The altering or updating of a set of beliefs in light of the introduction of new information. The formal study of belief revision typically represents the state of an agent’s beliefs (belief sets) as a logically closed set of sentences (i.e., a theory) and includes formal operations representing the revisions to an agent’s beliefs induced by the introduction of new information; the criterion of correctness for such operations is that they reflect the rationality of an ideal agent. The most well-known formal account of belief revision is the AGM model—named for Carlos Alchourrón (1931–1996), Peter Gärdenfors (1949– ), and David Makinson (1941– )—in which the basic operations on belief sets are:

• Contraction An operation in which a sentence $\phi$ is removed from a belief set $\Gamma$.

• Expansion An operation in which a sentence $\phi$ is added to a belief set $\Gamma$ without regard to consistency.

• Revision An operation in which a sentence $\phi$ is added to a belief set, which is then adjusted in the light of that. This may be done by expanding with $\phi$ and then contracting, or vice versa. The claim that these two processes give the same result is called the Levi Identity, and $\Gamma \star \phi$ is consolidated by removing formulae to maintain consistency with $\phi$.