argumentation tasks using existing answer set solvers.

We introduce a preferential-based setting for reasoning with different types of argumentation-based semantics, including those that are not necessarily conflict-free or admissible. The induced entailments are defined by n-valued labeling and may be computed by answer-set programs.

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., finding hypotheses that explain skeptical/credulous support) and we show that our model can be instantiated on the basis of abductive logic programs.

Dung-style abstract argumentation theory centers on argumentation frameworks and acceptance functions. The latter take as input a framework and return sets of labelings. This methodology assumes full awareness of the arguments relevant to the evaluation. There are two reasons why this is not satisfactory. Firstly, full awareness is, in general, not a realistic assumption. Second, frameworks have explanatory power, which allows us to reason abductively or counterfactually, but this is lost under the usual semantics. To recover this aspect, we generalize conventional acceptance, and we present the concept of a conditional acceptance function.