This paper presents an overview on the state of the art of semantics for abstract argumentation, covering both some of the most influential literature proposals and some general issues concerning semantics definition and evaluation. As to the former point, the paper reviews Dung's original notions of complete, grounded, preferred, and stable semantics, as well as subsequently proposed notions like semi-stable, ideal, stage, and CF2 semantics, considering both the extension-based and the labelling-based approaches with respect to their definitions. As to the latter point, the paper presents an extensive set of general properties for semantics evaluation and analyzes the notions of argument justification and skepticism. The final part of the paper is focused on the discussion of some relationships between semantics properties and domain-specific requirements.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0269888911000166

Review: an introduction to argumentation semantics

Semi-stable semantics offer a further extension based formalism by which the concept of "collection of justified arguments" in abstract argumentation frameworks may be described. In contrast to the better known stable semantics, one advantage of semi-stability is that any finite argumentation framework always has at least one semi-stable extension. Although there has been some development of the formal logical theory of semi-stable semantics so that several computational properties of these extensions have been identified, with the exception of some algorithmic studies, more detailed investigation of computational complexity issues has been neglected. Our purpose in this article is to present a number of results on the complexity of some natural decision questions for semi-stable semantics.

Computational Complexity of Semi-stable Semantics in Abstract Argumentation Frameworks

In this paper we examine, from an abstract point of view, a number of properties to be satisfied not only by formalisms for paraconsistent reasoning, but also for formalisms that aim to improve on logic programming by warranting the existence of models.

J. Ben-Naim

Papers

Postulates for Paraconsistent Reasoning and Fault Tolerant Logic Programming