**Talk given at **the Dynamics in Logic Workshop (Brussels)

**Abstract.** Adaptive logics provide a general framework for all kinds of defeasible reasoning in terms of, on the one hand, a preferential semantics, and, on the other hand, a dynamic proof-theory. In a previous paper I described a class of Kripke-models that allowed for the reformulation of the consequence relation of adaptive logic in a modal logic. I also claimed that the modal reconstruction would facilitate the comparison and the interaction with other formalisms like preference logics, conditional logics, and the conditional doxastic models from Baltag & Smets [2008]. In the present paper I substantiate this claim. This is done by (a) describing the class of adaptive preference models, which is based on an abnormality-ordering of the states in a model and thus allow for the reconstruction of the consequence relation of adaptive logics,; (b) introducing a modification of that approach that is even closer to the plausibility orderings used to formalise belief and conditional belief; (c) comparing a number of distinctive features of the different approaches, and showing how we can combine the techniques of both approaches. In particular, I shall comment on how abnormality-orderings can be used in doxastic logics, and how awareness can be used to fine-tune the modal reconstruction of the adaptive consequence-relation.