belief-revision-complexity-second-level-ph

IN premise — summaries/2026/08/24/wiki-Belief_revision-chunk-3.md

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

The computational complexity of query answering (K*P ⊨ Q) and model checking for most belief revision operators and schemes resides at the second level of the polynomial hierarchy (Σ₂ᴾ / Π₂ᴾ), not in P or NP

Summary

Updating a knowledge base with new information and then checking what conclusions follow is provably far harder than typical search problems; it sits at a level of difficulty involving nested "there exists a scenario where, for every counter-scenario, a check passes" reasoning that no known algorithm can shortcut. In practice, this means the system should not expect fast, guaranteed answers to revision-and-query tasks and should plan for exponential blowup or approximate methods as the knowledge base grows.