Recovering Consistency by Forgetting Inconsistency

International audienceIn this paper, we introduce and study a new paraconsistent inference relation |=c in the setting of 3-valued paraconsistent logics.Using inconsistency forgetting as a key mechanism for recovering consistency, it guarantees that the deductive closure Cn|=c(Σ) of any belief base Σ is classically consistent and classically closed. This strong feature, not shared by previous inference relations in the same setting, allows to interpret an inconsistent belief base as a set of classical worlds (hence to reason classically from them)