Presuppositional exhaustification

Grammatical theories of Scalar Implicatures make use of an exhaustivity operator exh , which asserts the conjunction of the prejacent with the negation of excludable alternatives. We present a new Grammatical theory of Scalar Implicatures according to which exh is replaced with pex , an operator that contributes its prejacent as asserted content, but the negation of scalar alternatives at a non-at-issue level of meaning. We show that by treating this non-at-issue level as a presupposition , this theory resolves a number of empirical challenges faced by the old formulation of exh (as well as by standard neo-Gricean theories). The empirical challenges include projection of scalar implicatures from certain embedded environments (‘ some under some ’ sentences, some under negative factives), their restricted distribution under negation, and the existence of common ground-mismatching and oddness-inducing implicatures. We argue that these puzzles have a uniform solution given a pex -based Grammatical theory of implicatures and some independently motivated principles concerning presupposition projection, cancellation and accommodation.