Philosophy
The Logic of Belief Revision and the AGM Model
Quick fact
The AGM model, proposed in 1985, provides a set of rational postulates that any belief revision operation should satisfy, such as success (the new belief is always accepted) and consistency (the revised belief set must be logically consistent, unless the new belief itself is contradictory).
Why this is interesting
You’ve probably changed your mind about something you were once certain of. But what does it mean to change your beliefs rationally? How can we decide which old beliefs to keep and which to give up when new evidence arrives?
Read the full explanation
Understanding The Logic of Belief Revision and the AGM Model
Imagine your beliefs as a large collection of statements you accept as true—like a library of facts. When you learn something new, you might add it to the library (expansion). But if the new fact conflicts with something you already believe, you can’t just add it; you must remove something (contraction) and then add the new fact (revision). The AGM model formalizes this process by defining three types of change: expansion (adding a belief, even if it causes inconsistency), contraction (removing a belief), and revision (removing a belief that conflicts with the new one, then adding the new one). The key is to do this with 'minimal mutilation': change as little as possible to accommodate the new information, while preserving as much of the old knowledge as you can.
A deeper explanation
The AGM postulates are the heart of the model. They capture rational constraints on belief change. For instance, the success postulate says that after revising by a new belief, that belief must be in the revised set. The consistency postulate requires that the revised set be consistent, unless the new belief itself is contradictory. The inclusion postulate says that contraction only removes beliefs, not adds new ones, while vacuity says that if the new belief doesn’t conflict, contraction does nothing. The recovery postulate is more subtle: if you contract a belief and then expand by the same belief, you should get back all your original beliefs. These postulates ensure that belief revision follows a principle of minimal change: you don’t throw away more than necessary, and you don’t keep beliefs that are inconsistent with the new information. The AGM model also introduces the idea of epistemic entrenchment: some beliefs are more deeply held and harder to give up than others, which guides which beliefs to retract first. This model is not just theoretical; it underpins how intelligent agents in AI update their knowledge bases, and how philosophers think about rational belief change.