Argumentation theory and alternative semantics for non-classical logics

Abstract

We present argumentation frames defined on an intermediary level of abstraction between Dung’s abstract argumentation frames and logical (fully instantiated) argumentation frames. On these semi-abstract frames, we define attack principles that refine the definition of the attack relations and allow us to recover new argumentative semantics for classical and non-classical logics. By interpreting the attack principles in sequent-based argumentation frames, we introduce additional elimination rules that can be used to make the dynamic derivations shorter, but with unchanged results. Through weighted attack principles, we introduced alternative semantic for the three main t-norm fuzzy logics: Gödel, Łukasiewicz and Product logic. Additional semantics for these logics are also recovered using bipolar argumentation frames and principles.