Abstract
In the second part of this contribution we investigate in general the notion of inconsistency lemmas recently introduced by James Raftery. We generalize inconsistency lemmas in analogy to deduction theorems, and explain relation between the two.
We will see that the class of protonegational logics, introduced in the rst part of this contribution, provides a natural framework for the study of inconsistency lemmas, as the protoalgebraic logics do for deduction theorems. As an application of the interplay between inconsistency lemmas and deduction theorems, we obtain a local deduction detachment theorem for innitary Lukasiewicz logics, which has the interesting feature that it necessarily has innite deduction sets.
Again the talk will be held in spirit of abstract algebraic logic. Moreover, we