 A standard approach is to propose that negation is ambiguous between a presupposition-preserving negation and a presupposition-denying negation; see e.g., the discussion by Horn (1985, 1989). The presupposition-preserving negation (aka choice negation) we have already seen, and it is found in both the Weak and Strong Kleene systems. The presupposition-denying (or exclusion) negation is typically taken to map true to false and false to true, as usual, but also to map an argument lacking a classical value to true. Thus if (14) is interpreted in a model where there is no knave, but “not” is understood as a presupposition-denying negation, then “the tarts were stolen by the knave” would lack a classical value, but “The tarts were not stolen by the knave”, and (14) as a whole, would be true.