Editing Belief revision (section)

==Revision and update==
Two kinds of changes are usually distinguished:<ref name=":0" />

; update : the new information is about the situation at present, while the old beliefs refer to the past; update is the operation of changing the old beliefs to take into account the change;

; revision : both the old beliefs and the new information refer to the same situation; an inconsistency between the new and old information is explained by the possibility of old information being less reliable than the new one; revision is the process of inserting the new information into the set of old beliefs without generating an inconsistency.

The main assumption of belief revision is that of minimal change: the knowledge before and after the change should be as similar as possible. In the case of update, this principle formalizes the assumption of inertia. In the case of revision, this principle enforces as much information as possible to be preserved by the change.

===Example===
The following classical example shows that the operations to perform in the two settings of update and revision are not the same. The example is based on two different interpretations of the set of beliefs <math>\{a \vee b\}</math> and the new piece of information <math>\neg a</math>:

; update : in this scenario, two satellites, Unit A and Unit B, orbit around Mars; the satellites are programmed to land while transmitting their status to Earth; and Earth has received a transmission from one of the satellites, communicating that it is still in orbit. However, due to interference, it is not known which satellite sent the signal; subsequently, Earth receives the communication that Unit A has landed. This scenario can be modeled in the following way: two [[propositional variable]]s <math>a</math> and <math>b</math> indicate that Unit A and Unit B, respectively, are still in orbit; the initial set of beliefs is <math>\{a \vee b\}</math> (either one of the two satellites is still in orbit) and the new piece of information is <math>\neg a</math> (Unit A has landed, and is therefore not in orbit). The only rational result of the update is <math>\neg a</math>; since the initial information that one of the two satellites had not landed yet was possibly coming from the Unit A, the position of the Unit B is not known.

; revision : the play "Six Characters in Search of an Author" will be performed in one of the two local theatres. This information can be denoted by <math>\{a \vee b\}</math>, where <math>a</math> and <math>b</math> indicates that the play will be performed at the first or at the second theatre, respectively; a further information that "Jesus Christ Superstar" will be performed at the first theatre indicates that <math>\neg a</math> holds. In this case, the obvious conclusion is that "Six Characters in Search of an Author" will be performed at the second but not the first theatre, which is represented in logic by <math>\neg a \wedge b</math>.

This example shows that revising the belief <math>a \vee b</math> with the new information <math>\neg a</math> produces two different results <math>\neg a </math> and <math>\neg a \wedge b</math> depending on whether the setting is that of update or revision.