  The aim of this paper is to introduce a new framework for defining abductive
reasoning operators based on a notion of retraction in arbitrary logics defined
as satisfaction systems. We show how this framework leads to the design of
explanatory relations satisfying properties of abductive reasoning, and discuss
its application to several logics. This extends previous work on propositional
logics where retraction was defined as a morphological erosion. Here weaker
properties are required for retraction, leading to a larger set of suitable
operators for abduction for different logics.
