New Weak Admissibility Semantics for Abstract Argumentation

Defining Defense and Defeat in Abstract Argumentation From Scratch -- A Generalizing Approach

“…Our research induces several interesting future work directions. First, our Theorem 4.16 does not hold for the alternatives proposed in (Dauphin, Rienstra, and van der Torre 2021), thus finding suitable refute operators would broaden the results. The same is true for SCC-based semantics like the ones introduced in (Dauphin, Rienstra, and van der Torre 2020).…”

“…As mentioned in the introduction, several recent proposals attempt to find a middle ground between naivity-based and admissibility-based semantics (Bodanza and Tohmé 2009;Dondio 2018;Dondio and Longo 2021;Baumann, Brewka, and Ulbricht 2020b;Dauphin, Rienstra, and van der Torre 2021), but also semantics defined by the SCC-recursive scheme (Baroni, Giacomin, and Guida 2005), in particular cf 2 and stage2 (Dvořák and Gaggl 2014), can be seen as semantics of this kind. The recently introduced weak admissibility (Baumann, Brewka, and Ulbricht 2020b) is already well-studied (Baumann, Brewka, and Ulbricht 2020a; Dauphin, Rienstra, and van der Torre 2020; Dvorák, Ulbricht, and Woltran 2021) and interestingly, the approach discussed in (Dondio and Longo 2021) also contributes a principle-based comparison.…”

“…But since they completely disregard the notion of defense we then would also accept b in G. This is clearly undesired though since in G, b is attacked by the undisputed argument a. Naivity-based semantics which also make use of the SCC-recursive scheme (Baroni, Giacomin, and Guida 2005) would handle F and G quite well, but due to their reliance on the structure of the given graph, the AF H would be treated unsatisfactory: It consists of a single SCC only and therefore this approach collapses to the underlying base function (we refer the reader to (Baroni, Giacomin, and Guida 2005) for more details on SCC-recursive semantics). These observations motivated the proposal of some recent approaches which are tailored to find "good" ways to disregard some of the attacking arguments in certain situations (Bodanza and Tohmé 2009;Dondio and Longo 2021;Baumann, Brewka, and Ulbricht 2020b;Dauphin, Rienstra, and van der Torre 2021). Comparing the characteristics of such non-classical semantics in a formal way is a challenging endeavor, since all of them make (more or less implicit) use of different defense notions by disregarding certain attackers of the given extension.…”

Non-Admissibility in Abstract Argumentation

“…Dung's admissibility-based (AB) semantics have been challenged in various ways, leading to a variety of new semantics [8,9,11,5]. These have been compared and classified on the basis of general principles as well as their computational complexity, such that the best semantics can be chosen for an application.…”

“…We focus our complexity analysis on complete and preferred variants of various semantics. Due to space limitations, we do not repeat all the variants of WA semantics described by Dauphin et al [9], but we do include their semantics in the complexity analysis. For the same reason, for some of the proofs, we are only able to include proof sketches.…”