The area of theory change in which preservation of the information in the theory to be changed plays a key role.
A fundamental issue in belief revision is how to decide what information to retract in order to maintain consistency, when the addition of a new belief to a theory would make it inconsistent. Usually, an ordering on the sentences of the theory is used to determine priorities among sentences, so that those with lower priority can be retracted. This ordering can be difficult to generate and maintain.
The postulates of the AGM Theory for Belief Revision describe minimal properties a revision process should have.