Weakening and Truth

BRUNO DA RE

Seminario; WIP; 2018

Recently, a number of authors have pointed out that substructural logics are suitable to develop theories representing semantical concept, such as truth, and logical concepts, such as validity, capturing their naive behaviours. Among them, three proposals have been explored: dropping cut, dropping contraction and dropping reflexivity. However, as faras I know, in substructural literature no one has proposed to reject the structural rule ofweakening, while keeping the others. In this paper, I introduce a theory for naive truth andnaive validity based on the logic resulting of dropping weakening from classical logic. I callthis logicCLNWand this theory CLNW+.