Cumulativity & Distributivity Interaction of Polyadic Quantifiers

Abstract

We show how to relate triadic quantifiers that express mixed readings of distributivity and cumulativity within a single 3-place predicate to the dyadic quantifiers that express distributivity (function composition of monadic quantifiers) and cumulativity (Scha 1981). We discuss problems with the standard approaches and propose that cumulativity necessarily takes precedence over distributivity. Consequently, for mixed readings cumulativity is reanalyzed as a quantifier that relates a type (1) and a type (2) quantifier. This new account of cumulativity generalizes conveniently to cumulative quantifiers of arbitrary type.