SCC-recursiveness: a general schema for argumentation semantics

Abstract

In argumentation theory, Dung’s abstract framework provides a unifying view of several alternative semantics based on the notion of extension. In this context, we propose a general recursive schema for argumentation semantics, based on decomposition along the strongly connected components of the argumentation framework. We introduce the fundamental notion of SCC-recursiveness and we show that all Dung’s admissibility-based semantics are SCC-recursive, and therefore a special case of our schema. On these grounds, we argue that the concept of SCC-recursiveness plays a fundamental role in the study and definition of argumentation semantics. In particular, the space of SCC-recursive semantics provides an ideal basis for the investigation of new proposals: starting from the analysis of several examples where Dung’s preferred semantics gives rise to questionable results, we introduce four novel SCC-recursive semantics, able to overcome the limitations of preferred semantics, while differing in other respects

Strong Equivalence for Argumentation Semantics Based on Conflict-Free Sets

“…Such redundant attacks exist for all semantics (at least when self-loops are present), except for cf2 semantics, which follows from our main result, that F ≡ cf2 s G holds, if and only if, F = G. In other words, each attack plays a role for the cf2 semantics (at least, an attack closes a cycle and thus is crucial for the actual partition into SCCs of the AF). Our result also strengthens the observations from Baroni et al [5], who claim that cf2 semantics treats self-loops in a more sensitive way than other semantics. Besides our characterization for strong equivalence, we also analyzed some variants of that problem, namely local and symmetric strong equivalence.…”

“…We continue with the cf2 semantics [5] and use the characterization from [11]. We need some further terminology.…”

“…One of the key features abstract argumentation provides is a clear separation between logical content and non-classical reasoning (which is solely done over abstract entities, the arguments A, and a certain relationship R between those entities; forming so-called argumentation frameworks of the form (A, R)). For abstract argumentation, many semantics have been proposed to evaluate such frameworks including Dung's famous original semantics [9], but also alternative semantics like the stage semantics [13] or the cf2 semantics [5] received attention lately. The aim of argumentation semantics is to select possible subsets of acceptable arguments (the so-called extensions) from a given argumentation framework.…”

Propositional discourse logic

“…9 For instance, the graph D from (2.4) has no kernel, but {d, b} is its local kernel, and so is {e} (the latter inducing the subdiscourse F from Example 2.13. (2).) The lack of any kernel suggests some anomaly, as we can see considering the triangle a − b − c or the whole graph D .…”

Dilemmas and paradoxes: cycles in argumentation frameworks

“…This dissatisfaction has motivated the development of semantics which do not have this property [2] 2 . But dilemmas and paradoxes do arise in natural language, and so we should be able to accommodate them in argumentation frameworks, and we should expect some peculiar things to happen if we allow a paradox into our framework 3 .…”