Abstract
In this talk, we investigate variants of a recently introduced notion of in- consistency lemma following a closely related development in study of general versions of deduction theorems in non-classical logics. To this end, we present the class of protonegational logics, a natural generalization of protoalgebraic logics: in fact, protonegational logics play the same role for the theory of inconsistency lemmas as protoalgebraic logics do for the theory of deduction theorems.