Drawing Sound Conclusions from Unsound Premises

Given sets Φ1 = {φ11, . . . , φ1u(1)}, . . . ,Φz = {φz1, . . . , φzu(z)} of boolean formulas, a formula ω follows from the conjunction ∧ Φi = ∧ φij iff ¬ω ∧ ∧z i=1 Φi is unsatisfiable. Now assume that, given integers 0 ≤ ei < u(i), we must check if ¬ω ∧ ∧z i=1 Φ ′ i remains unsatisfiable, where Φ ′ i ⊆ Φi is obtained by deleting ei arbitrarily chosen formulas of Φi, for each i = 1, . . . , z. Intuitively, does ω stably follow, after removing ei random formulas from each Φi? We construct a quadratic reduction of this problem to the consequence problem in infinite-valued Lukasiewicz logic L∞. In this way we obtain a self-contained proof that the L∞-consequence problem is coNP-complete.