Presupposition projection from the scope of 'say'

In this work, we investigate the projection behavior of presuppositions embedded under the predicate say. Drawing from new data elicited in French, German, Italian and English, we show that with say presuppositions from embedded declaratives and those from embedded interrogatives pattern in opposite ways. Specifically, presuppositions from declaratives must be satisfied at the attitude holder's level, in their 'presented beliefs', but not at the matrix level; from interrogatives, presuppositions project to the matrix level, but not the attitude holder's level. This result differs from the general pattern observed with responsive predicates. To capture this projection behavior, we propose a mechanism for declarative embedding that ensures for presuppositions to be satisfied in the same worlds at which the prejacent will be evaluated, here the attitude holder's presented beliefs. In addition, we assume that say cannot directly embed interrogatives, and instead, when it appears to embed a question Q, it is selecting for a silent DP 'the answer to Q'. Matrix projection follows on standard assumptions.