The Attack as Strong Negation, Part I

TL;DR

This paper introduces a new way to interpret argumentation networks using strong negation in classical logic, simplifying their analysis and connecting models to argumentation extensions.

Contribution

It proposes a novel interpretation of attack relations via strong negation, linking argumentation networks to classical logic models and simplifying their study.

Findings

Models correspond to complete extensions of argumentation networks

Approach simplifies analysis of abstract argumentation networks

Comparison with other logical translations and frameworks

Abstract

We add strong negation $N$ to classical logic and interpret the attack relation of "$x$ attacks $y$" in argumentation as $(x\to Ny)$. We write a corresponding object level (using $N$ only) classical theory for each argumentation network and show that the classical models of this theory correspond exactly to the complete extensions of the argumentation network. We show by example how this approach simplifies the study of abstract argumentation networks. We compare with other translations of abstract argumentation networks into logic, such as classical predicate logic or modal logics, or logic programming, and we also compare with Abstract Dialectical Frameworks.