Talk given at the Logic, Reasoning and Rationality Congress (Gent).

Abstract. Adaptive logics have evolved from systems for handling inconsistent premises to a unifying framework for all kinds of defeasible reasoning—with the standard format (Batens [2007]) as one of its major strengths. Modal logics have gone through a similar evolution. They were originally conceived as an analysis of alethic modalities, but have now become the privileged language to reason about all kinds of relational structures. One field where modal logics have been used as a unifying framework is in the analysis of what Makinson [1993] describes as the different “faces of minimality” in defeasible inference, conditional logic, and belief revision. Modal translations of so-called minimality semantics are found in Boutilier [1990], and more recently in van Benthem et al. [2006]. Given the hypothesis that the standard format of adaptive logic is sufficiently general to incorporate most (if not all) forms of defeasible inference (Batens [forthcoming: Chapt. 1]), it is natural to ask whether the adaptive consequence relation can also be formulated in a modal language. The main reason why a similar reconstruction is possible, is that adaptive logics are obtained by (i) ordering models in a certain way, and (b) using that ordering to select a subset of all models of the premises to obtain a stronger consequence relation.