Duality, metainferences and hierarchies of metainferential logics

PAILOS, FEDERICO MATÍAS; DA RÉ, BRUNO; TEIJEIRO, PAULA; SZMUC, DAMIÁN

Buenos Aires

Workshop; Workshop on Metainferences and Substructural Logics; 2019

IIF-SADAF

According to the usual notions of duality, at the level of the inferences, ST and TS are self-dual. However, there are some intuitions regarding the duality of ST and TS, as metainferential logics, and of cut and reflexivity, as metainferences, and, so far, there has not been provided any appropriate notion of duality that fullfils these intuitions. In this talk, we offer such a notion and show that ST and TS are dual, we discuss the case of cut and reflexivity, and build a hierarchy of dual logics that capture classical logic (not only its validities, but also its antivalidities).