graph-traversal-is-complete-and-terminating-in-both-directions
OUT derived (depth 5)
Both forward truth propagation and backward retraction cascades achieve complete graph traversal (reaching all transitively affected nodes through all relationship types including outlists) with guaranteed termination, ensuring the system converges from both assertion and retraction operations.
Summary
When the system marks something as true, that status spreads to everything that depends on it, and when something is retracted, the retraction similarly ripples out to all affected downstream conclusions. Together these two directions of propagation are thorough enough to reach every affected node and guaranteed to stop rather than loop forever. This matters because it means the system reliably converges to a consistent state after any change, whether adding or removing a belief. This belief is currently marked OUT, meaning one or both of its supporting claims about forward propagation completeness or backward retraction transitivity are not currently accepted.
Justifications
SL — Forward propagation is topology-complete even under graph inconsistency; backward retraction is transitive and terminating — together they show all graph traversal is both complete and bounded regardless of direction.
Antecedents (all must be IN):
- propagation-is-topology-complete-and-inconsistency-safe — Truth propagation is both topologically complete — reaching all transitively dependent nodes including those connected through outlist entries, not just antecedent references — and safe under graph inconsistency, skipping dangling dependent references with structured warnings rather than crashing, ensuring correct cascading even in networks with imperfect structural integrity such as nodes deleted without full reference cleanup.
- retraction-cascade-is-transitive-and-terminating — Retraction cascades are both transitive in reach (propagating OUT to all transitively dependent SL-derived nodes, not just direct children) and guaranteed to terminate safely (BFS prevents oscillation, retracted nodes are skipped, and the cascade stops when no truth values change) — ensuring thorough impact without risk of runaway propagation.
Dependents
These beliefs depend on this one:
- structural-modifications-exhaust-topology-and-converge — All structural modifications to the belief network — additions, retractions, replacements, and bulk operations — both exhaust their effects through complete bidirectional graph traversal (reaching all transitively affected nodes in forward propagation and backward retraction) and converge to stable states with network topology fully preserved (all antecedent and outlist references correctly rewired)