system-converges-from-addition-and-removal
OUT derived (depth 4)
The system reaches deterministic stable states from both directions: import reconciliation converges through fixpoint iteration and dual reconciliation modes when beliefs are added, while retraction cascades terminate through BFS with stop-on-unchanged when beliefs are removed — bidirectional convergence guarantees that no sequence of additions or removals leaves the network in an oscillating or indeterminate state.
Summary
When new beliefs are added and old ones are removed, the system always settles into a stable, predictable state rather than getting stuck in a loop or flip-flopping. This matters because it guarantees that any sequence of changes — no matter the order or combination — will reliably converge, so operators never have to worry about the network getting into an inconsistent or unresolvable condition.
Justifications
SL — Addition-side convergence (depth-3) and removal-side convergence (depth-3) together close all instability vectors — the network reaches quiescence regardless of operation direction.
Antecedents (all must be IN):
- import-reconciliation-converges-deterministically — Import reconciliation achieves both completeness and convergence: dual import/sync modes handle heterogeneous truth states with namespace isolation and topological cycle tolerance (completeness), while all reconciliation operations — individual propagation, agent sync, and global recompute — converge to deterministic fixed points on repeated application (convergence), ensuring that import never introduces oscillation or nondeterminism.
- 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:
- system-reaches-equilibrium-from-all-modification-paths — The system converges to deterministic stable states through every modification path: import achieves ordered convergent reconciliation (add → propagate → retract sequencing with fixpoint convergence), retraction cascades terminate through BFS with stop-on-unchanged, and both addition and removal operations reach equilibrium — no modification can leave the system in a non-convergent state.