But Not Because You Said So! Implicitly Accepting Information with Abductive Belief-Base Change

Abductive expansion is an AGM-style belief-change operation that accommodates new information by adding explanatory hypotheses rather than incorporating the input outright. In contrast to belief sets, belief bases are finite and non-deductively closed, allowing a distinction between explicit and implicit beliefs. We extend abductive belief-change operations to belief bases relative to a hypothesis space, treating the base as firm beliefs and maintaining a separate space of tentative hypotheses that is conditioned on new inputs. Inspired by partial meet and kernel construction from classical belief revision, we provide concrete instances of three different types of abductive change: expansion, suspension (which corresponds to contraction), and revision. In the form of representation theorems, all these operators are shown to be characterized axiomatically by intuitive postulates. Along the constructions, counterparts of the well-known Levi identity and the Harper identity are exploited.