Alchourrón, C. E., Gärdenfors, P. and Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50(2), 510–530. DOI 10.2307/2274239
Key takeaways
Read in full (NOTE-874). For a logically closed theory A, the contractions satisfying Gärdenfors’s six basic postulates are exactly the partial meet contractions, A ∸ x = ⋂γ(A ⊥ x), where γ picks a nonempty subset of the maximal subsets of A not implying x (Observation 2.5); adding the two supplementary postulates gives exactly the contractions whose γ is generated by a transitive relation over those subsets (Corollary 4.5). Revision is defined from contraction by the Levi identity and inherits the corresponding postulates. The result needs, besides A, a selection function or ordering that A itself does not supply: different selection functions give different contractions of the same theory, and in the finite case distinct selection functions always give distinct contractions (Observation 4.6). The setting is one-step change of a single fixed theory; nothing is said about iterated change, about where the selection function comes from, or about the reasons for which a belief is held.
Why this is here
A4 and A10 said the belief-revision literature matters to the exchange’s questions “as much as the recent prompting literature”. It is registered for QUESTION-105 and CLAIM-294. The reading (NOTE-874) corrects how it was first described here. AGM’s state is not the closed theory alone: a revision needs the theory plus a selection function or ordering, and different ones give different results on the same theory. That backs CLAIM-294’s general point that current conclusions do not fix their revision. But what AGM adds is a preference over what to keep, not a record of what each belief depended on, and the paper does not discuss why beliefs are held; that point is Hansson’s (LIT-1072). For QUESTION-105 it answers only a one-step version: a theory and a transitive ordering suffice for single revisions.