equilibria-are-negation-transparent-with-complete-fidelity
OUT derived (depth 9)
The system's convergent equilibria simultaneously satisfy two independent completeness criteria: negation transparency (the final stable state is uniquely determined by declarative semantics with no hidden procedural effects from negation) and complete propagation fidelity (every truth change cascades to every transitively dependent node with topology preservation and guided recovery).
Summary
When the system settles into a stable state, that state would be fully determined by the logical content alone — with no hidden side effects from how negation is handled — and every change would correctly ripple through to all dependent nodes without losing track of any connections. This is currently retracted, meaning at least one of its two supporting properties (transparent negation handling or complete change propagation) no longer holds, so the combined guarantee cannot be asserted.
Justifications
SL — Semantic completeness (negation fully resolved) and structural completeness (every dependent reached) together establish that equilibria leave no unresolved state in any dimension
Antecedents (all must be IN):
- canonical-equilibria-are-negation-transparent — The system converges to canonical evaluation-invariant equilibria where negative semantics are fully transparent — the final stable state is determined solely by the logical content of justifications, independent of both the transformation path taken and whether beliefs were established through positive assertion or negative defeat.
- convergent-equilibria-have-complete-propagation-fidelity — System convergence to evaluation-invariant equilibria achieves complete propagation fidelity — every truth change cascades to every transitively dependent node including outlist dependents — and topology preservation covers all reference types, provided the dependency tracking assumption holds.
Dependents
These beliefs depend on this one:
- knowledge-growth-reaches-transparent-equilibria — The system's knowledge growth converges to equilibria that are simultaneously negation-transparent (the final stable state is uniquely determined by evaluation order-invariant rules over negative semantics) and propagation-complete (every truth change cascades to every transitively dependent node), with indefinite self-correction ensuring these equilibrium properties are maintained across unbounded operational time