Bipolar argumentative semantics for t-norm based fuzzy logics

Abstract We investigate the relations between bipolar logical argumentation frames and the three main t-norm-based fuzzy logics: Łukasiewicz ( Ł ), Gödel ( $${\textbf {G}}$$ ) and product logic ( $$\varvec{\Pi }$$ ). The arguments that we consider are complex entities, and the inference relation between the support and the claim is instantiated with the standard consequence relation of one specific fuzzy logic. We introduce several argumentative principles defined in terms of the attack and the support relation that refine the existence of such relations whenever the involved arguments share some propositional formulas. Through the notion of argumentative immunity introduced in Corsi and Fermüller (2018a) we finally recover complete semantics for Ł , $${\textbf {G}}$$ and $$\varvec{\Pi }.$$