Metainferential Paraconsistency

Abstract

In this article, our aim is to take a step towards a full understanding of the notion of paraconsistency in the context of metainferential logics. Following the work initiated by Barrio et al (2018), we will consider a metainferential logic to be paraconsistent whenever the metainferentialversion of Explosion (or meta-Explosion) is invalid. However, our contribution consists in modifying the definition of meta-Explosion by extending the standard framework and introducing a negation for inferences and metainferences. From this new perspective, Tarskian paraconsistent logics such asLP will not result to be metainferentially paraconsistent, in contrast to, for instance, non-transitive logics like ST. Finally, we will end up by defining a logic which is metainferentially paraconsistent in every level, and discussing whether this logic is uniform through translations.