Cumulative reference

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In semantics, cumulative reference is the model-theoretic property that characterizes a mass noun like water in terms of the cumulative structure of its extension.


If w1 and w2 are two bits of water in the extension of water, then the sum of w1 and w2 (i.e. the result of putting w1 and w2 together) is also in the extension.


Plural count nouns also have the property of cumulative reference.


Utrecht Lexicon of Linguistics


  • Link, G. 1983. The logical analysis of plurals and mass terms: a lattice-theoretical approach. In Meaning, use and interpretation of language. Bauerle, R., Schwarze, C. & von Stechow, A. (eds.), 302-323. Berlin: De Gruyter.
  • Quine, W. 1960. Word and object.Cambridge, Mass: MIT Press.