canonical-equilibria-are-negation-transparent
OUT derived (depth 8)
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.
Summary
When the system settles into a stable state, that state depends only on the logical relationships between claims, not on the history of how they were added, removed, or defeated. Positive assertions and negative defeats are evaluated by exactly the same rules, so there are no hidden order-dependencies or special cases lurking in how negation was used to get there.
Justifications
SL — Evaluation invariance + negation transparency together mean equilibria are canonical regardless of how beliefs were established or defeated
Antecedents (all must be IN):
- convergence-produces-evaluation-invariant-equilibria — The system converges to equilibrium states where truth evaluation is transformation-invariant: regardless of the mutation path taken — order of additions, retractions, challenges, imports — the converged state evaluates all beliefs identically, because autonomous convergence reaches deterministic stable states and truth evaluation is agnostic to both temporal context and structural origin.
- negation-is-transparent-to-evaluation — The system's complete negative semantics — structural absence creating premise behavior, explicit outlist defeat with automatic reversal, and guided recovery — operate within transformation-invariant truth evaluation: negation mechanisms alter belief topology but never create special-case evaluation paths, because the same uniform rules evaluate all resulting structures identically regardless of how they were produced.
Dependents
These beliefs depend on this one:
- equilibria-are-negation-transparent-with-complete-fidelity — 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).