More on extension-based semantics of argumentation
This work provides theoretical advancements in the foundational understanding of argumentation semantics for researchers in computational argumentation, correcting flaws in existing work and offering new tools for analyzing infinite argumentation frameworks.
This paper investigates extension-based semantics in computational argumentation, specifically addressing graded extension-based semantics of abstract argumentation frameworks (AAFs). It provides an alternative fundamental lemma that generalizes previous work by relaxing parameter constraints, leading to a new sufficient condition for preserving conflict-freeness and a Galois adjunction between admissible sets and complete extensions. Additionally, the paper introduces a 'reduced meet modulo an ultrafilter' operator for infinite AAFs, demonstrating its distributivity over neutrality and defense functions, and its closure for fundamental semantics like conflict-free, admissible, complete, and stable semantics.
After a few decades of development, computational argumentation has become one of the active realms in AI. This paper considers extension-based concrete and abstract semantics of argumentation. For concrete ones, based on Grossi and Modgil's recent work, this paper considers some issues on graded extension-based semantics of abstract argumentation framework (AAF, for short). First, an alternative fundamental lemma is given, which generalizes the corresponding result due to Grossi and Modgil by relaxing the constraint on parameters. This lemma provides a new sufficient condition for preserving conflict-freeness and brings a Galois adjunction between admissible sets and complete extensions, which is of vital importance in constructing some special extensions in terms of iterations of the defense function. Applying such a lemma, some flaws in Grossi and Modgil's work are corrected, and the structural property and universal definability of various extension-based semantics are given. Second, an operator so-called reduced meet modulo an ultrafilter is presented, which is a simple but powerful tool in exploring infinite AAFs. The neutrality function and the defense function, which play central roles in Dung's abstract argumentation theory, are shown to be distributive over reduced meets modulo any ultrafilter. A variety of fundamental semantics of AAFs, including conflict-free, admissible, complete and stable semantics, etc, are shown to be closed under this operator. Based on this fact, a number of applications of such operators are considered. In particular, we provide a simple and uniform method to prove the universal definability of a family of range related semantics. Since all graded concrete semantics considered in this paper are generalizations of corresponding non-graded ones, all results about them obtained in this paper also hold in the traditional situation.