levi-harper-identities-link-revision-contraction

IN premise — summaries/2026/08/24/wiki-Belief_revision.md

Created 2026-08-24T17:11:07+00:00

The Levi identity (K * P = (K − ¬P) + P) and Harper identity (K − P = K ∩ (K * ¬P)) provide exact mathematical equivalences between belief revision and contraction operators, guaranteeing that an AGM-compliant revision operator maps to a contraction satisfying all 8 contraction postulates including Recovery.

Summary

These two identities show that updating a system's knowledge and retracting a piece of it are exact mathematical mirrors of each other, so each can be derived from the other without approximation. The practical upshot is that the system only needs to verify its revision logic once; the corresponding contraction logic is guaranteed to satisfy all eight required properties, including Recovery, without any separate check.