Three Kinds of Belief Changes

Taken from 'Belief Revision' (1992) (page 3), Edited by Peter Gardenfors

A belief revision occurs when a new piece of information that is
inconsistent with the present belief system (or database) is added to that system in such a way that the result is a new consistent belief system. But this is not the only kind of change that can occur in a belief system. Depending on how beliefs are represented and what kinds of inputs are accepted, different typologies of belief changes are possible.

In the most common case, when beliefs are represented by sentences in some code, and when a belief is either accepted or rejected in a belief system (so that no degrees of belief are considered), one can distinguish three main kinds of belief changes:

(i) Expansion: A new sentence is added to a belief system together with the logical consequences of the addition (regardless of whether the larger set so formed is consistent).

(ii) Revision: A new sentence that is inconsistent with a belief system is added, but, in order to maintain consistency in the resulting belief system, some of the old sentences are deleted.

(iii) Contraction: Some sentence in the belief system is retracted without adding any new facts. In order for the resulting system to be closed under logical consequences some other sentences must be given up.