Evaluative multiple revision based on core beliefs

We introduce a new belief revision operator called evaluative multiple revision. Belief states in the revision are belief bases with core beliefs. New information that triggers the revision is evaluated beliefs, some of which are evaluated by the core beliefs as plausible and the others implausible. We characterize this operator by axiomatic postulates in the AGM (named after the three authors, i.e. C.E. Alchourron, P. Gardenfors, and D. Makinson, in literature of belief revision) style. Two functional constructions are given for the operator based on evaluative kernel sets and evaluative remainder sets, respectively, with representation theorems proved. We also compare some related works with ours and show the generality of the operator.