contradiction-triggers-deterministic-resolution
IN derived (depth 2)
When contradictions are detected, resolution and propagation form a deterministic pipeline: backtracking identifies the least-entrenched culprit premise, retraction triggers BFS propagation that terminates via stop-on-unchanged, producing a new consistent state with minimal network disruption and guaranteed convergence.
Summary
When the system finds a contradiction, it follows a fully predictable sequence to fix it: it traces back to find the weakest supporting assumption, removes it, then ripples that change outward through the network in a controlled way that always finishes and always settles into a stable state. This means contradiction handling is not ad hoc — it is a mechanical pipeline that produces consistent, reproducible outcomes with the smallest possible collateral damage to other conclusions.
Justifications
SL — depth-2 — contradiction resolution selects what to retract (minimal disruption), propagation determines how to settle (deterministic termination); the pipeline composition is the emergent property
Antecedents (all must be IN):
- contradiction-resolution-is-minimal-disruption — The nogood resolution system minimizes network disruption through layered heuristics: the primary path traces justification chains back to premises and selects the least-entrenched for retraction, the fallback uses dependent count when no traceable chain exists, and all contradictions are unconditionally recorded regardless of resolution outcome.
- propagation-terminates-deterministically — Truth propagation is guaranteed to terminate: BFS prevents stack overflow, stop-on-unchanged prevents oscillation, and fixpoint iteration bounds the outer loop
Dependents
These beliefs depend on this one:
- contradiction-resolution-is-lifecycle-safe — When contradictions are detected, the entire resolution pipeline respects node lifecycle: backtracking identifies the least-entrenched culprit premise deterministically, retraction cascades through BFS propagation that skips retracted nodes and stops on unchanged truth values, ensuring resolution terminates without disturbing lifecycle-inert nodes.
- tms-handles-all-conditions-safely — The TMS core handles both normal operation (crash-free truth propagation via BFS with stop-on-unchanged) and exceptional conditions (deterministic contradiction resolution via backtracking with least-entrenched selection) through shared propagation infrastructure — no reachable execution state leads to undefined behavior.