 Both strong and weak Kleene systems predict  (9)  to be undefined/meaningless, since both disjuncts are undefined/meaningless. However, the predictions of the two systems with respect to  (10)  and  (11)  diverge: the strong Kleene system predicts both  (10)  and  (11)  to be true since at least one of the disjuncts is true (assuming Barack Obama is in fact tall), while the weak system predicts both  (10)  and  (11)  to be meaningless since at least one of the disjuncts is meaningless. Intuitively, however,  (10)  is true while  (11)  is more readily judged as undefined/meaningless. Thus the predictions of neither systems are in agreement with common sense judgments. Linguists have observed that the intuitive difference between  (10)  and  (11)  is that in the former, but not in the latter the existence of a unique king of France (the presupposition of one of the disjuncts) is entailed by the negation of the other disjunct. Karttunen (1973), who systematically studied the projection behavior of presuppositions (i.e., how the presupposition of a constituent projects at the level of the complex sentence), described disjunction as a filter. In his taxonomy of embedding operators, plugs block all presuppositions in their scope (an example is told that), holes allow presupposition to project freely (e.g., negation), while filters allow only some presuppositions to project. Various analyses have been proposed attempting to capture how presuppositions project when embedded in disjunctions or other complex sentences. A prominent example is Peters (1979), who showed how Karttunen’s observations can be accounted for within a multi-valued logic with special non-symmetric connectives (see the entry on  presupposition  for an overview).