This paper studies the realizability of belief revision and belief contraction operators in epistemic spaces. We observe that AGM revision and AGM contraction operators for epistemic spaces are only realizable in precisely determined epistemic spaces. We define the class of linear change operators, a special kind of maxichoice operator. When AGM revision, respectively, AGM contraction, is realizable, linear change operators are a canonical realization.

In this paper, we address the problem of applying AGM-style belief revision  to non-classical logics. We discuss the idea of minimal change in revision and show that for non-classical logics, some sort of minimality postulate has to be explicitly introduced. We also present two constructions for revision which satisfy the AGM postulates and prove the representation theorems including minimality postulates.