Some Supplementaries to The Counting Semantics for Abstract Argumentation

TL;DR

This paper extends the counting semantics for abstract argumentation by exploring how to select damaging factors, relating it to existing semantics, and providing an axiomatic perspective on the induced ranking semantics.

Contribution

It introduces supplementary methods for choosing damaging factors, analyzes relationships with existing semantics, and offers an axiomatic framework for the ranking semantics.

Findings

Guidelines for selecting damaging factors in counting semantics

Connections established between counting semantics and classical semantics

Axiomatic characterization of the ranking semantics

Abstract

Dung's abstract argumentation framework consists of a set of interacting arguments and a series of semantics for evaluating them. Those semantics partition the powerset of the set of arguments into two classes: extensions and non-extensions. In order to reason with a specific semantics, one needs to take a credulous or skeptical approach, i.e. an argument is eventually accepted, if it is accepted in one or all extensions, respectively. In our previous work \cite{ref-pu2015counting}, we have proposed a novel semantics, called \emph{counting semantics}, which allows for a more fine-grained assessment to arguments by counting the number of their respective attackers and defenders based on argument graph and argument game. In this paper, we continue our previous work by presenting some supplementaries about how to choose the damaging factor for the counting semantics, and what relationships with some existing approaches, such as Dung's classical semantics, generic gradual valuations. Lastly, an axiomatic perspective on the ranking semantics induced by our counting semantics are presented.