An empirical and axiomatic comparison of ranking-based semantics for abstract argumentation.

AbstractArgumentation is the process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such semantics have been proposed independently, often associated with some desirable properties. In this work, we provide a thorough analysis of ranking-based semantics in two different ways. The first is an empirical comparison on randomly generated argumentation frameworks which reveals insights into similarities and differences between ranking-based semantics. The second is an axiomatic comparison of all these semantics with respect to the proposed properties aiming to better understand the behaviour of each semantics.Keywords: Argumentationranking-based semanticscomparison Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 http://debategraph.org2 https://www.kialo.com3 It was discovered (Amgoud et al., Citation2017) that the conjecture about the uniqueness of social models only holds up to 3 arguments in the argumentation framework. The study done on SAF semantics in Bonzon et al. (Citation2016a) only related to the result obtained when the algorithm introduced in Correia et al. (Citation2014) is used. But this result only corresponds to one possible social model.4 If there is no cycle, the threshold is equal to the longest branch in the argumentation framework. But if cycles are permitted, the discussion count of some arguments can be infinite because Disi(x) evolve cyclically. However, the authors strongly conjecture that there exists a threshold t after which it is no longer possible to distinguish the arguments: if ∀i≤t, Disi(x)=Disi(y), then ∀i>t, Disi(x)=Disi(y).5 Also called Tarski's fixed point theorem (Tarski, Citation1955).6 Concretely, for a partially ordered set (A,≻), one represents each argument of A as a vertex in the diagram and draws a line segment that goes upward from x to y whenever y≻x.7 Ideally, we would have liked to create a set of AFs from real online debates but actual online debates have additional features (e.g. a support relation, or votes on arguments) that are not taken into account by the semantics studied in this paper.8 https://networkx.org9 The code and benchmarks are available online at https://github.com/jeris90/comparison_rankingsemantics.git10 For more information about a particular property, we point the reader to the paper where the property has been introduced.11 We add here a defense branch in order to leave the ‘role’ of the branch unchanged: a defense (respectively attack) branch stays a defense (respectively attack) branch.12 Defining the weak version of a property means replacing the strict comparison operator between two arguments with a strict or equal comparison operator without changing the conditions (as is done for VP and wVP where x≻AFσy for VP becomes x⪰AFσy for wVP).13 We point out that the result of the paper (Bonzon et al., Citation2016a) saying that SCT implies CT is incomplete. Indeed, it lacked the very special case where attacking arguments can be equally acceptable, hence the need to include OE.Additional informationFundingThis work benefited from the support of the project AGGREEY ANR-22-CE23-0005 of the French National Research Agency (ANR).