When searching for an explanation for a (puzzling) phenomenon, people often reason backwards: from the explanandum to possible explanations. As such, they perform a reasoning process usually called `abduction'. All abduction processes share a common element: inferences based on the argumentation schema known as Affirming the Consequent (*AC*): [*AC*] A=> B, B |- A. If the classical inference relation is considered, *AC* is clearly not deductively valid. Moreover, adding *AC* to Classical Logic (*CL*) as an extra inference rule would result in the trivial logic. This is called the "irrelevance problem" towards abduction. In order to provide a nice formal account of abduction processes, this problem has to be faced. In this lunch talk, I will present several adaptive logics (*AL*) that satisfactorily deal with the irrelevance problem: they only allow for the relevant instances of *AC*. More specifically, I will present: 1) *AL* for both practical and theoretical abduction, 2) *AL* for abduction processes based on inconsistent background knowledge, and 3) *AL* for prioritized abduction processes.