The Attack as Intuitionistic Negation

TL;DR

This paper models argumentation networks within intuitionistic logic, translating attacks into negation-based formulas, enabling richer semantics including higher-level attacks and meta-statements.

Contribution

It introduces a novel translation of argumentation networks into intuitionistic logic, allowing for the representation of higher-level attacks and meta-statements.

Findings

Models argumentation networks using intuitionistic logic.

Enables representation of higher-level attacks.

Provides semantics for meta-statements in argumentation.

Abstract

We translate the argumentation networks ${\cal A}=(S, R)$ into a theory $D$ of intuitionistic logic, retaining $S$ as the domain and using intuitionistic negation to model the attack $R$ in ${\cal A}$: the attack $xRy$ is translated to $x\to\neg y$. The intuitionistic models of $D$ characterise the complete extensions of ${\cal A}$. The reduction of argumentation networks to intuitionistic logic yields, in addition to a representation theorem, some additional benefits: it allows us to give semantics to higher level attacks, where an attack "$xRy$" can itself attack another attack "$uRv$"; one can make higher level meta-statements $W$ on $(S, R)$ and such meta-statements can attack and be attacked in the domain.