A Brief Introduction to Belief Revision∗

Running against this principle are Cartesian foundationalist views which contend that, with the exception of core foundational beliefs, the mere fact that a person starts out believing something gives it no privileged position regarding immunity from dismissal, and that only a justification built on foundational beliefs warrants continued belief. Alchourrón, Gärdenfors and Makinson (AGM) carried out pioneering formal work in the area of belief change [3, 2, 1], crafting axiomatizations for operators of belief expansion, contraction and revision. These axioms reflect the principle of Conservatism in that the axioms guarantee a minimum abandonment of beliefs when a contraction is carried out. Specifically, among the axioms for contraction is Recovery, which basically says (in the presence of the other contraction axioms) that the contraction operator is such that: if we first contract a target sentence φ from a set K of beliefs and then use our expansion operator to put φ back in, the resulting set of beliefs is precisely K; thus the name, and we see that this axiom insures that contraction keeps K intact as much as possible. Recovery is the most controversial of the AGM axioms, having received more than its share of criticism. My goal in these notes is merely to survey a few results regarding Recovery’s place in the formal framework of AGM, as well as to take a quick look at some competing frameworks, as a means to introduce the concepts (and the literature) of belief revision and theory change. As such, I will not delve deeply into philosophical tensions between foundationalism and coherentism, or concomitant formal issues such as whether to operate on whole