More on extension-based semantics of argumentation
Lixing Tan, Zhaohui Zhu, Jinjin Zhang

TL;DR
This paper advances the theory of extension-based semantics in argumentation by generalizing key lemmas, correcting previous flaws, and introducing new operators to analyze infinite argumentation frameworks.
Contribution
It provides a generalized fundamental lemma, corrects prior work, and introduces the reduced meet operator for infinite frameworks, enhancing the structural understanding of argumentation semantics.
Findings
Generalized the fundamental lemma for graded semantics.
Corrected flaws in Grossi and Modgil's previous work.
Introduced the reduced meet operator and proved its properties.
Abstract
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…
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Taxonomy
TopicsMulti-Agent Systems and Negotiation · Logic, Reasoning, and Knowledge · Logic, programming, and type systems
