Extension-ranking Semantics for Abstract Argumentation Preprint
Kenneth Skiba, Tjitze Rienstra, Matthias Thimm, Jesse Heyninck, Gabriele Kern-Isberner
TL;DR
This work introduces extension-ranking semantics, a general framework for ranking sets of arguments by their plausibility of acceptance in abstract argumentation frameworks. It maps an AF $F=(A,R)$ to a preorder over the power set $2^A$, enabling fine-grained comparisons beyond binary extension acceptance. The authors define a principled basis via base relations (e.g., conflicts, undefended, consistently defended, unattacked) and aggregate them lexicographically or via Copeland-style rules to recover and generalize classical semantics (admissible, complete, grounded, preferred, semi-stable). They also explore cardinality-based and numerical-evaluation variants, study robust properties (composition, decomposition, reinstatement, addition robustness), and compare several extension-ranking families (notably LD$^ au$, $r$-$ au$, and $r$-$c$-$ au$), offering design guidance for selecting suitable semantics in different applications. The framework supports applications in belief dynamics, decision under constraints, and extension enforcement, and clarifies how to balance expressiveness with desirable rationality principles.
Abstract
In this paper, we present a general framework for ranking sets of arguments in abstract argumentation 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 extension-ranking 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. We also adapt a number of approaches from the literature for ranking extensions to be usable in the context of extension-ranking semantics, and evaluate their behaviour.