Overemphasizing the features of abduction as it occurs in scientific practices and daily life scenarios has led to overlook some features that abduction in those circumstances shares with other phenomena in which some given outputs fail to stand in a certain relation with some given inputs and thus a modification on those inputs is in order. We propose here a top-down, conceptual and taxonomic investigation on what the most general purely logical features of abduction could be, as well as a research program to investigate to what extent it is a pervasive notion in logic. We start by motivating some broadenings in the most common approaches to abduction, then we characterize inferential problems and finally give general characterizations of the notions of abductive problem, abductive solution and abductive inference.