The left-CONS2 constraint

Abstract

We propose a new generalization over determiner denotations. We claim that, for any determiner Det, Det(P)(Q) entails Det(P⋂ Q)(Q) (the left-CONS2 Constraint, as we elaborate in the paper). We discuss potential counterexamples to the validity of this constraint including restricted universals (e.g. every ... but John, approximately/almost all/every...) and proportional expressions with an upper bound (e.g. fewPROP, at most one-third..., fewer than seventy percent...). Following earlier proposals, we provide evidence that problematic inferences associated with determiners arise not from their denotations but either from the operator Exh or from degree operators.