Item 113: Settlement defeat for strength rows: a linear row contraposes
Deference line — second wave · difficulty open · project normativity · closed · node item-113
— *answered 2026-10-21 by the rule settleForm (projects/normativity/rounds/2026-10-21-rebuttal-and-end-to-end/REBUTTAL.md): rebuttal, vacuity, retirement; registered rebuttal.settleform-sound, rebuttal.liability-rebutted; the monotonicity it loses is restated as settledRegion_anti_of_survivors_eq and reopening_bound; what remains is the sharp bankroll across a reopening, item 123*
A strength row P(X∧A∧Y) ≥ c_S P(X∧A) is a linear constraint and so contraposes: once its consequent is settled false it forces its antecedent to 0. A defeasible warrant does not contrapose — "if X∧A then probably Y" says nothing about X∧A when Y turns out false — so the row says more than the warrant did, and the round's item 112 fixture shows the market paying for the difference without bound. Two repairs are candidates: a settlement defeat condition (a strength row leaves the region when its consequent settles, since an inference rule has nothing to say once its conclusion is known), or a non-linear form. The first is cheap and interacts with defeat_widens and IsForcedInterval.mono (settlement would no longer shrink the region monotonically); the second reopens the compiler.
Deliverable shape: the chosen condition as a Form-level rule, the monotonicity statement it keeps or loses, and the fixture's liability under it. Acceptance check: Lean green; the round's harmonic-buyer exhibit no longer applies. Context: .../2026-10-20-warrant-enforcement-semantics/SETTLEMENT_FORK.md (iv); WarrantEntitlement.Form.strength_sat_iff; item 112.
Deliverable shape: the chosen condition as a Form-level rule, the monotonicity statement it keeps or loses, and the fixture's liability under it.
Acceptance check: Lean green; the round's harmonic-buyer exhibit no longer applies.
Registered results bearing on this item
- inductor.contraposition-blocked: At date 9 of Scenario B the specialized strength row reads 2/3·P(X∧A) ≤ 0 while the enforced applicability row with X settled true forces P(X∧A) ≥ 3/4 (antecedent_open): the date-9 bundle with the str
- rebuttal.liability-rebutted: Under the rule, with Y refuted at nE and the applicability port defeated at n0, the enforcer's assessed net worth is at least -3 rho (2 + rho) at every live world at every date, through netWorth_ge_ne
- rebuttal.settleform-sound: The rule of M1-M2 as a function on the form; a form whose premise, antecedent or consequent coordinate is pinned false contributes no row, every other form contributes its specialized row with its own
Where it hangs
- held by normativity