Item 121: Transitive retirement, and the closure a settlement must carry
Deference line — second wave · difficulty entry · project normativity.seed · closed · node item-121
— *answered 2026-10-22: the grounded rule propagates retirement, vacuity, rebuttal and undercut along citation chains of every length without a closure on the settlement (mem_survivors)*
The rule settleForm (lean/Workspace/Normativity/Contrib/WarrantEntitlement.lean, Grounds.survivors) retires a premise whose sentence is pinned false and removes, one step along cites, the occurrences that cite it; conditional forms further down a chain leave only when the settlement's closure pins their antecedent false. The round's fixtures carry their closure (X false pins X∧A, X∧A∧Y false) and the rule reaches the whole warrant; without closure a chain of three keeps its last link (projects/normativity/rounds/2026-10-21-rebuttal-and-end-to-end/tests/test_rebuttal.py::test_retirement_needs_closure). Wanted: either the transitive closure of citation as the retirement rule (a terminating recursion on the finite grounds, with survivors_anti re-proved), or the closure requirement on settlements as a stated hypothesis of the statics, with the theorem that a propositionally closed settlement makes the one-step rule complete.
Deliverable shape: the chosen rule as a def, the re-proved monotonicity lemmas, and the chain-of-three fixture under it. Acceptance check: Lean green; the round's tests/run.py extended and green. Context: projects/normativity/rounds/2026-10-21-rebuttal-and-end-to-end/REBUTTAL.md A1; DECISIONS.md 2026-10-21 (M2).
Deliverable shape: the chosen rule as a def, the re-proved monotonicity lemmas, and the chain-of-three fixture under it.
Acceptance check: Lean green; the round's tests/run.py extended and green.
Context: DECISIONS.md; projects/normativity/rounds/2026-10-21-rebuttal-and-end-to-end/REBUTTAL.md
Registered results bearing on this item
None registered.
Where it hangs
- held by seed-theory
Rounds and decisions that touch it
- decision the rule is a specialization step on the form, vacuity before rebuttal, retirement one step along citation under a closed settlement, the reopening account, and the names
- decision the survivors are the grounded fixed point, defeaters are shared defeat ports, the warrant enforcer runs on the deductive market, the licence reads the compiled bundle, coherence is declared structure, the public defect is the displayed excess, and the names