# The Attack as Intuitionistic Negation

arXiv: https://arxiv.org/abs/1510.00077 · HTML: https://mlsanity.com/paper/1510.00077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2015.

## Built on by (most cited first, 2 of 2)

- [Encoding Argumentation Frameworks to Propositional Logic Systems](https://mlsanity.com/paper/2503.07351/) (2025)
- [Abstract argumentation and answer set programming: two faces of Nelson's logic](https://mlsanity.com/paper/2203.14405/) (2022)

## Abstract (arXiv)

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→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.