Information About

Cumulativity




Cumulativity has proven relevant to the linguistic treatment of the Mass/count distinction and for the characterization of grammatical Telicity .

Formally, cumulativity can be defined as follows, where capital ''X'' is a Variable over Set s, ''U'' is the Universe Of Discourse , ''p'' is a Mereological part Structure on ''U'', and \oplus_p is the Mereological sum operation.


( orall X\subseteq U_p)(CUM(X)\iff \exists x,y(X(x) \wedge X(y) \wedge x
eq y) \wedge orall x,y(X(x) \wedge X(y) \Rightarrow X(x \oplus_p y)))


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:
: John ate an apple and Mary ate a pear.
: John and Mary ate an apple and a pear.

This shows that the relation "eat" is cumulative. In general, an ''n''-ary predicate ''R'' is ''cumulative'' if and only if the following holds:


( orall x_1,\ldots, x_n, y_1,\ldots, y_n)(R(x_1, \ldots,x_n)\wedge R(y_1, \ldots,y_n)) ightarrow R(x_1\oplus y_1, \ldots,x_n\oplus y_n)




REFERENCES


Krifka, Manfred 1989. Nominal reference, temporal constitution and quantification in event semantics.
In Renate Bartsch, Johan van Benthem and Peter van Emde Boas (eds.), Semantics and
Contextual Expressions 75-115. Dordrecht: Foris.

Krifka, Manfred. 1999. At least some determiners aren’t determiners. In The
semantics/pragmatics interface from different points of view, ed. K. Turner,
257–291. North-Holland: Elsevier Science.

Scha, Remko. 1981. Distributive, collective, and cumulative quantification. In
Formal methods in the study of language, ed. T. Janssen and M. Stokhof,
483–512. Amsterdam: Mathematical Centre Tracts.