Characterization of AGM Belief Contraction in Terms of Conditionals
This work addresses a foundational issue in formal epistemology and belief revision for researchers in logic and AI, but it appears incremental as it builds on existing AGM and conditional frameworks.
The paper tackles the problem of characterizing AGM belief contraction semantically by proposing a framework that combines Kripke belief relations and Stalnaker-Lewis selection functions, showing that a formula B is in the contracted set K-A if and only if the agent believes B and conditionally believes B under not-A at the actual state.
We provide a semantic characterization of AGM belief contraction based on frames consisting of a Kripke belief relation and a Stalnaker-Lewis selection function. The central idea is as follows. Let K be the initial belief set and K-A be the contraction of K by the formula A; then B belongs to the set K-A if and only if, at the actual state, the agent believes B and believes that if not-A is (were) the case then B is (would be) the case.