bidirectional-modification-achieves-topology-completeness

IN derived (depth 6)

Bidirectional belief modification — contradiction resolution through traceable backtracking and defeat reversal with guided recovery — achieves topology-complete truth changes that are robust across all graph states, ensuring both directions of modification propagate through the complete dependency graph including under adverse conditions.

Summary

When the system needs to change what it considers true — whether by resolving a contradiction or restoring a previously defeated conclusion — those changes reliably ripple through every affected node in the entire dependency network. This means no matter how tangled the reasoning graph gets, the system can both break and repair chains of inference completely, without leaving any node in an inconsistent state.

Justifications

SL — Bidirectional completeness (both directions of truth change are handled) combined with topology completeness (all reachable nodes are updated) ensures no modification direction leaves orphaned state

Antecedents (all must be IN):

  • belief-modification-is-bidirectionally-complete-and-traceable — Belief modification is complete in both directions: contradictions that create truth changes are resolved through traceable dependency-directed backtracking with consistent nogood IDs, AND defeats that suppress truth values reverse automatically through BFS propagation with surgical restoration hints — no truth change is either irresolvable or irreversible without full traceability.
  • all-truth-changes-are-topology-complete-and-robust — All forms of truth change — both cascading propagation and justification addition — achieve topology-complete multi-dimensional consistency under all graph states: truth values, dependents index, and access tags cascade to every transitively dependent node including through outlist connections, even when the graph contains dangling references.

Dependents

These beliefs depend on this one:

Details