Information AboutCumulativity |
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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 is the Mereological sum operation. 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: 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. |
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