On acceptance conditions in abstract argumentation frameworks

Dealing with controversial information is an important issue in several application con-texts. Formal argumentation enables reasoning on arguments for and against a claim to decide on an outcome. In abstract argumentation frameworks, each argument can be asso-ciated with an acceptance condition that may be either implicit (e.g., Dung's framework where they are encoded in the attack relation) or explicit (e.g., Dialectical Framework where propositional formulae are associated with arguments/statements). Explicit accep-tance conditions allow for expressing reasoning tasks in a more natural and compact way. However, in some cases, current argumentation frameworks allowing explicit condi-tions do not permit to express in a compact and intuitive way some general acceptance conditions, such as those that could be expressed by first-order logic formulae. In this paper, we propose an argumentation framework where arguments' acceptance conditions allow for checking general properties also concerning sets of arguments/state-ments by exploiting aggregate functions (e.g., is the number of nearby agents greater than 5?). Notably, though providing such versatile and easily understandable acceptance condi-tions, the complexity of credulous and skeptical reasoning does not increase w.r.t. that for Dung's framework under the well-known non-deterministic semantics, i.e., preferred, stable, and least-undefined (a.k.a. semi-stable) semantics. (c) 2022 Elsevier Inc. All rights reserved.