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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Belief revision | 1/7 | https://en.wikipedia.org/wiki/Belief_revision | reference | science, encyclopedia | 2026-05-05T14:44:59.576343+00:00 | kb-cron |
Belief revision (also called belief change) is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents. What makes belief revision non-trivial is that several different ways for performing this operation may be possible. For example, if the current knowledge includes the three facts "
A
{\displaystyle A}
is true", "
B
{\displaystyle B}
is true" and "if
A
{\displaystyle A}
and
B
{\displaystyle B}
are true then
C
{\displaystyle C}
is true", the introduction of the new information "
C
{\displaystyle C}
is false" can be done preserving consistency only by removing at least one of the three facts. In this case, there are at least three different ways for performing revision. In general, there may be several different ways for changing knowledge.
== Revision and update == Two kinds of changes are usually distinguished:
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
{
a
∨
b
}
{\displaystyle \{a\vee b\}}
and the new piece of information
¬
a
{\displaystyle \neg a}
:
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 variables
a
{\displaystyle a}
and
b
{\displaystyle b}
indicate that Unit A and Unit B, respectively, are still in orbit; the initial set of beliefs is
{
a
∨
b
}
{\displaystyle \{a\vee b\}}
(either one of the two satellites is still in orbit) and the new piece of information is
¬
a
{\displaystyle \neg a}
(Unit A has landed, and is therefore not in orbit). The only rational result of the update is
¬
a
{\displaystyle \neg a}
; 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
{
a
∨
b
}
{\displaystyle \{a\vee b\}}
, where
a
{\displaystyle a}
and
b
{\displaystyle b}
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
¬
a
{\displaystyle \neg a}
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
¬
a
∧
b
{\displaystyle \neg a\wedge b}
. This example shows that revising the belief
a
∨
b
{\displaystyle a\vee b}
with the new information
¬
a
{\displaystyle \neg a}
produces two different results
¬
a
{\displaystyle \neg a}
and
¬
a
∧
b
{\displaystyle \neg a\wedge b}
depending on whether the setting is that of update or revision.
== 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; extraction extracting a consistent set of beliefs and/or epistemic entrenchment ordering; 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.