Cumulativity has proven relevant to the linguistic treatment of the mass/count distinction and for the characterization of grammatical telicity.
Formally, a cumulative predicate CUM can be defined as follows, where capital X is a variable over sets, U is the universe of discourse, p is a mereological part structure on U, and
In later work, Krifka has generalized the notion to n-ary predicates, based on the phenomenon of cumulative quantification.
For example, the two following sentences appear to be equivalent: This shows that the relation "eat" is cumulative.
In general, an n-ary predicate R is cumulative if and only if the following holds: Krifka, Manfred (1989).
"Nominal reference, temporal constitution and quantification in event semantics".