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Inlinguistic semantics, an expression X is said to havecumulative reference if and only if the following holds: If X is true of both ofa andb, then it is also true of the combination ofa andb. For example, the English word "water" has cumulative reference, since if two separate entities can be said to be "water", then combining them into one entity will yield more "water". On the other hand, two separate entities which each are "a house" do not combine to form "a house". Hence, the expression "a house" does not have cumulative reference. Theplural form "houses", however,does have cumulative reference. If two (groups of) entities are both "houses", then their combination will still be "houses".
Cumulativity has proven relevant to the linguistic treatment of themass/count distinction and for the characterization of grammaticaltelicity.
Formally, a cumulative predicateCUM can be defined as follows, where capitalX is avariable oversets,U is theuniverse of discourse,p is amereological partstructure onU, and is themereological sum operation.
In later work, Krifka has generalized the notion ton-ary predicates, based on the phenomenon ofcumulative quantification. For example, the two following sentences appear to be equivalent:
This shows that the relation "eat" is cumulative. In general, ann-ary predicateR iscumulative if and only if the following holds:
