The development of the adaptive logic programme forced us time and again to go beyond the traditional view on logic. The aim of the project is to develop and study adaptive logics that will enable us to gain better insights in a set of theoretical problems such as (i) the limits of adaptive logics and of dynamic proof theories, (ii) the relation between logical and heuristic rules– these turn out to be partly interchangeable, and (iii) the relations between inconsistency-adaptive and modal adaptive logics.