In this article, we provide a new kind of belief revision operator that we call Moderated Revision. At first glance, it is a non-prioritized operator that combines a basic classical AGM operator with a credibility-limited one. The underlying idea is this: when new observation μ is received, it is accepted but with doubts, i.e., uncertainty. We use a revision operator to model the accepted part and a credibility-limited one to represent uncertainty, whenever necessary. In the presence of uncertainty, a selection of the old knowledge balances the result of the revision through a disjunction, allowing the agent to accept part of the new observation and remain unsettled about the rest.

In this article, we provide the weak version of ensconcement which characterizes an interesting family of Shielded base contractions. In turn, this characterization induces a class of AGM contractions satisfying certain postulates that we reveal here. Finally, we show a connection among the class of contractions given by our weak ensconcement and other kinds of base contraction operators. In doing so, we also point out a flaw in the original theorems that link the epistemic entrenchment with ensconcement (which are well established in the literature), and then we provide two possible solutions.

In this note, we introduce the local version of the operator for belief promotion proposed by Schwind et al. We propose a set of postulates and provide a representation theorem that characterizes the proposal. This family of operators is related to belief promotion in the same way that updating is related to revision, and we provide several results that allow us to show this relationship formally. Furthermore, we also show the relationship of the proposed operator with features of credibility-limited revision theory.