**Talk given at** Ninth International Tbilisi Symposium on Language, Logic and Computation

**Abstract.** Adaptive logics are logics for defeasible inference that are characterised by, on the one hand, a formula preferential semantics, and, on the other hand, a dynamic proof-theory (Batens 2007). Because adaptive logics rely on a truly dynamic perspective on logical inference, one would expect that a comparison and integration of adaptive logics with other dynamic logics should be a fruitful enterprise. It does, for instance, make sense to define a class of Kripke-style models that allow us to reformulate the adaptive consequence relation with the standard tools of modal logic (Allo 2011a), or to develop a dynamic doxastic logic where the relation between an agent’s knowledge (or firm beliefs) and defeasible beliefs is governed by an adaptive logic (Allo 2011b). In either case, we get a better idea of how adaptive logics are related to modal logics, but we still miss out on the one crucial aspect of adaptive logics: its dynamic proof-theory. The main aim of this paper is to fill this gap.