The Attack as Strong Negation, Part I

Dov Gabbay; Michael Gabbay

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arXiv · 1506.03266

The Attack as Strong Negation, Part I

Dov Gabbay·Michael Gabbay

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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.

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Dov Gabbay, Michael Gabbay. 2015-06-10. The Attack as Strong Negation, Part I. https://arxiv.org/abs/1506.03266

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