 Another problem concerns the expressiveness of a finitely-valued truth-functional account. McGee (1981) shows that the common “flat” \(L_1\)-fragment of the logics of conditionals of Adams, Stalnaker and Lewis, i.e., the system P, cannot be characterized in terms of the preservation of a designated set of truth-values in a finite-valued logic. Prima facie, this results appears in tension with Adams’s as well as Dubois and Prade’s trivalent characterization of P. As pointed out by M. Schulz (2009), however, the trivalent characterization proposed by Adams—or indeed Dubois and Prade—differs from the one entertained by McGee (it asks for more than the preservation of a fixed set of designated values, and allows quantification over subsets of the  premises).[1]  As discussed by Schulz, whether a similar characterization can be given for the non-flat logics of Stalnaker and Lewis is an open question.