It's usually assumed that paraconsistency is a phenomenon related with negation. In fact, in a sequent-calculus, most often the way of making the rule of explosion invalid is to impose restrictions to the rule of introduction of negation on the left-side. However, once the structural rule of weakening is rejected, it's possible to keep the standard rules for negation, but nonetheless invalidating the rule of explosion. In this talk, I will present a logic of this kind (CLNW) that is also suitable to support a non-trivial theory for transparent truth.