Belief Revision - Contraction, Expansion, Revision, Consolidation, and Merging

Contraction, Expansion, Revision, Consolidation, and Merging

In the setting in which all beliefs refer to the same situation, a distinction between various operations that can be performed is made:

contraction

removal of a belief;

expansion

addition of a belief without checking consistency;

revision

addition of a belief while maintaining consistency;

consolidation

restoring consistency of a set of beliefs;

merging

fusion of two or more sets of beliefs while maintaining consistency.

Revision and merging differ in that the first operation is done when the new belief to incorporate is considered more reliable than the old ones; therefore, consistency is maintained by removing some of the old beliefs. Merging is a more general operation, in that the priority among the belief sets may or may not be the same.

Revision can be performed by first incorporating the new fact and then restoring consistency via consolidation. This is actually a form of merging rather than revision, as the new information is not always treated as more reliable than the old knowledge.